Question

when earth and moon are separated by a distance of 3.84×10^8 meters, the magnitude of the gravitational force of attraction between them is 2.0×10^20 newtons. what would be the magnitude of this gravitational force of attraction if earth and moon were separated by a distance of 1 92×10^8 meters?​

Answer 1

The gravitational force would be $8\cdot 10^{20} N$

Explanation:

The magnitude of the gravitational force between two objects is given by

$F=G\frac{m_1 m_2}{r^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

m1, m2 are the masses of the two objects

r is the separation between them

In this case, we can write the gravitational force between the Moon and the Earth as:

$F=G\frac{M m}{r^2}$

where M is the Earth's mass and m is the Moon's mass.

We know that:

$r=3.84\cdot 10^8 m$ is their separation

$F=2.0 \cdot 10^{20}N$ is the force between them

So we can find:

$GMm = Fr^2 = (2.0\cdot 10^{20})(3.84\cdot 10^8)^2=2.95\cdot 10^{37} Nm^2$

Now, we are asked to find the gravitational force when the Earth and the Moon are separated by

$r'=1.92\cdot 10^8 m$

In this case the new force would be

$F'=G\frac{M m}{r'^2}$

And substituting the values of (GMm) found previously and r', we find

$F'=\frac{2.95\cdot 10^{37}}{(1.92\cdot 10^8)^2}=8\cdot 10^{20} N$

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