Planet Impact
Teacher Page: Lesson Plan

Index:

Goal / Purpose:

A primary objective of this lesson is to allow students to investigate the effects of gravity on a comet's trajectory by changing the angle of approach, the speed, and the masses of the large and small bodies. In the assessment activities, students will use their knowledge to crash a comet into Jupiter or make a comet fly past the planet without colliding with it.

Desired Learning Outcomes:

• State the relationship between the mass of an object and the gravitational force it exerts on other objects. (A large mass means a large force of gravity.)
• Explain the relationship between the distance from a planet and the force of gravity it exerts on an object.
• Explain how speed affects the path of a body when it is near a more massive one.
• Explain the relationship between the mass of a body and its acceleration when it is near a more massive body.
• Investigate how an object will be trapped by a planet's unbalanced gravitational force.
• Apply acquired knowledge to launch a comet with the intent to hit or miss a planet.
• Explain the significance of the crash of Shoemaker-Levy 9 on Jupiter.

Prerequisites:

Before attempting to complete this lesson, the student should:

• Understand that the solar system consists of planets, moons, asteroids, meteoroids, comets, and the Sun.
• Understand that objects have mass.
• Know the relative masses of solar system objects.
• Understand that all objects are attracted to other objects by the force of gravity.
• Understand that the universe is bound by gravity.
• Understand that an unbalanced force causes changes in an object's speed and/or direction.

New Vocabulary:

Acceleration-
The rate of change of velocity. An object is accelerating if its speed and/or direction are changing. An object accelerates, for example, when an unbalanced force acts on it.

Angle of Approach-
The direction at which one object arrives near another object, such as a boat docking at a pier. In the case of two celestial objects, changing the angle will change the distance between the pair.

Asteroid-
A minor planet (also referred to as a planetoid), varying in size from larger than 100 meters up to the size of small moons that orbit between Mars and Jupiter. The region between Mars and Jupiter is known as the asteroid belt and is between two and four astronomical units from the Sun. A few have erratic orbits, which cause them to wander outside the asteroid belt.

Astronomical Unit-
The mean distance between the Sun and Earth. An astronomical unit's abbreviation is AU. This distance is equal to 149,597,870 km (92,955,806 miles).

Auroral Heating-
Heat that is produced when charged particles interact with Jupiter's magnetic field. This interaction also produces auroras — bright bands of visible, ultraviolet, and infrared light near the planet's poles.

Comet-
A loosely held together mixture of dust and ice — also called a dirty snowball or icy mudball — that revolves around the Sun. When a comet travels near the Sun, some of its material vaporizes (turns into a gas), forming a large coma of rarefied gas called the "head." A "tail" or "tails" (the number depends on the composition of the nucleus) is formed when the Sun's solar wind drives the gas off the head of a comet.

Crater-
A circular depression on a planet or moon caused by the impact of another celestial body, such as a meteoroid, asteroid, or comet. Other phenomena, such as volcanoes, also produce craters.

Force-
A push or a pull exerted by one object on another. A force is anything that can cause acceleration.

Gravity-
The tendency of all matter to attract all other matter. The size of the force depends on the masses of the bodies and their distance from each other. As the mass of a body increases, the force it can exert on another body also increases. The closer the objects are to each other, the stronger the attraction will be. The equation for the force of gravity, F, between two masses, M and m, separated by distance, R is: F = GMm/R2 where G = the universal gravitational constant.

Gravitational Potential Energy-
The energy of a body due to its position relative to the center of a large body, such as a planet or star. The gravitational potential energy varies directly with the mass, m, of the bodies and inversely with the distance between the bodies, R. The equation is P = Gm/R. If the mass of a body doubles, the gravitational potential energy doubles. If the separation of the bodies doubles, the gravitational potential energy is half of what it was before. An object at a very large distance is said to have zero potential energy, and the potential energy becomes more negative as the distance decreases. If there is no friction or other loss of energy, the potential energy decrease becomes an increase in kinetic energy, the energy due to the motion of the object

Hubble Space Telescope-
A telescope that orbits above the Earth's atmosphere. The Hubble Space Telescope was launched in the spring of 1990 and placed in orbit about 600 km (370 miles) above the Earth. It is as large as a school bus: 13.3 m (43.5 feet) long, weighs 12 tons (24,500 pounds), has a mass of 11,110 kg, and its mirror has a diameter of 2.4 m (7 feet 10.5 inches). Since it orbits above Earth's atmosphere, Hubble can obtain images that are especially clear.

Impact-
A collision of two objects. Some examples of impacts in space include a meteor colliding with the moon or a comet slamming into a planet, such as Shoemaker-Levy 9 (SL-9) crashing into Jupiter.

Impact Event-
An impact event occurs when astronomers have prior knowledge of a collision between two celestial bodies, giving them the opportunity to observe the impact.

Infrared (IR) Images-
Pictures taken with instruments that detect electromagnetic wavelengths that are longer than visible light. Infrared wavelengths span from 710 nm to 1 mm (from the width of a pinpoint to the size of small plant seeds). The main source of infrared light is heat. All objects emit heat that can be seen as infrared light. The human body radiates most of its heat energy at infrared wavelengths near 9,000 nm.

Ion-
An atom that has either lost or gained one or more electrons. If the ion has lost an electron, then it has a positive charge (called a cation). If the ion has gained an electron, then it is negatively charged (called an anion).

Jovian Atmosphere-
Jupiter's atmosphere consists mostly of hydrogen (about 90 percent) and helium (about 10 percent). Some of the other minor ingredients are water, hydrogen sulfide, methane, and ammonia [http://www.seds.org/billa/tnp/jupiter.html].

Kinetic Energy-
The energy of a body due to its motion. Kinetic energy depends on the mass of the body and its speed. Doubling the mass of the body doubles the kinetic energy. But doubling the speed causes the kinetic energy to quadruple.

