# Universal Gravity Question

1. Sep 30, 2007

### kasiu

1. The mass of a robot is 5370 kg. This robot weighs 3520 N more on planet A than it does on planet B. Both planets have the same radius of 1.33 x 10^7 m. What is the difference MA - MB in the masses of these planets?

2. attached picture

3. I was wondering what to do with the 3520 N. Do I find a ratio of weight between the planets and then multiply the original weight by that ratio? Do I need to use (G*mass/radius^2)? I'd appreciate some pointers or hints. I don't need the solution, just help with setting up the equation and understanding what I am looking for.

#### Attached Files:

• ###### physics.JPG
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2. Sep 30, 2007

### dynamicsolo

I'd say a comparison ratio for the weight of the robot on the two different planets would be a better place to start.

Last edited: Sep 30, 2007
3. Sep 30, 2007

### kasiu

So,
would I set it up like this:

W_subB + 3520 N = M * (g_subB)
Or
M * (g_subA) = W_subB +3520 N
So, would I solve for the acceleration of planet A to get g_subA and then use 5370 Kg for my M (mass) and solve for W_subB

4. Sep 30, 2007

### dynamicsolo

Yeah, I'm going to take back what I said: because of the types of information provided, a comparison ratio won't really help. Write out both weights in terms of the appropriate Mg in one of those equations. Insert the appropriate expressions for g on each planet. You will now be able to factor your equation, with one of the terms being the difference between the planetary masses, which you can solve from there. (I thought initially that the problem set-up would be nicer...)

5. Sep 30, 2007

### kasiu

How would I find weight?
Would I use the equation attached?

6. Sep 30, 2007

### kasiu

so:
(5370*acceleration due to gravity) + 3520 N = 5370 * gravity....
that's not right I can see, but how do I find the weight.
I can't solve for acceleration because I don't have the weight of the planet.....
I feel confused :(

7. Sep 30, 2007

### dynamicsolo

Your attachment still hasn't been cleared yet. You have

M * (g_subA) = W_subB +3520 N , so replace W_subB also:

M * (g_subA) = M * (g_subA) +3520 N .

How do you find g on each planet? (You mentioned this in your earlier post.) If you put that in for g_subA and g_subB, what do you get?

8. Sep 30, 2007

### kasiu

I know that the equation has to equal (mass of planet A)-(mass of planet B)

9. Sep 30, 2007

### kasiu

do i get the acceleration?

10. Sep 30, 2007

### kasiu

G(Ma)(m)/d^2 - G(Mb)(m)/d^2= N* r^2/Gm

Would I use that

11. Sep 30, 2007

### dynamicsolo

It won't be equal to it, it will let you solve for that.

How do you find the gravitational acceleration at the surface of a planet? (Have you already written this?)

12. Sep 30, 2007

### kasiu

so acceleration= F/m
or
a=g=6.67e-11* mass/distance^2

13. Sep 30, 2007

### kasiu

ooooooh!
I get it so,

Ma-Mb =N* r^2/Gm
So, what I posted before was right :)
thank you so much!!!

I understand it now!
:):):)
wow, that took me a while
finally my brain made some connections
thanks once again!!

14. Sep 30, 2007

### dynamicsolo

The distance in this application is the distance from the surface of the planet to its center, that is, the planet's radius. (Why that is so is due to a theorem of Newton's you may have discussed by now...)

You can save a little writing and use the universal gravitation constant G, instead of writing 6.67e-11, for now.

So you can now use that, for each planet, in this equation:

M * (g_subA) = M * (g_subA) +3520 N .

15. Sep 30, 2007

### dynamicsolo

Provisionally glad to hear it! The equation should be Ma-Mb = (3520 Newtons) * r^2/Gm , m being the robot's mass. (I wasn't sure what your N was supposed to be -- that's the force unit, not a value itself.) So you do need all the info in the problem... You'll get a pretty big number (in kg).