Question

the mass of moon is 1/64 times that of earth is 1/64 times that of sun find the ratio of gravitational force bw Earth & moon & Earth &sun if distance new earth &moon is same as distance between Earth &sun
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Answer 1

The ratio of the gravitational force between Earth & moon and Earth & sun is 1:4096

Step-by-step Explanation:

Given: mass of the earth = 1/64 times the mass of the sun

mass of the moon = 1/64 times the mass of the earth

distance between moon & earth = distance between earth & sun

To Find: The ratio of the gravitational force between Earth & moon and Earth & sun

Solution:

• Finding the ratio of the gravitational force between Earth & moon and Earth & sun

Let the mass of the sun is $m_s$ such that the mass of the earth is $m_e = m_s/64$ and the mass of the moon is $m_m = m_e/64 = m_s/(64)^2$

Therefore, the gravitational force between earth & moon is,

$F_{EM} = G \frac{m_e m_m}{r^2} = G \frac{m_s^2 / (64)^3}{r^2} = G \frac{m_s^2}{(64)^3 r^2} \ \cdots \cdots (1)$

And, the gravitational force between earth & sun is,

$F_{ES} = G \frac{m_e m_s}{r^2} = G \frac{m_s^2 / 64}{r^2} = G \frac{m_s^2}{64 r^2} \ \cdots \cdots (2)$

Dividing (1) by (2), we get,

$\frac{F_{EM}}{F_{ES}} = \frac{Gm_s^2}{(64)^3 r^2} \times \frac{64 r^2}{Gm_s^2} = \frac{1}{(64)^2} = \frac{1}{4096}$

$\Rightarrow F_{EM} : F_{ES} = 1 : 4096$

Hence, the ratio of the gravitational force between Earth & moon and Earth & sun is 1:4096