Kuiper Belt-
A doughnut-shaped region of our solar system that is the home of many short-period comets. The Kuiper Belt begins beyond the orbit of Neptune and encompasses an estimated distance of between 30 and 100 astronomical units. Sometimes the giant planets can disrupt the orbit of a Kuiper Belt comet, causing the icy body to cross Neptune's orbit. When this occurs, the comet may be ejected from the solar system or alter its trajectory to cross the orbit of the other outer planets. At times, the comet's path will bring it into the inner solar system. Some astronomers estimate that there may be as many as 100 million Kuiper Belt comets [http://www.seds.org/nineplanets/nineplanets/kboc.html].

Mass-
The quality of matter that resists changes in its state of motion. Inertia is a measure of a body's resistance to changes in its state of motion. For example, a large-mass truck has more inertia than a small-mass car and thus requires a greater force to get it moving. Mass also determines the gravitational force an object can exert (see Gravity).

Mass extinction-
The sudden and complete die-off of life on a planet.

Matter-
Anything that has mass and occupies space.

Meteoroid-
A rocky body orbiting the Sun that is less than 100 meters in extent.

Nucleus-
The solid part of a comet's head, which makes up the central part of the icy body.

Oort Cloud-
A spherical cloud of comets surrounding the outer reaches of the solar system (well beyond the orbit of Pluto at about 50,000 astronomical units), where an estimated 1 trillion cometary bodies are located. Occasionally, the gravitational forces of a passing star may alter the path of a comet in the Oort Cloud, and it travels into the inner solar system, where people observe it. Usually, these comets remain far from the solar system and are not visible [http://www.seds.org/nineplanets/nineplanets/kboc.html].

Orbit-
The path followed by a small body as it revolves around a larger body to which it is gravitationally bound.

Planetesimals-
A class of hypothetical bodies that formed from gaseous matter early in our solar system and eventually coalesced to form the planets.

Short-period Comets-
Comets whose return to the inner solar system occurs within 200 years of its previous visit. These comets never venture far beyond the orbit of Pluto and spend most of their time in the Kuiper Belt.

SL-9-
Shorthand designation for destroyed comet Shoemaker-Levy 9. This was the 9th comet discovered by the team of Gene and Carolyn Shoemaker and David Levy. Comets are named after their discoverers.

Solar Wind-
Consists of a flow of ionic particles, mostly helium and hydrogen, emanating from the Sun at speeds of 450 to 750 km/s (1 million to 1.6 million mph). These electrically charged particles influence matter throughout the solar system.

Speed-
The rate of change in distance. Speed indicates how fast an object is moving.

Sungrazers-
Comets that travel very close to or even plunge into the Sun, pouring out brightly glowing vapor in the intense heat. Sungrazers are normally detected by SOHO (Solar and Heliospheric Observatory).

Trajectory-
The path taken by a body moving in three-dimensional space.

Tidal forces-
A force that is caused when the gravity tugging on one side of a celestial body is stronger than that on the other side, causing the object to stretch. This force can exist between any two celestial objects that orbit each other. Tidal forces are so named because of their effect on Earth's oceans.

Ultraviolet (UV) Images-
Pictures taken with instruments that detect electromagnetic wavelengths that are shorter than visible light. Ultraviolet radiation ranges in wavelength from 10 to 310 nm. These wavelengths cannot be seen by the human eye and are about size of a virus. UV light can be used to study features in the upper atmosphere of planets.

Unbalanced Force (Net Force)-
Any force that causes an object to accelerate, unless an equal and opposite force is present. Acceleration can occur by changing speed, direction, or both. Here are some examples of unbalanced forces. An unbalanced gravitational force: the Sun exerting a force on the planets to keep them in orbit around it. An unbalanced magnetic force: a magnet pulling a paper clip toward it. An unbalance electrical force: a charged comb picking up pieces of paper.

Unbalanced gravitational force-
This lesson illustrates how an unbalanced force of gravity can cause an object to move in a curved path. Jupiter's powerful gravity changes the speed and direction of a comet's motion. An unbalanced gravitational force near the surface of the Earth, for example, causes objects to fall toward the planet and a dropped book falls to the floor.

Velocity-
The rate of change in position of an object. Velocity is a measure of motion: It identifies or quantifies an object's speed and direction. For example, an object moving toward the north at 35 m/s (116 ft/s) has a speed of 35 m/s, and a velocity of 35 m/s, north.

General Misconceptions:

• Students may have misconceptions regarding the concept of gravity.
• Students think that a body in orbit is weightless because the force of gravity is no longer acting on it. However, a body stays in orbit because of the force of gravity. Based on Newton's first law, the object wants to travel in a straight line. But the unbalanced force of gravity pulls it toward the center of the planet, causing the orbiting body to continually change direction (accelerate) and "drop" toward the planet. A body experiences weightlessness because it is in a state of constant free fall. We experience free fall on Earth when we're in a car that crests a hill at high speeds. The car is momentarily weightless while in the air. That's why you "lose your stomach."
• Students also think that weight and mass are the same, believing that when an object is weightless, it is also massless. Mass is a measure of a body's resistance to changes in its state of motion; weight is the force of gravity exerted on a body due to its mass and its location near another more massive object. A person can be weightless but cannot be massless. Weightless, massive objects can be difficult to move in space due to their resistance to changes in their state of motion.
• Students may have difficulty comprehending the actual distances between objects in our solar system.
• The effects of mass, angle, and velocity may also require some explanation because science fiction movies and television shows have given false and/or misleading information about the interactions of objects with each other.
• Students might confuse comets and asteroids. The following table may help teachers explain the difference:
Comets Asteroids
Made up of ice and dust Made up of rock
Orbit through our solar system Always in our solar system
In an eccentric orbit around the Sun

Usually orbit the Sun in a belt between Mars and Jupiter

Only visible when near the Sun Not visible with the naked eye
Meteor showers occur when the earth passes through a comet's orbit

Preparation Time:

1. Time necessary to download computer software to support the lesson.
2. Time necessary to become familiar with the lesson.

Execution Time by Module:

The following times are approximate. The execution time for each module could vary, depending on your school's Internet location (e.g., classroom, library, computer lab), the number of computers available with Internet access, and the number of students in the class.

