Answer to Question #104301 in Classical Mechanics for Joseph Se

Question

1. The Earth is 8 light minutes from the sun and the speed of light is 3 × 10^8 m/s. Let's assume that earth's orbit is exactly circular. Its mass is 5.972 × 10^24 kg.

Using the values given above (and your knowledge about time units), determine the magnitude of the gravitational force that the Sun exerts on the Earth.

The magnitude of the force is _____ newtons.

2. How does the force that the Sun exerts on the Earth compare with the Earth's force on the sun?

A. The magnitude of the force the earth exerts on the sun equals that of the force that the sun exerts on the earth.
B. The magnitude of the force the earth exerts on the sun exceeds that of the force that the sun exerts on the earth.
C. The magnitude of the force the earth exerts on the sun is less than that of the force that the sun exerts on the earth.

Answer 1

As per the given data in the question,

The distance between the earth and the sun is =8 light minute

Speed of light =$3\times 10^8m/sec$

So, the distance between the earth and the sun =$3\times 10^8\times8\times60\times60 m$

$=86400\times 10^8 m$

Mass of the earth = $5.972 × 10^{24} Kg$

As we know that mass of the sun $=1.989 × 10^{30} Kg$

Where G is the gravitational constant $G=6.67\times 10^{-7}$

Hence the required force $F=\dfrac{GmM}{d^2}$

$\Rightarrow F=\dfrac{6.67\times10^{-11}\times5.972\times6.67\times10^{30}\times 10^{24}}{(86400\times10^8)^2}N$

$\Rightarrow F=\dfrac{265.687\times 10^{43}}{746496\times10^{20}}N$

$\Rightarrow F=0.0003559\times 10^{23}N$

$\Rightarrow F=3.56\times 10^{19}N$