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).

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.

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.

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.

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.

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 (E_k = 1/2 mv² where E_k = 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.