What is the period of a satellite orbiting around the earth in a radius which is one half that of the distance from the earth to the moon?

The satellite has a period of 204.90 days

Explanation:

The period can be determine by means of Kepler's third law:

 (1)

Where T is the period of revolution and r is the radius.

(2)

The distance between the moon and the Earth has a value of 384400 km, therefore:

Finally, equation 2 can be used:

However, the period can be expressed in days, to do that it is necessary to make the conversion from kilometers to astronomical units:

An astronomical unit (AU) is the distance between the Earth and the Sun ()

⇒

But 1 year is equivalent to 1 AU according to Kepler's third law, since 1 year is the orbital period of the Earth.

⇒

⇒

Hence, the satellite has a period of 204.90 days.