Finding the mass of two planets

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The discussion revolves around calculating the mass difference between two planets based on the weight of a robot on each planet. The robot's mass is 5720 kg, and it weighs 3720 N more on planet A than on planet B. The radius of both planets is given as 1.33x10^7 m. The participants are struggling with applying the gravitational force formula and setting up the system of equations needed to find the mass difference. The key points include understanding the relationship between weight, mass, and gravitational force at the surface of the planets.
prlion16
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Ok well, I have used up 2 out of 3 of my submissions for this question. I have tried to do a system of equations and failed twice. I really don't even know where to start so I was hoping that you guys could help me.
The problem is.
The mass of a robot is 5720 kg. This robot weighs 3720 N more on planet A than it does on planet B. Both planets have the same radius of 1.33x10^7 m. What is the difference MA - MB in the masses of these planets?

Thank you.
 
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Use the defintion of weight. Assume that it's evaluated at the surface of the planets.
 
ok... I still don't get what I am supposed to do. Sorry. I get that weight is going to be calculated at the surface of the planets so d=1.33x10^7. I got the equation F=6.67x10^-11(5720m1/((1.33x10^7)^2)). I really just don't get what I am supposed to do after this.
 
You are provided with the difference in weight (of the robot), right?
 
For planet B it is 5720a and Planet A is 5720a+3720. right?
 
WA - WB = Gm(MA-MB)/d2
 

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