How far is it to the center of the earth

Asked by maham237 @ 03/01/2021 in Physics viewed by 295 People

(a) How far is the center of mass of the Earth-Moon system from the center of the Earth? (Appendix C gives the masses of the Earth and the Moon and the distance between the two.) m
(b) Express the answer to (a) as a fraction of the Earth's radius.'

Answered by maham237 @ 03/01/2021

Answer:

a) $r_{cm} = 4672 km$

b)r_cm = 0.733 R_{earth}

Explanation:

Location of center of mass of Earth- moon system is

$r_{cm}= \frac{M_{earth}r_{earth}+M_{moon}r_{moon}}{M_{moon}+M{earth}}$

$r_{cm}= \frac{6\times10^{24}(0)+7.34\times10^{22}384000\times1000}{6\times10^{24}+7.34\times10^{22}}$

=4.672×10^(6) m

a) $r_{cm} = 4672 km$

b) $\frac{r_{cm}}{R{earth}} = \frac{4672}{6371} = 0.733$

therefore

r_cm = 0.733 R_{earth}

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