The equation for the force of gravity between two objects is:

Using this equation, we can select arbitrary values for our original masses and distance. This will make it easier to solve when these values change.

is the gravitational constant. Now that we have a term for the initial force of gravity, we can use the changes from the question to find how the force changes.

We can use our first calculation to see the how the force has changed.

To solve this problem, use the law of universal gravitation.

Remember that  is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

This force will be the same for both objects. The Earth will exert the same force on the satellite as the satellite exerts on the Earth. This makes sense, given Newton's third law.

To solve this problem, use the law of universal gravitation.

Remember that  is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

This force will be the same for both objects. The Earth will exert the same force on the satellite as the satellite exerts on the Earth. This makes sense, given Newton's third law.

To solve this problem, first recognize that the force due to gravity of the Earth on the satellite is the same as the centripetal force acting on the satellite. That means .

Solve for  for the satellite. To do this, use the law of universal gravitation.

Remember that  is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleration. Remember that centripetal force is . Set our two forces equal and solve for the centripetal acceleration.

Now we can find the tangential velocity, using the equation for centripetal acceleration. Again, remember that the radius is equal to the sum of the radius of the Earth and the height of the satellite!

To solve this problem, use the law of universal gravitation.

Remember that  is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the mass of the Earth, force of gravity, and distance to solve for the mass of the satellite.

To solve this problem, we need to set up the law of universal gravitation.

When the satellite was whole:

After the satellite breaks:

We can now compare these two equations. Start by expanding the second equation.

We can substitute our first equation into the second.

and 

This tells us that the final force of gravity is equal to one half the original force of gravity.

We can use the conservation of momentum to solve. Since the satellites stick together, there is only one final velocity term.

We know the masses for both satellites are equal, and the second satellite is initially stationary.

Now we need to find the velocity of the first satellite. Since the satellite is in orbit (circular motion), we need to find the tangential velocity. We can do this by finding the centripetal acceleration from the centripetal force.

Recognize that the force due to gravity of the Earth on the satellite is the same as the centripetal force acting on the satellite. That means .

Solve for  for the satellite. To do this, use the law of universal gravitation.

Remember that  is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleration. Remember that centripetal force is . Set our two forces equal and solve for the centripetal acceleration.

Now we can find the tangential velocity, using the equation for centripetal acceleration. Again, remember that the radius is equal to the sum of the radius of the Earth and the height of the satellite!

This value is the tangential velocity, or the initial velocity of the first satellite. We can plug this into the equation for conversation of momentum to solve for the final velocity of the two satellites.

The period describes how long it takes the satellite to make one full orbit. If you go back to the definition of velocity, , we can apply that to our new circular orbit, in which the distance is equal to the circumference of the circle and the time is equal to the period: . The circumference divided by the period will give us the average velocity.

The problem gives us the radius, but we need to find the tangential velocity. We can do this by first solving for the centripetal acceleration from the centripetal force.

Recognize that the force due to gravity of the Earth on the satellite is the same as the centripetal force acting on the satellite. That means .

Solve for  for the satellite. To do this, use the law of universal gravitation.

Remember that  is the distance between the centers of the two objects. That means it will be equal to the radius of the earth PLUS the orbiting distance.

Use the given values for the masses of the objects and distance to solve for the force of gravity.

Now that we know the force, we can find the acceleration. Remember that centripetal force is . Set our two forces equal and solve for the centripetal acceleration.

Now we can find the tangential velocity, using the equation for centripetal acceleration. Again, remember that the radius is equal to the sum of the radius of the Earth and the height of the satellite!

We now have a value for the tangential velocity, which we can use in the equation for velocity from the beginning to find the period.

To solve, use Newton's law of universal gravitation:

We are given the values for the mass of each planet, as well as the distance (radius) between them. Using these values and the gravitational constant, we can solve for the force of gravity.

Remember that Newton's second law states that . The force acting upon the planet in question will be the force due to gravity. Once we find that, we can find the acceleration.