- #1

BitterSuites

- 38

- 0

**[SOLVED] Gravitation Force Using Differentials**

## Homework Statement

Three part question:

1. Consider a solar system similar to our Sun and Earth, where the mass and radius of the planet are 4.22e24 kg and 6.63e6 m, respectively, the mass of the sun is 2.08e30 kg and the planet-sun distance is 1.423e11 m.

Find the magnitude of the change in F in gravitational force that the Sun exerts on a 50.1kg woman standing on the equator at noon and midnight. Assume the Sun and the planet are the only masses acting on the woman. Since change in r is so small, use differentials. Answer in units of N.

2. Find the magnitude of the factional percent change theta F/F % in the Sun's gravitational force on the woman due to the rotation of the Earth in the 12 hours between noon and midnight. Assume the SUn and the Earth are the only masses acting on the woman. Answer in units of %.

3. If the moon orbiting the planet has mass 7.26e22 kg and the planet-moon distance is 3.71e8 m, find the magnitude of the fractional percent change in the moon's gravitational force on the woman due to the rotation of the Earth in the 12 hours between noon and midnight. Assume the Earth and the Moon are the only masses acting on the woman. Answer in units of %.

## Homework Equations

Force of the sun on the woman at noon - Force of the sun on the woman at midnight.

## The Attempt at a Solution

F of the sun on the woman at noon = Gm1m2/r^2 = ((6.67 x 10^-11)(50.1)(2.08 x 10^30))/(1.423 x 10^11)^2 = .343255

F of the sun on the woman at midnight = Gm1m2/r^2

Since the woman is now 6.63 x 10^6 m further away from the sun, the new r is 1.4230663 x 10^11

So F = ((6.67 x 10^-11)(50.1)(2.08 x 10^30))/(1.4230663 x 10^11)^2 = .343223

So the difference is .343255 - .343223 = .000032 N

However, this answer is incorrect.

Question 2 will simply be the change in force divided by the force, but I can't answer until I figure out #1. Question 3 should just be repeating the same process used for #1 and #2.

What is the flaw in my thinking? Any help is appreciated.