# Gravitational Forces

1. Jan 15, 2008

### Lyphta

[SOLVED] Gravitational Forces

1. The problem statement, all variables and given/known data
A 1000 kg weather satellite is orbiting the earth at a constant speed. It is 500 km above the earth's surface. The earth has a mass of 5.976 x 10^24 kg and a radius of 6370 km. (a) How much gravitational force exists between the Earth and the satellite? (b) How long does it take the satellite to go around the Earth once? (c) How are is that (measured in meters)? (d) how fast is the satellite moving (in m/sec)?

2. Relevant equations
F=G(m1 m2)/r^2
C=2πr
v=rω

3. The attempt at a solution
(a) F=6.67 x 10^-11 N.m^2/kg^2)((1000kg)(5.976 x 10^24 kg)/6870000 m^2)
= 8445.5 N

(b) I have no idea how to do this one with the numbers that was given... the answer is 94.49 min...

(c) C=2(π)(6870000 m)
= 4.32 x 10^7m

(d) all I know is to do v=rω. But I don't know what to plug in.... the answer is 7617.1 m/sec

Last edited: Jan 15, 2008
2. Jan 15, 2008

### Kurdt

Staff Emeritus
3. Jan 17, 2008

### Lyphta

i know that stuff on the website. the only thing i dont understand is how to apply it to part b and d because i'm not sure of how to convert them into minutes. and without that, i can't figure out how to find the velocity...

4. Jan 17, 2008

### Tom Mattson

Staff Emeritus
I would do part d before doing part b, actually. Since you already know the force acting on the satellite, you can use Newton's second law F=ma. The acceleration a is centripetal accleration, the expression for which is given on the site provided by Kurdt.

Do you see what I mean?

5. Jan 17, 2008

### Lyphta

oh yeah i got it! thanks!