How Does Gravitational Force Vary Between Two Planets with Identical Radii?

[pinky2468]

Another question! Gravitaional Force ?

I know this is easy, but for some reason I am getting stuck!
The mass of a robot is 5450kg. This robot weighs 3620N more on Planet A than on Planet B. Both planets have a radius of 1.33^7. What is the difference Ma-Mb in the masses of these planets.
I think that I need to set the gravitaional force on A(minus 3620) equal to gravitaional force on B. I know the G and the r's are the same. I am confused on how to put it into the formula and figure out what I am looking for?

 

[arildno]

Hint:
Let the weight of planet A be given by $$W_{A}$$, while the mass of planet A by $$m_{A}$$ (similarly for planet B; mass of robot:$$m_{R}$$
We then have, for example:
$$W_{B}=\frac{Gm_{B}m_{R}}{r^{2}}$$
which you may rewrite as:
$$m_{B}=\frac{r^{2}}{Gm_{R}}W_{B}$$

 

[pinky2468]

I see where you are going, but what are you using for W of planet A or B. We only know the weight and mass of the robot. Are you saying to do each planet separately and then subtract the answers?

 

[arildno]

You do know the weight difference, don't you?

 

[arildno]

Oh, I'm sorry, I just saw my mistake:
I meant "Weight of robot on planet A" and so on..
Shame on me..