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Answer:
The orbital speed of Dactyl is
Explanation:
The orbital speed can be determined by the combination of the universal law of gravity and Newton's second law:
(1)
Where G is gravitational constant, M is the mass of the asteroid, m is the mass of the moon and r is the distance between them
In the other hand, Newton's second law can be defined as:
(2)
Where m is the mass and a is the acceleration
Then, equation 2 can be replaced in equation 1
(2)
However, a will be the centripetal acceleration since the moon Dactyl describe a circular motion around the asteroid
(3)
(4)
Therefore, v can be isolated from equation 4:
(5)
Finally, the orbital speed can be found from equation 5:
Notice, that it is necessary to express r in units of meters.
⇒
Hence, the orbital speed of Dactyl is