Gravitational Force on different planets

[BlackMamba]

I thought I did this problem correctly but when I submit my answer it says other wise.

Here is the problem: The mass of a robot is 5440kg. This robot weighs 3610N more on planet A than it does on planet B. Both planets have the same radius of $$1.33 * 10^7m$$. What is the difference $$M_{A} - M_{B}$$ in the masses of these planets?

And I my answer must be in kg.

So I know to use:

$$W = G \frac{M_{E}m}{r^2}$$

My answer for the mass on planet B was 12272.1 and for planet A was 13103.1. But when subtracting A - B my answer is wrong.

What am I doing wrong?

Thanks in advance for any help provided.

 

[tony873004]

My answer for the mass on planet B was 12272.1 and for planet A was 13103.1.

This doesn't make sense. The mass will be the same on both planets. It's the force or Newtons, or pounds that will change from planet to planet.

Just my guess...
It looks like a simultaneous equation problem.

weight of robot on planet A:

$$W_{a} = G \frac{M_{a} M_{robot}}{r^2}$$

weight of robot on planet B:
$$W_{b} = G \frac{M_{b} M_{robot}}{r^2}$$

Since the robot weighs 3610N less on planet B than on planet A:
$$W_{b} = W_{a}-3610$$

so...

$$G \frac{M_{a} M_{robot}}{r^2} = G \frac{M_{b} M_{robot}}{r^2} - 3610$$

G is known, mass of robot is known, radius is known.
Now solve for Mass of planet A and Mass of planet B.

 

[M98Ranger]

It seems like you have correctly used the equation for calculating the weight of an object on different planets. However, the problem is asking for the difference in the masses of the two planets, not the weight of the robot on each planet.

To find the difference in masses, you need to rearrange the equation to solve for the mass of each planet. This can be done by dividing both sides of the equation by G and multiplying by r^2:

M_{E} = \frac{W r^2}{G m}

Once you have the mass of each planet, you can subtract them to find the difference in mass:

M_{A} - M_{B} = \frac{W_{A} r^2}{G m} - \frac{W_{B} r^2}{G m}

Plugging in the given values, you should get a difference of approximately 2.5 * 10^24 kg.

Remember that the mass of an object is constant, but its weight can change depending on the gravitational force of the planet it is on. So, while the robot may weigh more on planet A, its mass remains the same on both planets.

I hope this helps clarify the problem and your solution. Keep in mind to always double check the units and what the problem is asking for. Good luck!