When a comet travels near a planet, there is a gravitational force between the comet and the planet (F_g = GMm/r² where F_g = 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. (F_c= ma_c where F_c = centripetal force and a_c = 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.

F_c = F_g
ma_c = GMm/r²
a_c = GM/r²

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.

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.

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.

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.

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.

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.

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.