# Gravitational fields

1. Dec 9, 2013

### Coco12

1. The problem statement, all variables and given/known data

What is the centripetal acceleration of a satellite orbiting Saturn at the location exactly one Saturn radius above the surface of Saturn

2. Relevant equations
Ac=v^2/r
In the previous question found out that the fg at that location is 1/4 of 36.0 N

3. The attempt at a solution
I read somewhere that they made centripetal acceleration equal to Gm/4pi ^2

But why?? How are those two linked?

2. Dec 9, 2013

### rude man

I would not lend much credulity to what you read. The dimensions of Gm/4pi^2 are not the dimensions of acceleration.

Equate gravitational acceleration to centripetal acceleration.

3. Dec 9, 2013

### Coco12

The answer is the same as the gravitational intensity which is 2.60N . How does that work??

4. Dec 9, 2013

### rude man

Not too well. Acceleration is not measured in Newtons either ...

5. Dec 9, 2013

### Coco12

Then how do u do this question?

6. Dec 9, 2013

### rude man

I have two masses m1 and m2. What is the (gravitational) force of m1 on m2 (or m2 on m1)?

Picking the force on m2, then use F = ma on m2. Your answer is a. What is gravitational F?

7. Dec 9, 2013

### Coco12

The mass being saturn's mass?

8. Dec 9, 2013

### zahbaz

Well, you have two masses to consider, the satellite's mass and Saturn's mass. After you make some cancellations in your equations, you may not need both values, though.

Anyway, if this satellite is in orbit, it's experiencing a centripetal force. The real question: what force IS PROVIDING this centripetal force? What's the equation for this force that rude man is getting at? Equate this to your centripetal.

9. Dec 9, 2013

### Coco12

Mv^2/r=gm1m2/r^2???

10. Dec 9, 2013

### rude man

How come three different masses?

11. Dec 9, 2013

### Coco12

Oh no, the m in the first equation is the same as m1 in the equation after the equal sign.

So when cancelled would be: v^2/r=Gm/ r^2?

Last edited: Dec 9, 2013
12. Dec 9, 2013

### rude man

Looking better.
So which is your m? The planet or the satellite? And what is r?

13. Dec 9, 2013

### Coco12

Mass would be the mass of Saturn and radius would be the radius of Saturn *2? The thing is , all of this info is not given in the problem, so how are we supposed to know it?

14. Dec 9, 2013

### rude man

Yes.

Take a trip to Saturn? Dunno, but you need both the mass and the radius of Saturn.

15. Dec 9, 2013

### Coco12

i will try it out and see whether I can it.

16. Dec 10, 2013

### Coco12

I tried it out and did not get the answer. Could it be any way that the gravitational field intensity is equal to the centripetal acceleration, since in the book, the answer to both is the same

17. Dec 10, 2013

### zahbaz

What's the book's answer? I was anticipating the reasoning you said you followed.

Below I pulled Saturn's mass and radius from Google, thought if it's a book problem, I'm sure your text has similar values printed inside.

mv^2/r = GmM/r^2
v^2/r = GM/r^2
where M = mass of saturn = 568.3 x 10^24 kg
r = two saturn radii = 2(58,232,000 m)
a = GM/r^2
a = 2.79 m/s^2

18. Dec 10, 2013

### Coco12

The answer is 2.60 m/s^2 which is the same as the gravitational intensity

19. Dec 10, 2013

### zahbaz

What is this gravitational intensity you keep bringing up?

PS... I edited my post in the time you replied. I had made a calc error. I got a = 2.79 m/s^2, which is pretty close to 2.60m/s^2. I'm wondering if your book has different, perhaps rounded values for Saturn's mass and radius.

20. Dec 10, 2013

### Coco12

This was a two part question. In the first it asked for gravitational intensity.