Answer to Question #106051 in Classical Mechanics for Jose Madrigal

Question

1. The Earth is 8 light minutes from the sun and the speed of light is 3×10^8 m.s^−1. 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.

Format: if your answer is 2×10^3 N, enter 2*10^3 (and do think about significant figures).

Answer 1

The gravitation force

$$F=G\frac{mM}{r^2},$$

$$F=6.67\times 10^{-11}\frac{5.972\times 10^{24}\times 1.989\times 10^{30}}{(3\times 10^8\times 8\times 60)^2}$$

$$F=3.82\times 10^{22}\:\rm N.$$