Planet and speff problem find mass

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To find the mass of planet X, the gravitational force equations are utilized, specifically F = G·m1·m2/r². Spaceman Speff's weight at the planet's surface is 389N, and at a height of 1.86*10^4 km, it is 24.31N. Two equations are established using these weights to solve for the mass of the planet, with Speff's mass given as 75 kg. The calculated mass of planet X is 2.96*10^24 kg. This approach effectively applies gravitational principles to determine planetary mass based on weight changes at different distances.
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Homework Statement


The weigh tof spaceman speff, soley due to the gravitational pull of planet x at its surface is 389N. If he moves to a distance of 1.86*10^4km above the planets surface his weight changes to 24.31N. What is the mass of planet xif speffs mass is 75 kg.


Homework Equations



f=ma
f=gm1+m2/r^2

The Attempt at a Solution


i know the answers is 2.96*10^24 kg. nut idk how to get it
 
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I would double check your second equation.
 
it m1*m2
 
what else?? I am still not getting it
 
Use the F=G·m1·m2/r2 equation, and plug in the given information. There are two sets of information, so you would get two equations:

(1) 389 N = G · __ · __ / __
(2) Use the other weight given in the problem to set up the second equation
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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