Ap physics gravitational force on satellites. Any help appreciated

[astru025]

1. Homework Statement


A 450 kg satellite orbits at a distance from the Earth's center of about 6.5 Earth radii. What gravitational force does the Earth exert on the satellite?
2. Homework Equations

Gravitational force= G* ((mMe)/(r^2))

3. The Attempt at a Solution
G times mass times Earth's mass divided by radius squared.
G= 6.67E-11
m= 450 kg
Me(Earth's mass)= 5.98E24
r(radius)= 6.5 x 6370 (Earth's radius)
I inserted this into the equation but came up with the wrong answer it said. I don't know what I'm doing wrong and am getting very frustrated !

 

[Doc Al]

Make sure your distances are in meters.

Even easier would be to use ratios. By what factor is the weight of the object reduced when the distance is multiplied by 6.5?

(Please don't post the same thing twice!)

 

[astru025]

I made sure my distances were in meters and still cannot come up with the answer.

 

[Doc Al]

I made sure my distances were in meters and still cannot come up with the answer.

What answer did you get?

 

[astru025]

I came up with 104964.74.
This is how I came up with that: G (6.67E-11 N*m^2/kg^2) times ((450 kg.) * (5.98E24 kg)) / (1.71E12 m)

I got 1.71E12 m by taking 6.5 times 6.37E6 and squaring that.

 

[Doc Al]

I got 1.71E12 m by taking 6.5 times 6.37E6 and squaring that.

Redo that calculation; you are off by a factor of 1000.

 

[astru025]

Thank you so much. Fixed it and came up with a final answer of 103.75 and it was correct! Thanks so much!

 

[Doc Al]

You are very welcome. :thumbs:

 

[astru025]

I have another problem that is really challenging me and I was going to see if you could tell me what I'm doing wrong.
Problem: A 135 kg satellite experiences a gravitational force by the Earth of 960 N. What is the radius of the satellite's orbit?

I used the equation for gravitational force: F=G * ((m*Me) / (r^2)).
I put 135 in for m. 5.98E24 for Me( the Earth's mass), and for r I put in (x*6.4E6)^2. And I put 960 in for F.
I got an answer of 1.17 and it said it was wrong. And idea why? Thanks so much.
Reply

 

[voko]

One problem - one thread.

 

[Doc Al]

and for r I put in (x*6.4E6)^2

Why would you do that?

 

[astru025]

6.4E6 is Earth's radius and then you square that. I'm not sure why I had that x in there.

 

[Doc Al]

6.4E6 is Earth's radius and then you square that. I'm not sure why I had that x in there.

r is the radius of the orbit; that's what you're solving for. So just leave it as "r" and solve for it.

 

[astru025]

Thank you. I came up with 7489.99 and that was the correct answer!

 

[astru025]

Now how do I find the altitude from this same problem?

 

[Doc Al]

Now how do I find the altitude from this same problem?

Altitude means how far above the earth. Hint: Make use of the Earth's radius.

 

[astru025]

I'm so dumb. I subtract the Earth's radius (6370) from my radius and I got the correct answer! Thanks so much.