• Introduction to "Planet Impact!" – 2 minutes
• "What's Your Angle?" – 10 -15 minutes
• "Step On It!" – 10 -15 minutes
• "Pick a Comet – Any Comet" – 10 -15 minutes
• "It's a Matter of Mass" – 10 -15 minutes
• "Target Practice: Hit or Miss?" – 10 -15 minutes

Physical Layout of Room:

Teachers may decide whether students will work individually or in small groups of two or three. To maximize learning, no more than three students should share a computer. Adaptations can be made to accommodate a classroom that has one computer with Internet access. Some suggestions include using an overhead projector with an LCD to project the computer image onto a screen or connecting the computer to a television monitor.

"Planet Impact!" can be used offline. Different software programs provide offline access to the Internet. These programs allow students to save Web pages to a local hard drive. Using the Netscape browser, students can open the Web pages locally and complete the lesson as if they were on the Internet. However, if this option is selected, students will not be able to view the references in the "Grab Bag" section on the Web.

Materials:

This lesson requires a computer with a color monitor and an Internet connection. The Web browser must have at least the capability of Netscape's Navigator 3.0, or Internet Explorer 4.0 and the most recent version of the Flash player. For additional information, see the "Computer Needs" section.

Procedure / Directions:

This is a self-directed, interactive computer activity. Students may work independently or in small groups to complete each activity. It may also be done as a teacher-directed activity in the classroom. Students will investigate the effects of gravity on a comet's trajectory by changing the angle of approach, the speed, and the masses of the large and small bodies. They also will learn about comet Shoemaker-Levy 9 and how to carry out a scientific investigation by changing one variable at a time.

Suggested Engagement Activities:

Teachers should select the first activity if they want to make the lesson inquiry-based and emphasize the crash of Shoemaker-Levy 9 on Jupiter. Teachers who want to underscore the role of physics in the lesson should select the second or third activity or a combination of both. Those activities emphasize gravity and the effects of air resistance.

1. Inquiry Activity – A Comet Hits Jupiter!

Description:

Students view images of Jupiter before and after the crash of comet Shoemaker-Levy 9. They ask questions and propose an explanation for what they see.

Materials:

"Images of Jupiter before and after the crash," taken from the "Grab Bag."

Instructions to the Teacher:

Display images of Jupiter before and after the crash of comet Shoemaker-Levy 9 on a screen or television monitor. First, ask students to compare the two images of Jupiter, and jot down questions they want answered. You also could ask them to explain how Jupiter acquired its characteristic markings. Give the students some time to write their questions and to think about what might have caused the changes. Then ask them to present their ideas. Don't be surprised if your students haven't heard of the crash of comet Shoemaker-Levy 9 on Jupiter. As a logical follow-up, you might want the students to write down the answers to their questions as they find them in the "Comet News" section of the lesson.

You may want to consider this alternate activity: Instead of using the images of Jupiter to spark the interest of your students, ask them to consider what they would want to know if they knew in advance that a comet was going to strike a planet like Jupiter. Tell them to write down their thoughts concerning what they would want to know or hope to learn from the event.

Instructions to the Student:

Look at the images of Jupiter. Describe the changes to the surface of the planet and write down five questions you want answered. Then try to explain why the planet has its characteristic markings. Use your imagination. Be prepared to share your questions and explanation with the class.

Instructions to the Student for the Alternate Activity:

We know in advance that a comet is going to strike a planet like Jupiter. What would you want to know or hope to learn about the comet slamming into the planet? Write your questions down.

2. Demonstration: Paper falls as fast as a book when dropped from the same height.

Description:

Students investigate the role of air resistance when objects are dropped near the surface of Earth.

Materials:

• Sheet of paper
• Textbook about the size of the paper (if the textbook is smaller, trim the paper to the size of the book)

Instructions to the Teacher:

Show students a textbook and a sheet of paper. Ask them to predict which will hit the floor first if they are released at the same time from the same height. Poll the students by first asking them to raise their hands if they think the textbook will hit before the paper. Next, those who think the paper will hit first should raise their hands. And finally, those who think the two objects will fall at the same rate should raise their hands. Most of the students will say the book will hit first; a few might decide they will hit at the same time.

Place the paper under the book and drop them. The paper hits first. Several students will say, "you cheated." The book really didn't hit the floor. Ask them to explain why you had to put the paper under the book. They will come up with the idea that air resistance makes the paper float only when it is not on top or under the book. (You can also place the paper on top of the book and drop them. The paper should stay right on top of the book. In this case, the book hits first. The prediction of the majority of students is correct!

If the students aren't satisfied, try this one: Crumple the paper into a ball. Drop the crumpled paper and the book from the same height at the same time. They will hit the floor simultaneously. (Dropping two objects from the same height at the same time isn't as easy as it seems. You should practice this a few times before performing it in class.) Ask them to explain why the objects hit the floor at the same time. They will propose the idea that the paper has less air resistance when it's a crumpled ball than when it's a flat sheet.

Ask the students if you would need to do the same things on the moon (where there is no air resistance). Ask them if the two objects would hit at the same time if they were dropped from the same height. Then, ask what would happen to the book and paper on Jupiter, a gas giant, provided we could stand on the planet. (Since Jupiter is a gas planet, there will be "air" resistance. So, the same experiments must be played.) By the end of the discussion, the students will understand that the rate at which an object falls on a planet or the moon is independent of its mass, provided there is no air resistance.

Instructions to the Student:

Your teacher will show you a textbook and an ordinary piece of paper. If they are dropped from the same height at the same time, which of the following things will happen? (1) The book will hit the floor before the paper; (2) the paper will land before the book; or (3) they both will hit the floor at the same time. Be prepared to explain your choice.

3. Discrepant Event: A guinea (coin) and a feather fall at the same rate and hit simultaneously.

Description:

Students investigate the roll of air resistance when objects are dropped near the surface of the earth.

