Finding the mass of two planets

In summary, the conversation discusses a problem involving the mass and weight of a robot on two different planets with the same radius. The task is to find the difference in mass between the two planets using the definition of weight and an equation involving gravitational force. The conversation also mentions the use of submissions for the question.
  • #1
prlion16
3
0
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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  • #2
Use the defintion of weight. Assume that it's evaluated at the surface of the planets.
 
  • #3
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.
 
  • #4
You are provided with the difference in weight (of the robot), right?
 
  • #5
For planet B it is 5720a and Planet A is 5720a+3720. right?
 
  • #6
WA - WB = Gm(MA-MB)/d2
 

1. What is the formula for finding the mass of two planets?

The formula for finding the mass of two planets is M = (4π²a³)/(G(T²)), where M is the combined mass of the two planets, a is the distance between the two planets, G is the gravitational constant, and T is the time it takes for the two planets to orbit each other.

2. How is the mass of a planet determined?

The mass of a planet can be determined by observing the orbital motion of objects around the planet and using Newton's law of gravitation. Alternatively, the mass can also be calculated by measuring the planet's gravitational pull on nearby objects and using the equation F = (GMm)/r², where F is the force of gravity, G is the gravitational constant, M is the mass of the planet, m is the mass of the object, and r is the distance between the planet and the object.

3. Can the mass of a planet change over time?

Yes, the mass of a planet can change over time due to factors such as accretion of material from space, loss of atmosphere, or collisions with other objects. However, these changes are usually very gradual and do not significantly affect the overall mass of the planet.

4. How accurate are calculations of the mass of two planets?

The accuracy of calculations of the mass of two planets can vary depending on the quality and quantity of available data, as well as the complexity of the system. In general, the calculations are quite accurate, but there may be some margin of error due to uncertainties in measurements or incomplete understanding of the system.

5. Can the mass of two planets be determined if only one planet is known?

Yes, the mass of two planets can be determined if only one planet is known. This can be done by observing the orbital motion of other objects around the known planet and using the laws of gravitation to calculate the mass of the unknown planet. However, the accuracy of this calculation may be lower compared to when both planets are directly observed and measured.

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