The sidereal period of the moon around the Earth is 27.3 days. Suppose a satellite were placed in Earth orbit, halfway between Earth's center and the moon's orbit. Use Kepler's third law to find the period of this satellite. (Just use T2/r3 = constant. No need for Earth's mass or the value of G.) days.

Question

Physics

Madonna

26 May, 03:00

The sidereal period of the moon around the Earth is 27.3 days. Suppose a satellite were placed in Earth orbit, halfway between Earth's center and the moon's orbit. Use Kepler's third law to find the period of this satellite. (Just use T2/r3 = constant. No need for Earth's mass or the value of G.) days.

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Edith Mcbride · Answer 1

Answer: 9.7 days

Explanation:

Applying Kepler's 3rd law, we can write the following proportion:

(Tm) ² / (dem) ³ = (Tsat) ² / (dem/2) ³

(As the satellite is placed in an orbit halfway between Erth's center and the moon's orbit).

Simplifyng common terms, and solving for Tsat, we have:

Tsat = √ ((27.3) ²/8) = 9.7 days