Unit 7: Gravitation

If the distance between two masses is doubled, the gravitational force between them:

A satellite orbits Earth at radius R with period T. If the orbital radius is increased to 4R, the new period is:

The gravitational force between two masses is [math]. If the distance is tripled, the force becomes

The gravitational potential energy between two masses m and M separated by distance r is

The escape velocity from a planet of mass M and radius R is

Kepler's third law states that [math]. For a circular orbit, the orbital speed at radius r from a planet of mass M is

The gravitational field strength at distance r from a point mass M is

A satellite in circular orbit at radius 2R from a planet's center is moved to orbit at radius 4R. The ratio of orbital speeds [math] is

Inside a uniform solid sphere of mass M and radius R, at distance r from the center (r < R), the gravitational field strength is

The total energy of a satellite in circular orbit at radius r from a planet of mass M is

If Earth's mass were doubled but its radius stayed the same, the surface gravitational acceleration would be

A planet has period [math] at orbital radius [math]. Another planet orbits the same star at [math]. Its period [math] is

A geosynchronous satellite orbits Earth with a period of 24 hours. If a satellite has a period of 12 hours, its orbital radius is

According to Newton's law of universal gravitation, if the distance between two masses is doubled, the gravitational force:

For a satellite in a circular orbit of radius r around Earth, the orbital speed is proportional to:

The gravitational potential energy between two masses is:

Kepler's third law states that the square of a planet's orbital period is proportional to:

The escape velocity from the surface of a planet of mass M and radius R is:

The gravitational field strength at the surface of a planet of mass M and radius R is:

A geosynchronous satellite:

If an astronaut moves to a height equal to one Earth radius above the surface, the gravitational force on them becomes:

The total mechanical energy of a satellite in a circular orbit of radius r is:

The gravitational potential (V) at distance r from a mass M is:

A satellite has negative total mechanical energy. This means:

A satellite orbits a planet of mass [math] at radius [math]. The satellite is moved to orbit at radius [math]. The ratio of the new orbital period to the original is

The gravitational potential energy of an object of mass [math] at distance [math] from a planet of mass [math] is [math]. The escape velocity from the surface (radius [math]) is