Materials:

• Vacuum pump
• Guinea and feather tube apparatus

Instructions to the Teacher:

To make this a discrepant event, use the vacuum pump to evacuate the air from a column that contains a feather and a coin (guinea and feather tube apparatus). Do this before the demonstration, out of the sight of the students. Explain to the students that there is a guinea (coin) and a feather in the tube and that it will be inverted so the coin and feather can fall under the influence of gravity. Ask them to predict which will hit first by polling them as above. Invert the tube and let the students watch them fall. Since most of the air has been removed, they fall at the same rate. Ask the students to explain why they fell at the same time. After they realize that the air has been removed from the column, demonstrate what happens when the air has been returned. This really drives home the idea that objects near any planet will "fall" toward that planet at the same rate regardless of their mass when air resistance has been minimized.

Instructions to the Student:

Your teacher will show you a column containing a feather and a coin. If the tube is inverted, which will hit the end of the tube first, the coin or the feather? Or, will both land at the same time?

Step-by-Step Instructions:

"Planet Impact!" consists of four activities and an assessment. In the instructional activities, students learn how the velocity, angle of approach, and masses of the large and small bodies affect the comet's path. Each page of this activity, except the assessment section's cover page, has three extensions: "Science Scoop," "Comet News," and "Gravity Gallery."

In this interactive module, students can vary the comet's angle of approach to see the effect of gravity on its trajectory towards Jupiter. The speed and masses of the two bodies are held constant. The goal is for the student to understand the relationship between the distance from the planet and the force of gravity. Before introducing this module, help the students understand that as the angle decreases from 90 to zero degrees, the distance from the planet is also decreasing. An explanation of the science behind the animations can be found in "Science Scoop." More information on the crash of Shoemaker-Levy 9 on Jupiter can be obtained from "Gravity Gallery" and "Comet News."

Step On It!
In this interactive module, students change the comet's speed and observe the effect of gravity on its path. The angle of approach and the masses of the two bodies are held constant. The module's goal is to help students understand how a comet's speed affects its path. An explanation of the science behind the animations can be found in the "Science Scoop" section. More information on the crash of Shoemaker-Levy 9 on Jupiter can be obtained from "Gravity Gallery" and "Comet News." (Note: Comets travel fast. The icons on the speed button are used to indicate relative speeds. Students know that a rocket travels faster than a car; a car is quicker than a bicycle; and a bicycle is speedier than a skateboard. We are not suggesting that these objects travel at the speed of comets, nor are we suggesting that comets travel at the speed of these objects.)

Pick a Comet – Any Comet
In this interactive module, students learn that a comet's mass, compared with the size of a massive planet, does not affect the object's path. Students select comet masses from very light to heavy and observe the comets' paths. The angle, speed, and mass of the planet remain unchanged. An explanation of the science behind the animations can be found in "Science Scoop." More information on the crash of Shoemaker-Levy 9 on Jupiter can be obtained from "Gravity Gallery" and "Comet News."

It's a Matter of Mass
In this interactive module, students launch a comet at a variety of targets. The comet's angle, speed, and mass remain unchanged. Students will observe the difference in their comet's path when it passes an asteroid, the planet Earth, and the planet Jupiter to understand the relationship between the mass of the celestial object and the gravitational force it can exert on the comet. An explanation of the science behind the animations can be found in "Science Scoop." More information on the crash of Shoemaker-Levy 9 on Jupiter can be obtained from "Gravity Gallery" and "Comet News."

Target Practice: Hit…or Miss?
In this evaluation module, students apply the knowledge they gained in the previous modules to launch a comet at Jupiter that will either hit the planet or miss it. Students set the angle and speed prior to their comets' launch. "Comet News" and the "Gravity Gallery" are both available from the "Hit" and "Miss" modules.

Science Scoop
Science Scoop provides a further explanation of the science behind the animation for each of the four learning modules. The explanation begins with a question whose answer is only revealed when the student activates it. Encourage students to look at the question before beginning the module, and think about an answer. Students can check out their thinking by doing the activity and then reading the answer in the "Science Scoop." The "Science Scoop" questions are also included in the Grab Bag section of this document, under the heading Make It My Lesson.

Comet News
"Comet News" provides information, in a newspaper format, concerning the crash of comet Shoemaker-Levy 9 on Jupiter. Each part of the lesson provides a small piece of the story. The "Comet News" button on the home page allows access to all the news articles and the updates on recent remarkable comets. Teachers can use the articles to chronicle the history of the comet as outlined in the extension section below.

Gravity Gallery
"Gravity Gallery" provides images that take the viewer from the discovery of Shoemaker-Levy 9 through its crash on Jupiter.

Evaluation / Assessment:

After completing the first four modules – where students identify the effects of a comet's speed, angle, and mass and the mass of the planet – they will be asked to choose one of two activities in "Target Practice: Hit…or Miss?" In one of them, the aim is to launch a comet into Jupiter; in the other, to hurl a comet that misses Jupiter.

If students are trying to hit Jupiter with a comet, then they must apply the correct angle and speed. The buttons for choosing the angle and speed are similar to those used earlier, except that the lowest angle has been removed.

To miss Jupiter, students must select the proper parameters to avoid a collision between the comet and Jupiter. Again, the buttons are similar but, this time, the largest angle has been eliminated.

Solutions:

Solutions to all the activities are built into each page. In "What's Your Angle?," "Step On It!," "Pick a Comet – Any Comet," and "It's a Matter of Mass," students will see the results of their choices when the animation runs. The same format will be used in the assessment modules. Animations will run and pop-ups will appear that compare the student selections with the expected outcomes. For the assessment modules, when students select the right choice, after pop-ups, a reward animation will run.

Follow-up Activities / Interdisciplinary Connections:

1. "Target Practice" Analysis

Description:

Students collect "hit", "miss," and "breakup" information about their comets as they complete the lesson. Then they use the information to draw a graph of angle versus speed. The graph will help them determine the combinations of angle and speed that are needed to either hit or miss the planet.

