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Gravity
Q&A: Gravity

#### A 1:

Gravity is the attraction of every body to every other body due to the masses of each body. The larger the mass, the greater the force. It also depends on the distances: the closer the bodies, the greater the force. Gravity is directed toward the center of a body, and the distance is measured from the center. Gravity keeps the moon going around the Earth, the Earth going around the Sun, and the Sun going around the center of the Milky Way. Gravity is the weakest of the four fundamental forces of nature (electromagnetic, weak nuclear, and strong nuclear are the other three), yet it is the force that governs motion in the universe.

#### A 2:

The force of gravity (F) depends on the masses of the two bodies (m1, m2) and the distance between the bodies' centers (r). There is a direct proportion between mass and gravitational force. If you double the mass of one body, the gravitational force between them is also doubled. The gravitational force is inversely proportional to the square of the distance. If you double the distance between the two bodies, the force of gravity is reduced to one-fourth its original value. The equation relating these ideas is: F = G(m1m2)/r2, where G is the universal gravitational constant equal to 6.67 x 10-11 Nm2/kg2 or m3/s2kg).

#### A 3:

Objects remain in orbit around a massive body due to gravity and their sideways motion. Objects in orbit are moving sideways, approximately at right angles (90 degrees) to the force of gravity. An object would travel in a straight line with a constant speed if it were not for the gravitational attraction of a massive body. The attractive force changes the motion of the object from a straight line to a closed curve, as it begins orbiting the massive body. In effect, the object is falling around the massive body.

#### A 4:

An unbalanced or net force causes changes in an object's speed and/or direction. Only one force acting on a body is unbalanced because there is no counter-force to cancel the force's effects. A person remains at rest when sitting in a chair because there are two balanced forces acting on that person. One of those forces is gravity, which pulls the person downward. The other force is the chair pushing upward on the person. The two forces are equal in magnitude (size) and opposite in direction. So they balance each other, and the person doesn't change direction or speed.

On the other hand, Earth's gravitational influence on the moon is unbalanced. The moon is constantly changing its direction of motion, so it is experiencing acceleration. Any time there is an unbalanced force, the object will undergo a change in direction or speed. So, a change in direction or speed means there is an unbalanced force at work.

#### A 5:

According to Newton's First Law of Motion, an object in motion tends to remain in straight-line motion at a constant speed unless acted upon by an external, unbalanced force. When a comet or asteroid comes close to a body with a large gravitational force (a planet, for example), the path of the comet or asteroid is altered due to the unbalanced force of gravity on the body. It moves toward the planet as described in Newton's Second Law. When an unbalanced force acts on a body, the body experiences acceleration in the direction of the force. A force that tends to make a body move in a curved path is called a centripetal force.

Occasionally, the comet will be close enough to the planet to become trapped by the gravitational force and will begin orbiting the planet. The comet would like to continue traveling in a straight line, but the planet is pulling the smaller body toward its center, making it travel in a curved path around the planet.

#### A 6:

The more direct the approach, the easier it is for the planet to capture a comet because the comet comes closer to the planet. As discussed in question 5 above, the closer the objects come to each other, the stronger the force of gravity.

#### A 7:

The faster an object is moving, the greater the kinetic energy. In order for an object to be trapped by the gravity of a planet, the object's kinetic energy (Ek = 1/2 mv2 where Ek = kinetic energy, m = mass of comet, and v = speed) must be less than the gravitational potential energy (U = GMm/r where U = potential energy, G = gravitational constant, M = mass of planet, m = mass of comet, and r = distance from the center of the planet to the center of the comet).

The comet's total energy is equal to the kinetic plus potential energies. But the potential energy is negative, so a comet can only escape a planet's gravitational pull if the kinetic energy is larger than the gravitational potential energy.

#### A 8:

When a comet travels near a planet, there is a gravitational force between the comet and the planet (Fg = GMm/r2 where Fg = gravitational force and the others are as defined above). This force provides a centripetal acceleration, which changes the comet's path so that it begins orbiting the planet. (Fc= mac where Fc = centripetal force and ac = centripetal acceleration). These two forces are the same. If we set them equal to each other, the mass of the comet factors out of the equation.

Fc = Fg

mac = GMm/r2

ac = GM/r2

#### A 9:

As shown in the equation in question 8 above, the amount of centripetal acceleration on a comet depends on the mass of the body causing the acceleration. The greater the acceleration, the more easily the comet's path is changed and the more likely it is to be captured. This means that a massive planet can capture a comet more easily than could a less massive planet.

