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.

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

Remember that the weight of the astronaut is the same as the gravitational force acting between the planet and the astronaut.

We are given the gravitational constant, the radius of the planet, the mass of the astronaut, and the magnitude of the force generated. Using these values in the universal gravitation equation, we can solve for the mass of the planet.

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

We are given the value of the force, the distance (radius), and the gravitational constant. We are also told that the masses of the two satellites are equal. Since the masses are equal, we can reduce the numerator of the law of gravitation to a single variable.

Now we can use our give values to solve for the mass.