Materials:

A chart is needed that is similar to the one shown here. Show the students how to set it up (explanation below):

Angle Speed Result
0 degrees All Hit
30 degrees Skateboard & Bicycle Hit
Car Broke Up
Rocket Miss
60 degrees Skateboard Hit
Bicycle Broke Up
Car & Rocket Miss
90 degrees Skateboard Broke Up
Bicycle, Car, & Rocket Miss

Instructions to the Teacher:

Ask students to make a chart listing the angles and speeds that cause the comet to hit or miss Jupiter. Here is how the students should make the chart: Divide a sheet of notebook paper into three columns. Title the first column "Angle." Under that heading, write down each of the following angles four times: 0 degrees, 30 degrees, 60 degrees, and 90 degrees. Label the second column "Speed." Under that heading, write down skateboard, bicycle, car, and rocket four times. Instruct the students to fill in the last column of the chart, named "Result," as they are working on the lesson section entitled "Target Practice: Hit or Miss." Explain that they must go to the "miss" page to get a result for 0 degrees and to the "hit" page to obtain a result for 90 degrees. Students can obtain results for 30 degrees and 60 degrees by going to either the "hit" or the "miss" page.

Use the information from the students to generalize hit and miss zones. A small angle and slow speed mean the comet will hit Jupiter while a high speed and large angle mean it will miss the planet. A large angle and small speed can result in a hit and a small angle and large speed can result in a miss. Once the students understand this relationship, ask them to graph the angle versus speed for the breakup points. Then ask them to draw a smooth curve through the plotted points. They should make their line approach the x-axis asymptotically, since the comet will hit the planet if launched directly at it (0 degrees) regardless of the speed. The line will basically divide the graph into hit and miss zones. Ask the students to label the sections as such. The following diagram shows the relative speeds of the four vehicles:

 S B C R Low Speeds High Speeds where S = skateboard, B = bicycle, C = car, R = rocket

You can compare the students' charts to the "ideal" chart. Get the PDF version of the chart.

Instructions to the Student:

Your teacher will tell you how to make a chart to record a comet's hits, misses, and breakups. Fill in the "results" column while completing "Target Practice," noting whether the comet hit or missed Jupiter, or broke up near the planet. To obtain a result for 0 degrees, you must go to the "miss" page. For 90 degrees, you must go to the "hit" page to get a result. You can obtain results for 30 degrees and 60 degrees by going to either the "hit" or the "miss" page.

This chart will be used to make generalized statements about the "hit" and "miss" zones and to construct a graph of angle versus speed to show the hit and miss zones. The angle is plotted on the (vertical) y-axis, which is labeled from 0 to 90 degrees; the speed is plotted on the (horizontal) x-axis. Your teacher will help you put a scale on the speed axis using the four vehicles' relative speeds. Plot the angle and speed for each breakup point. Draw a smooth line through these points, and make the line asymptotically meet the x-axis. Explain why there is an asymptote on the x-axis. Once your line is drawn, label the two sections of the graph the "hit" and "miss" zones.

2. Boy, That was Some Comet!

Description:

Following the inquiry-based engagement activity (listed above as the first suggested engagement activity), students read "Comet News" to find the answers to as many of their questions as possible.

Materials:

Instructions to the Teacher:

A logical extension of the inquiry-based engagement activity is to ask students to read the story of the discovery of comet Shoemaker-Levy 9 and its crash into Jupiter. Direct the students to find answers to their questions by reading the seven articles on the comet.

If they don't find their answers in "Comet News," send them to the sections on "Gravity Gallery" and "Science Background," or to one of several websites devoted to the comet's crash listed in the Grab Bag section of this document. A link to "Gravity Gallery" is located on each section of the lesson. The gallery contains images of Jupiter and the comet.

Another activity is to ask students to read the eighth article on the breakup of comet LINEAR. Then students can make a graphic organizer (T-chart or Venn diagram) that lists the similarities and differences between the two comets, which are listed below:

Comet Shoemaker-Levy 9 Comet LINEAR
Pulled apart by Jupiter's gravity Sun's heat caused the pieces to come apart
Discovered after it fell apart Scientists watched it fall apart
Impacted Jupiter Just disappeared (implied)
Came from either the Kuiper Belt or the Oort Cloud Came from the Oort Cloud
First to be viewed impacting a planet Most recently viewed falling apart in inner solar system.

Instructions to the Student:

Read the eighth article about comet LINEAR. Make a list of qualities and characteristics that the comets Shoemaker-Levy 9 and LINEAR have in common and those that are unique to each comet. Arrange them in a graphic organizer such as a T-chart or Venn diagram. Then write a paragraph about what you observed.

3. Gravity Challenge

Description:

Students search HubbleSite's "News and Views" for examples of astronomical changes governed by gravity. The objective: finding the most articles.

Materials:

Instructions to the Teacher:

Tell students to click on "News & Views" from the HubbleSite top page. Once there, they should search the archives, arranged by year and subject, for examples of astronomical changes governed by gravity. These could be text or images as long as students can explain how gravity works. You can ask students to find as many examples as possible during an allotted time period. Then play an elimination game. The winners would be given a gravity-appropriate prize such as a ride in an elevator or no homework (they don't have to lift their textbooks). To play the game, a group would present the title of a press release and explain the influence of gravity on the celestial object in the release. Other groups that had selected the same press release would have to cross it off their list. Then another group would share one of their findings. Each group would present an example until there were no new ones left. An example of what the student might find is the press release: "He2-90's Appearance Deceives Astronomers," which explains how two stars are interacting gravitationally. http://hubblesite.org/news_.and._views/pr.cgi?2000+24 If you make this a two-day event, consider collecting students' lists at the end of the first day. The first day could be spent in the computer lab looking for examples and the second in the classroom discussing those examples. Collecting the lists ensures that they will be available on the second day (the one holding the list overnight might be absent the next day). It also prevents students with home Internet access from "padding" their lists overnight.

Instructions to the Student:

Use the website bookmarked by your teacher to search for examples of changes in celestial objects that were or are brought about by gravity. Write down the title of each press release and how gravity influences the astronomical object described in the release. Find as many as you can in the time allotted to you. The more you find, the better your chances of being the winner. Once time has expired, you will be asked to share one title and describe how that press release explains gravity's influence. Other students who have selected the same press release must cross it off their lists. The group with the most examples remaining after all have been shared is the winner and will receive an appropriate reward.

