An OSU-branded squishy moon ball has a mass of 25 g and a diameter of 60 mm. Consider two squishy moons located in deep space far from the Sun or any other massive body. The two squishy moons form a binary system with their centers separated by 0.5 meters, and they are in circular orbits around their common center of mass. a. Draw a sketch of the squishy moon system and correctly label the dimensions and orbits. b. What is the orbital period of the two squishy moons about their center of mass? c. What is their orbital speed?
An OSU-branded squishy moon ball has a mass of 25 g and a diameter of 60 mm. Consider two squishy moons located in deep space far from the Sun or any other massive body. The two squishy moons form a binary system with their centers separated by 0.5 meters, and they are in circular orbits around their common center of mass. a. Draw a sketch of the squishy moon system and correctly label the dimensions and orbits. b. What is the orbital period of the two squishy moons about their center of mass? c. What is their orbital speed?
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An OSU-branded squishy moon ball has a mass of 25 g and a diameter of 60 mm. Consider two squishy moons
located in deep space far from the Sun or any other massive body. The two squishy moons form a binary system
with their centers separated by 0.5 meters, and they are in circular orbits around their common center of mass.
a. Draw a sketch of the squishy moon system and correctly label the dimensions and orbits.
b.
What is the orbital period of the two squishy moons about their center of mass?
c.
What is their orbital speed?
d.
If the squishy moon binary system is 5au from the Sun, what is the Hill radius of the system in the tidal field
of the Sun? Compare the Hill radius to the semi-major axis of the squishy moon binary orbit radius and
comment on whether this binary squishy moon system is stable when it is 5au from the Sun.
e. Follow-up your answer to part d and estimate the distance from the Sun where the squishy moons in this
binary system are exactly twice their Hill radius apart. Express your answer in au and comment on what
would happen if the binary squishy moons were to get closer to the Sun than this distance.
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