Respuesta :
Answer:
[tex]F_{resultant} = 2.373\times 10^{20}\ N[/tex]
Solution:
As per the question:
We know that:
Mass of the moon, [tex]M_{m} = 7.36\times 10^{22}\ kg[/tex]
Mass of the Earth, [tex]M_{e} = 5.98\times 10^{24}\ kg[/tex]
Mass of the sun, [tex]M_{s} = 1.99\times 10^{30}\ kg[/tex]
Mean distance between the Earth and the sun, R = [tex]1.5\times 10^{11}\ m[/tex]
Mean distance between the Earth and the moon, R' = [tex]3.84\times 10^{8}\ m[/tex]
Now,
We know that the gravitational force is given by:
[tex]F = \frac{GMm}{r^{2}}[/tex]
Thus
Gravitational force between the Earth and the Moon:
[tex]F_{em} = \frac{6.67\times 10^{- 11}\times 5.98\times 10^{30}\times 7.36\times 10^{22}}{(3.84\times 10^{8})^{2}}[/tex]
[tex]F_{em} = 1.9908\times 10^{20}\ N[/tex]
The above force is towards the earth:
The force of gravitation between the sun and moon:
[tex]F_{sm} = \frac{6.67\times 10^{- 11}\times 1.99\times 10^{30}\times 7.36\times 10^{22}}{(1.5\times 10^{11} - 3.84\times 10^{8})^{2}}[/tex]
[tex]F_{sm} = 4.364\times 10^{20}\ N[/tex]
Thus net force is given by:
[tex]F_{resultant} = F_{sm} - F_{em} = 4.364\times 10^{20} - 1.9908\times 10^{20} = 2.373\times 10^{20}\ N[/tex]
The resultant force is directed towards the sun.
