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Which of the following is the gravitational force of attraction between the sun and the earth? (Given the mass of the earth is $6 \times 10^{24} kg$ , the mass of the sun $2 \times 10^{30} kg$ and distance between sun and earth is $1.5 \times 10^{11} m$ also gravitational constant $G = 6.67 \times 10^{- 11} N m^{2} {kg}^{- 2}$ )

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3.6 \times 10^{22} N

36 \times 10^{22} N

0.36 \times 10^{22} N

3.6 \times 10^{10} N

answer is A.

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Detailed Solution

The earth gravitational attraction between sun and earth with the given values is

3.6 \times 10^{22} N

.
As per Newton’s law of gravitation we know that

F = \frac{G m_{1} m_{2}}{r^{2}} . . . . . . . . . . . . (a)

where

G

is the gravitational constant (

6.67 \times 10^{- 11} N m^{2} {kg}^{- 2}

)

m_{1}

is the mass of the first object.

m_{2}

is the mass of the second object .

r

is the distance between them.
Here in this case, below mentioned are the given details.
Mass of earth

m_{1} = 6 \times 10^{24} kg

Mass of sun

m_{2} = 2 \times 10^{30} kg

Distance between the sun and earth

r = 1.5 \times 10^{11} m

Gravitational constant

G = 6.67 \times 10^{- 11} N m^{2} {kg}^{- 2}

Substituting these values in the equation for (a) we get

F = \frac{6.67 \times 10^{- 11} \times 6 \times 10^{24} \times 2 \times 10^{30}}{{(1.5 \times 10^{11})}^{2}}

\Rightarrow F = 3.6 \times 10^{22} N

Thus, the earth gravitational attraction between sun and earth is very large, with the given values it is

3.6 \times 10^{22} N

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