Teachers can use other disciplines to broaden their students' understanding of the force of gravity.

Art: Students can draw pictures of a comet slamming into Jupiter, creating plumes and flying debris. Images from the "Gravity Gallery" may help inspire the students to draw an artist's rendition of the impacts.

English: Students can write comet poems and stories. Perhaps they can research comet Shoemaker-Levy 9 or other remarkable comets, and write a newspaper article or a biography of one of the three discoverers of Shoemaker-Levy.

General Science: Students can expand their knowledge of gravity by studying microgravity. Information on this topic can be found in the microgravity teacher's guide, a PDF file: http://spacelink.nasa.gov/Instructional.Materials/Curriculum.Support/Physical.Science/Microgravity/Microgravity/

Biology: Students can draw and write about the kind of life that may have been brought to Earth from impacting comets and/or the effect that a large comet or asteroid impact might have on the existing life on Earth. Theories on the formation of the earth and moon due to impacts by other bodies (http://zebu.uoregon.edu/1996/ph123/l11.html) may start students on the right track.

Math: Students can read the NASA news brief "Microgravity – Fall into Mathematics," a PDF file that contains three "try this" math problems for students. http://spacelink.nasa.gov/Instructional.Materials/NASA.Educational.Products/Microgravity-Fall.Into.Mathematics/ A teachers' guide to the mathematics of microgravity also is available. http://spacelink.nasa.gov/Instructional.Materials/NASA.Educational.Products/Mathematics.of.Microgravity/

One-Computer Classroom:

It is recommended that teachers use an overhead, LCD, or television screen to project images from the computer onto a classroom screen. To facilitate a more organized and predictable large-group presentation and avoid last-minute glitches, consider "bookmarking" the lesson (such as one of the pages you wish to use) and downloading it onto your hard disk. This will eliminate the inconvenience of unexpectedly going off the Internet. Each of the four learning modules –"What's Your Angle," "Step On It," "Pick a Comet – Any Comet," and "It's a Matter of Mass" – has a question in "Science Scoop," which you can access before students view the animation. Students can conduct a "brainstorming" session to obtain answers. They can check their answers by using the activity and the explanation provided in "Science Scoop." (The question comes up first and the explanation is only revealed when activated.)

Classrooms without Computers:

Here are some suggestions:

• If you have access to a computer with World Wide Web capabilities and a printer at home or in the school library, you may print selected parts of the lesson as paper copies or transparencies. (See, in particular, the PDF files created for that purpose in the Grab Bag section of this document.)
• If your school has one or more computers located outside your classroom, students may experience the lesson individually or in small groups as a learning station.
• Some students might have computers at home with access to the Internet. If that's the case, you might consider assigning sections of the "Planet Impact!" activities as homework or extra credit.
• NASA offers FREE comet Shoemaker-Levy 9 and Solar System-related lithographs and posters, which are available at your closest NASA Educator Resource Center, http://spacelink.nasa.gov/Instructional.Materials/NASA.Educational.Products/ They can be used as teaching tools in the classroom.

Home Schooler:

This lesson is easily followed without additional teacher support if the prerequisites are met. Parents can preview the lesson and examine the teacher pages ahead of time. A wealth of information can be found at Hubblesite, the Hubble Space Telescope's website at the Space Telescope Science Institute. Here you can find background information on the telescope, pictures and news releases of past and present stories, education activities, and other science resources.

More information for the home-schooled can be found at:

Make It My Lesson:

The following list of questions can be used in a variety of ways, depending on a teacher's preferences. The first four are based on the prerequisites and could be used before beginning the lesson to check students' understanding of the prerequisites. Questions 7 ,9, 11, and 13 appear in the lesson's "Science Scoop" section and are repeated as a group at the end. Students have met the objectives if they can answer these four questions completely. Some questions are designed to guide the students' thoughts. For example, once students have correctly answered questions 5 and 6, they should be able to answer question 7 completely. Others target the "Comet News" and "Gravity Gallery" sections. Questions 5 to 24 can be used as a pre- and a post-test; as a guide to learning while the student completes the lesson; as an evaluation after the lesson; as a guide to class discussion; or as a drill or warm-up. Each question is marked with the section of the lesson to which it pertains.

Questions:

1. Arrange these in order of increasing mass: Jupiter, Earth, the Sun, an asteroid. (prerequisite)
2. All of the objects listed above are part of what? (prerequisite)
3. If an object changes speed and/or direction, it is experiencing (a balanced, an unbalanced) force. (prerequisite)
4. What force is responsible for keeping us on Earth? (prerequisite)
5. As the angle increases from 0 to 90 degrees, the change in the comet's direction (decreases, increases) because the distance between the comet and the planet (decreases, increases). (What's Your Angle?)
6. As the angle increases from 0 to 90 degrees, the force of gravity on the comet (decreases, increases). (What's Your Angle?)
7. What is the relationship between the distance from the planet and the force of gravity on the comet? (What's Your Angle?)
8. As the speed increases, it is (easier, harder, the same) for Jupiter to capture the comet. (Step On It!)
9. How does the speed of the comet affect its path? (Step On It!)
10. As the mass of the launched comet increases, the amount its path curves (decreases, increases, remains the same). (Pick a Comet)
11. What is the relationship between the mass of the comet and its acceleration? (Pick a Comet)
12. As the mass of an object increases, the gravitational force it can exert on another body (decreases, increases, remains the same). (It's a Matter of Mass)
13. What is the relationship between the mass of the celestial object and the gravitational force it exerts on the comet? (It's a Matter of Mass)
14. To hit Jupiter, the speed of the comet must (decrease, increase) as the angle increases. (Target Practice)
15. To hit Jupiter, the angle must (decrease, increase) as the speed of the comet increases. (Target Practice)
16. If the comet were replaced by a more massive comet, the challenge to hit Jupiter would be (easier, harder, the same). (Target Practice)
17. If the Sun replaced Jupiter, it would be (easier than, harder than, the same challenge as) trying to hit Jupiter. (Target Practice)
18. If Earth replaced Jupiter, it would be (easier than, harder than, the same challenge as) trying to hit Jupiter. (Target Practice)
19. In this lesson, each of the four factors (angle, speed, mass of small body, mass of large body) was changed one-at-a-time. From an experimental design point of view, why was it done this way? (all sections)
20. When the gravitational force causes a change in the comet's direction, the force is (balanced, unbalanced). (all sections)
21. What is Shoemaker-Levy 9? (Comet News)
22. What was the scientific significance of the crash of Shoemaker-Levy 9 on Jupiter? (Comet News)
23. Prior to impact, describe how the fragments of Shoemaker-Levy 9 changed with time. (Gravity Gallery)
24. Describe the impact site of a fragment of Shoemaker-Levy 9. (Gravity Gallery)

