A moon orbits a planet every 42 hours with a mean orbital radius of .002819 AU. The mass of the moon is 8.932 x 1022 kg. Using Newton’s modification to Kepler’s 3rd law, calculate the Mass of the Planet in kg.

The mass of the planet  is

Explanation:

Given that,

Time period = 42 hours = 151200 sec

Orbital radius = 0.002819 AU = 421716397.5 m

Mass of moon

We need to calculate the mass of the planet

Using Kepler’s third law

Where, a = orbital radius

T = time period

G = gravitational constant

M = mass of moon

m = mass of planet

Put the value into the formula

Hence, The mass of the planet  is

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