Asteroid Ida was photographed by the Galileo spacecraft in 1993, and the photograph revealed that the asteroid has a small moon, which has been named Dactyl. Assume the mass of Ida is 4.4 x 1016 kg, the mass of Dactyl is 2.6 x 1012 kg, and the distance between the center of Dactyl and Ida is 95 km. G = 6.672x10-11 N-m2/kg2 Part Description Answer Save Status A. Assuming a circular orbit, what would be the orbital speed of Dactyl? (include units with

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

wavelength divides in half and speed stays the same.