#### A 10:

The force that makes a comet orbit a planet is also responsible for the breakup of a comet. That force is gravity. Because the gravitational force increases as the distance between the bodies decreases, the force of gravity on the nearer side of a celestial body is stronger than the force of gravity on the far side, and a tidal force arises.

These forces can exist between any two celestial objects in orbit around each other. Some celestial bodies are not perfectly rigid, so they become distorted when subjected to such tidal forces. It is as if they are being pushed from the top and bottom, and a bulge forms on either side of the body — one directed toward the central body and the other on the opposite side. But there isn't a force above and below the body. What is happening is that the part of the orbiting body closest to the central body moves toward that body by a larger amount than the middle of the orbiting body. This causes a bulge on the side toward the central body.

To explain the bulge on the opposite side, apply the same logic: the middle of the orbiting body feels a greater pull than the far side, so it moves toward the central body more than the outer part. This leaves a bulge of material behind. If a celestial body is very rigid or is not held together well, instead of getting pulled out of shape, the tidal forces can actually tear the body apart. This is what happened with comet Shoemaker-Levy 9.

#### A 11:

Comets usually orbit the Sun, but Shoemaker-Levy 9 was captured by Jupiter's gravity and appears to have orbited the planet for about two decades before the breakup. After Shoemaker-Levy 9 broke into fragments, it was in an orbit around Jupiter that had a period of two years. The energy lost in the breakup of the comet lowered the point of closest approach (perijove) of the subsequent orbit to within one Jupiter radius of that planet's center.

#### A 12:

According to David Levy, a half-mile-wide object should hit the Earth on the average of once every 100,000 years. However, small objects the size of a grain of sand or a piece of gravel hit the Earth each minute. The frequency with which a 100-meter asteroid/comet hits Earth is about once every 100 years. The chances could be higher or lower because these small objects are not easy to see with our telescopes, so their number is not well known.

#### A 13:

The craters on the moon were caused by impacts with other objects. Craters on Earth are evidence that large objects have hit it. Many scientists believe that an asteroid or a comet was responsible for the extinction of the dinosaurs. The current theory of the formation of Earth's moon is linked to a collision or close encounter with a very large body. The oceans are believed to have formed from the impacts of many water-rich planetesimals and cometesimals.

An asteroid hit the sparsely-populated region of Tunguska, Siberia on June 30, 1908, causing destruction of many trees and reindeer. Craters on most solar system bodies provide evidence of collisions with asteroids or comets. If the impacted body is small, it can be forced into a different orbit and find itself captured by a nearby larger body. Some astronomers believe that the moons of Mars are really asteroids that ventured too close to the planet and were trapped by its gravity.

#### A 14:

The Roche limit is the distance at which the tidal forces of a planet (or other massive celestial body, such as a star) become greater than the internal cohesive forces of a comet (or other small object). As the comet approaches the Roche limit, the side closest to the planet experiences a stronger gravitational pull than does the far side. Thus the two sides of the comet tend to move apart because they are acted upon by different magnitude forces, and the comet breaks up. This mathematical limit is at different distances for different planets and depends on a planet's diameter.

#### A 15:

Centripetal forces are true forces, which cause a body to move in a curved path. The force of gravity on a satellite causes it to orbit a planet. The force is directed toward the center of the planet and causes the satellite to alter its path toward the planet. Otherwise, the satellite would travel in a straight line, tangent to the orbit.

Centrifugal forces are pseudo-forces that arise when a body is undergoing a centripetal acceleration. An example of this is the amusement park ride known as the Round-Up. You stand on the ride and it spins in a circle (and then tips upwards). You feel as if you are being pushed backwards, toward the outside of the ride. This force is a centrifugal force. In reality, the ride is exerting a force on you toward the inside of the circle. Your body would like to go in a straight line, tangent to the circle, and you feel an outward force because of the inward force of the ride that keeps you moving in a circle.

Description

"Q&A: Gravity" is a series of questions and answers about gravity written for teachers and students. The questions are ones that students might ask while studying gravity. Teachers can use this Q&A to gain additional knowledge about gravity, or use it in the classroom as outlined below.

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How to use in the classroom

• An engagement activity. Use selected questions to start a discussion.

• An inquiry tool. Use selected questions and answers to help students generate questions. Propose a question, such as "What keeps Earth from falling into the Sun?"(see question 5 in Q&A: Gravity). Have students read the answer to the question and write down any questions they would like answered as a result of reading the material.

• A source of information. Students can use the questions and answers as part of their research on gravity.

• A form of review. Use the questions as a review at the end of a unit on gravity.