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In this lesson, we will learn how to calculate the kinetic energy, gravitational potential energy, and total energy of objects with orbital trajectories.

Q1:

Assuming a circular orbit for the Sun about the centre of the Milky Way Galaxy, calculate its orbital speed. The mass of the galaxy is equivalent to a single mass that is 1 . 5 × 1 0 1 1 times that of the Sun’s mass, which is 2 . 0 × 1 0 3 0 kg, located at a distance of 3 0 0 0 0 ly from the Sun.

Q2:

There are two planets in orbit around a star. Both planets have circular orbits. Planet 𝐴 has a speed of 𝑣 , and Planet 𝐵 has a speed of 2 𝑣 . (Give your answers to these questions as a decimal if necessary.)

What is the ratio of the orbital radii of the two planets, 𝑟 𝑟 𝐵 𝐴 ?

What is the ratio of the orbital periods of the two planets, 𝑇 𝑇 𝐵 𝐴 ?

Q3:

A small satellite is placed in a circular orbit around a nearby asteroid. The orbital period of the satellite is 1 0 9 0 0 seconds and the orbital radius is 2 . 0 0 0 0 × 1 0 3 km. What is the mass of the asteroid?

Q4:

The asteroid Vesta has a mass of 2 . 6 7 × 1 0 2 0 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?

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?

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