Solve Gravity Fun: Exploring Earth, Moon & Sun

[smashingtime]

[SOLVED] gravity fun

Homework Statement

1. Calculate the speed of objects on the Earth's surface caused by the Earth's own rotation around its own axis.

2. Find the mass of the Earth using its time period of revolution of the moon around the earth.

3. Find the mass of the sun using the time period of the Earth around the sun.

4. What is the radius for a geo-synchronous satellite?

Homework Equations

The time period of revolution of the moon around the Earth is 28 days?

The Attempt at a Solution

1. v= 2piR/T = 2pi (6.4E6) / (24hours*60min*60s) = 4.65E2

2. I know how to solve this using F = GmM/(R^2) = mg but I don't know how to use the given 28 days. The answer to this problem should be around 6E24 kg

3. The answer is around 2E31 kg

4.

Thanks in advance!

 

[G01]

HINT: What type of motion is the moon in?

 

[smashingtime]

oooh circular motion? I tried using V = 2piR/T, but I can't get to the right answer. What value would I use for R?

 

[smashingtime]

Anyone? ):

 

[Dick]

oooh circular motion? I tried using V = 2piR/T, but I can't get to the right answer. What value would I use for R?

Maybe R should be the radius of the moon's orbit? You are working on 2), right?

 

[alphysicist]

Hi smashingtime,

2. I know how to solve this using F = GmM/(R^2) = mg but I don't know how to use the given 28 days. The answer to this problem should be around 6E24 kg

[/b]

This should be F = GmM/(R^2) = ma. (g is the gravitational acceleration at the Earth's surface.) Once you have a in your equation, since it is circular motion, you have a formula for the acceleration in terms of speeds and orbital radius.

You will still need to use your relation V = 2piR/T to get the period into the equation, and I think you will need either the orbital radius of the moon or the orbital speed of the moon.

 

[smashingtime]

The radius of the moon's orbit is 3.84 * 10^8 m. (I just googled it haha).
I plugged that into v = 2piR/ T to find v, then used v^2 = Gm/R to find the mass, but my answers still don't match up :/

 

[Dick]

What did you get for a number on v and m? That should have worked.

 

[smashingtime]

v = 2piR/T
= 2pi(3.84E8)/(28*60^60)
=2.41 E 4

v^2 = 5.82E8 = Gm/R
5.82E8 = (6.67E-11)(m)/(3.84E8)
m = 3.35 E27 kg
What the answer is supposed to be: m = 5.98 E24 kg

 

[Dick]

Well, there you go. 28*60*60sec is 28 hours. 28 days is 28*24*60*60sec. Oh, try to put units on everything, ok?

 

[smashingtime]

ahaha *smacks forehead*
thanks so much!

 

[smashingtime]

I just worked out (3.) using the same method.
I found the distance between the Earth and the sun to be 1.5E11m.

v=2piR/T
= 2pi (1.5 E 11) / (365*24*60*60)
= 2.99 E 4
V^2 = 8.95 E 8 = Gm/R
8.95 E 8 = (6.67E-11)(m) / (1.5E11)
m = 2 E 30 kg
Established answer: m = 2 E 31 kg

 

[smashingtime]

oh nvm.
yay, the established answer IS 2E30 kg.