1. Arrange these in order of increasing mass: asteroid, Earth, Jupiter, the Sun. (prerequisite)
2. All of the objects listed above are part of what? The solar system (prerequisite)
3. If an object changes speed and/or direction, it is experiencing an unbalanced force. (prerequisite)
4. What force is responsible for keeping us on Earth? Gravity (prerequisite)
5. As the angle increases from 0 to 90 degrees, the change in the comet's direction decreases, because the distance between the comet and the planet increases. (What's Your Angle?)
6. As the angle increases from 0 to 90 degrees, the force of gravity on the comet decreases. (What's Your Angle?)
7. What is the relationship between the distance from the planet and the force of gravity? The angle at which the comet is launched is changing the distance between the comet and Jupiter. The change in the comet's path is caused by Jupiter's gravity, which is providing an unbalanced force. This unbalanced gravitational force increases as the distance between Jupiter and the comet decreases. When the comet is fired at 90 degrees, its path remains unchanged. The comet is far enough away from Jupiter that there is no unbalanced force acting on it. As the angle decreases, the comet comes closer to Jupiter and thus experiences a greater and greater unbalanced gravitational force, until at 0 degrees the comet's path is changed so much that it hits the planet.
8. As the speed increases, it is harder for Jupiter to capture the comet. (Step On It!)
9. How does the speed of the comet affect its path? As the speed of the comet increases, its energy of motion increases. The comet also has energy due to its position near the planet and the strong gravitational force. For a comet to escape a planet's gravitational pull, the energy associated with the comet's motion must be greater than the energy associated with its position. So, as the comet's speed increases, it has more energy of motion and is able to escape the planet's gravitational pull.
10. As the mass of the launched comet increases, the amount its path curves remains the same. (Pick a Comet)
11. What is the relationship between the mass of the comet and its acceleration? The comet's mass doesn't matter because its acceleration (how quickly it will change its path) depends only on a planet's mass and how near it is to the planet. This is similar to objects falling on Earth: they fall at the same rate regardless of their mass (as long as air resistance is minimal). Want to know the math behind this? To calculate the acceleration, a, of a body, divide the force, F, applied to the body by the mass, m, of the body: a = F/m. In the case of a comet, the force applied depends on its mass, the mass of the planet, and the distance between the two. Dividing the comet's mass by the mass of the planet equals one. So the comet's mass doesn't affect its acceleration near the planet. Since we are keeping the mass of the planet and the distance from the planet (expressed as the angle) constant, the accelerations of all comets are the same, and they follow the exact same path.
12. As the mass of an object increases, the gravitational force it can exert on another body increases. (It's a Matter of Mass)
13. What is the relationship between the mass of the celestial object and the gravitational force it exerts on the comet? According to Newton's Law of Gravitation, as the mass of one body increases, its ability to exert a gravitational force on the other body also increases: the larger the mass, the greater the gravitational force. The asteroid didn't have much mass, so the unbalanced gravitational force was small and the asteroid was unable to influence the comet's path. Earth's mass was great enough to exert a small unbalanced gravitational force on the comet. This force changed the comet's path, but was not large enough to actually capture the comet. Massive Jupiter not only captured the comet but exerted such a large unbalanced gravitational force that the comet impacted the planet.
14. To hit Jupiter, the speed of the comet must decrease as the angle increases. (Target Practice)
15. To hit Jupiter, the angle must decrease as the speed of the comet increases. (Target Practice)
16. If the comet were replaced by a more massive comet, the challenge to hit Jupiter would be the same. (Target Practice)
17. If the Sun replaced Jupiter, trying to hit it would be easier than trying to hit Jupiter. (Target Practice)
18. If Earth replaced Jupiter, trying to hit it would be harder than trying to hit Jupiter. (Target Practice)
19. In this lesson, each of the four factors (angle, speed, mass of small body, mass of large body) was changed one-at-a-time. From an experimental design point of view, why was it done this way?
If more than one variable is changed at one time, it is impossible to know which change made the difference.
20. When the gravitational force causes a change in the comet's direction, the force is unbalanced.
21. What is Shoemaker-Levy 9? (Comet News) A comet that broke up while orbiting Jupiter. An orbit later, its fragments crashed into Jupiter over a seven-day period.
22. What was the scientific significance of the crash of Shoemaker-Levy 9 on Jupiter? (Comet News) It marks the first time scientists knew ahead of time that two solar system bodies were going to collide.
23. Prior to impact, describe how the fragments of Shoemaker-Levy 9 changed with time. (Gravity Gallery) Over time, the fragments moved farther apart.
24. Describe an impact site of a fragment of Shoemaker-Levy 9. (Gravity Gallery) The impact site is a circle of dark debris that dissipates over time due to motion in the atmosphere.

