# Calculating the mass of the Earth

## Homework Statement

The distance between the centres’ of the Earth and Moon is estimated to be 3.84x10^8 m. If the lunar month is 27.3 days, calculate the approximate mass of the Earth. (Assume the gravitational constant G=6.67x10^-11 Nm2 kg-2)

## Homework Equations

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T = 2pi / sqroot(G * Mearth) * r^3/2

## The Attempt at a Solution

27.3 = 6.283 / sqroot(6.67x10^-11 * Mearth) * 3.84x10^3/2
27.3 * sqroot(Mearth) = (6.283 / 8.14 x10^-6) * 7.525x10^12
27.3 * sqroot(Mearth) = 771867.3 * 7.525x10^12
27.3 * sqroot(Mearth) = 5.81x10^18
sqroot(Mearth) = 5,81x10^18 / 27.3
sqroot(Mearth) = 2.13x10^17
Mearth = 4.53x10^34

Lunar Month / Earth Month = 30.4/27.3 = 1.114

Mass Earth = 4.53x10^34 * 1.114 = 5.04x10^34 kg

This is far too large a nuber for the mass of the earth, considering that it is in the region of Nx10^24 kg,
What am i doing wrong?

## Answers and Replies

Bandersnatch
Science Advisor
Hi ccapani

You did not convert time units of the lunar month to conform with the SI units in which G is expressed.

Lunar Month / Earth Month = 30.4/27.3 = 1.114
This bit is irrelevant and shouldn't be included in the solution.

lightgrav
Homework Helper
the Orbit Time using the center-to-center distance results in the TOTAL mass of the 2 objects.
Earth's Mass is about 81x Moon's mass, so (instead of multiplying by 1.114, that relates to orbit around the Sun)
you should make your answer "specific to Earth" : multiply it by 81/82 (=0.988)