# Worksheet: Gravitational Potential Energy in Radial Gravitational Fields

In this worksheet, we will practice calculating the kinetic energy, gravitational potential energy, and total energy of objects with orbital trajectories.

Q1:

Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital speed. The mass of the galaxy is equivalent to a single mass that is times that of the Sun’s mass, which is kg, located at a distance of 30,000 ly from the Sun.

• A m/s
• B m/s
• C m/s
• D m/s
• E m/s

Q2:

There are two planets in orbit around a star. Both planets have circular orbits. Planet has a speed of , and Planet has a speed of . (Give your answers to these questions as a decimal if necessary.)

What is the ratio of the orbital radii of the two planets, ?

What is the ratio of the orbital periods of the two planets, ?

Q3:

The asteroid Vesta has a mass of kg and a radius of 520 km. What would be the orbital period for a space probe in a circular orbit of 10.0 km from Vesta’s surface?

• A s
• B s
• C s
• D s
• E s

Q4:

A small satellite is placed in a circular orbit around a nearby asteroid. The orbital period of the satellite is 10,900 seconds and the orbital radius is km. What is the mass of the asteroid?

• A kg
• B kg
• C kg
• D kg
• E kg

Q5:

What is the gravitational potential energy between two spheres, each of mass 9.5 kg, separated by a center-to-center distance of 20.0 cm?

• A J
• B J
• C J
• D J
• E J