Science Scoop Questions:

1. What is the relationship between the distance from a planet and the force of gravity on a comet? (What's Your Angle?)
2. How does the speed of a comet affect its path? (Step On It!)
3. What is the relationship between a comet's mass and its acceleration? (Pick a Comet)
4. What is the relationship between the mass of a celestial object and the gravitational force it exerts on a comet? (It's a Matter of Mass)

1. What is the relationship between the distance from a planet and the force of gravity? The gravitational force increases as the distance between Jupiter and a comet decreases. A comet fired at a 90-degree angle is far enough away from Jupiter that it is not influenced by the planet's gravitational force. Its path, therefore, doesn't change. As the angle decreases, the comet comes closer to Jupiter. Thus, the comet experiences a greater and greater gravitational force until, at 0 degrees, Jupiter's gravity changes the comet's path so much that the comet hits the planet.

2. How does the speed of a comet affect its path? As the speed of a comet increases, the energy associated with its motion increases. If the energy is high enough, the comet will be able to escape Jupiter's gravitational force. If a comet is close to Jupiter, the planet's gravitational field primarily determines the comet's motion. The comet falls toward Jupiter because of the planet's gravitational pull, just like a dropped book falls to the floor on Earth because of Earth's gravitational pull. Objects fall toward Jupiter's surface due to the unbalanced force of the planet's gravity. The faster the launched comet is traveling, the farther it will go before hitting the surface. If the speed is low, it will travel only a short distance before crashing. At slightly higher speeds, it will cover more ground before hitting the surface. The comet won't hit Jupiter if it is traveling fast enough. Instead, it will travel into orbit around Jupiter. At the fastest speeds, it will escape Jupiter's gravity completely.

3. What is the relationship between a comet's mass and its acceleration? A comet's mass doesn't affect its acceleration. Its acceleration (how quickly it will change its speed or direction) depends only on two things: a planet's mass and the comet's distance from that planet. This happens on Earth. Objects fall at the same rate regardless of their mass. Want to know the math behind this? To calculate the acceleration, a, of a body, divide the force, F, applied to the body by the mass, m, of the body. The equation is: a = F/m. In this case, the m is the mass of the comet and the F is the gravitational force between the comet and the planet. This force depends on the mass of the comet, the mass of the planet, and the distance between the two. When this gravitational force, F, is substituted into the equation a = F/m, the mass of the comet, m, appears in the numerator and denominator, so it factors out of the equation. The comet's mass doesn't affect its acceleration near the planet. Since we are keeping the mass of the planet and the comet's distance from the planet (expressed as the angle) constant, the accelerations of all comets are the same, and they follow the exact same path.

4. What is the relationship between the mass of a celestial object and the gravitational force it exerts on a comet? According to Newton's Law of Gravitation, as the mass of one body increases, its ability to exert a gravitational force on the other body also increases. Thus, the larger the mass, the greater the gravitational force. Because the asteroid didn't have much mass, it exerted a small gravitational force on the comet passing close to it. Therefore, the asteroid was unable to influence the comet's path. Earth's mass was great enough to exert a small gravitational force on the comet. This force changed the comet's path but was not large enough to actually capture the small body. Massive Jupiter not only captured the comet but exerted such a large gravitational force that the comet slammed into the planet.

Extensions to Planet Impact!

Comet Cratering

Students will discover what happens when comets or asteroids hit the surface of a Jovian planet and a terrestrial planet/moon. Using marbles of different sizes, they will drop them into a variety of materials. To make a Jovian-like atmosphere for the impact, try using non-diary whipped topping or make gelatin in addition to the flour suggested in the directions. This activity is found in "Think SMALL in a Big Way" at http://stardust.jpl.nasa.gov/classroom/educators.html

The Math/Science Connection

Description:

Students estimate the mass of Shoemaker Levy-9 based on the best estimate of its diameter and on the assumptions of its shape and composition.

Materials:

• Calculator capable of using scientific notation

Instructions to the Teacher:

Depending on the capabilities of your students, you can work through these calculations with them or let them figure them out by trial and error.

As the lesson develops, use the following as a guideline and elicit student assumptions.

Based on the brightness of the fragments, scientists have estimated the diameter of SL-9 to be 5 km (5000 m).

A good assumption is that SL-9 is shaped like a sphere. So its volume can be estimated from the formula for the volume of a sphere:

V = (4/3)r3, where r = 2500 m, half the diameter and = 3.14
The volume, V, is 6.5 x 1010 m3

There is still a question whether SL-9 was a comet (basically a dirty snowball) or an asteroid (whose composition could be mostly iron). The density range can be estimated from the densities of ice and iron.

Dice = 0.92 g/cm3= 920 kg/m3
Diron = 7.8g/cm3= 7800 kg/m3

Once the volume and density range are known, the range of masses (m) can be determined from m = DV.

Range of masses is from 6.0 x 1013 kg to 5.1 x 1014 kg (or about 100,000,000,000,000 tonnes)

You can take this one step further and estimate the gravitational force on SL-9 at its closest approach to Jupiter using:

Distance from the center of Jupiter, r = 96,000 km = 96,000,000 m,
the mass of Jupiter, MJ = 1.9 x 1027 kg,
the estimated masses of comet SL-9, mc = 6.0 x 1013 kg to mc = 5.1 x 1014 kg,
the gravitational constant, G = 6.67 x10-11 N-m2/kg2.

The formula F = (GmcMJ)/r2
which yields a force, F, between 8.3 x 1014 N and 7.0 x 1015 N.

Note: the density range varies by one order of magnitude and so do the range of masses and forces. If we could narrow down the density, the range of forces would also decrease. Pointing this out to students may help them see how important a good "guess" can be. You might assign them research to find the estimated densities of the "average" comet and asteroid either before or after these calculations. Some components of SL-9 are silicon, magnesium, and iron, as revealed in the press release (http://hubblesite.org/newscenter/1994/48/) from the Space Telescope Science Institute. This would lower the high end of the density estimate. Included in the Grab Bag section of this document is a list of other websites, which may help students do research on the densities of comets and asteroids.

Instructions to the Student:

Estimate the mass of SL-9 based on the best estimate of its diameter and on the assumptions of its shape and composition. Based on the brightness of the fragments, scientists have estimated the diameter of SL-9 to be 5 km (5000 m). Use this information, along with your best estimation of the shape and composition of the comet, to estimate the mass.