Question

Think about this hypothetical (not real) situation: Astronaut Dustin and Astronaut Barb are floating in space. The force of gravity between Astronaut Dustin and Planet Demi
120,265 Newtons. The force of gravity between Astronaut Barb and Planet Demi is 354,999 Newtons. What can you infer about the relative DISTANCE of each astronaut
from planet Demi? Explain your answer. ​

Answer 1

The distance between Dustin and the planet is larger than the distance between Barb and the planet

Explanation:

The magnitude of the gravitational force between each astronaut and the planet is given by

$F=G\frac{Mm}{r^2}$

where :

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

M is the mass of the planet

m is the mass of the astronaut

r is the separation between the astronaut and the planet

In this problem, we have:

• The force of gravity between Dustin and the planet is 120,265 N
• The force of gravity between Barb and the planet is 354,999 N

We see that the force exerted by the Planet on Barb is much greater than the force exerted by the planet on Dustin. Assuming that the mass of Dustin and Barb is similar, then we can say that the magnitude of the force of gravity depends mainly on the distance:

$F=\frac{1}{r^2}$

And since the force is inversely proportional to the square of the distance, this means that the distance between Dustin and the planet is larger than the distance between Barb and the planet.

Learn more about gravitational force:

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Answer 2

The magnitude of the gravitational force between each astronaut and the planet is given by

where :

is the gravitational constant

M is the mass of the planet

m is the mass of the astronaut

r is the separation between the astronaut and the planet

In this problem, we have:

The force of gravity between Dustin and the planet is 120,265 N

The force of gravity between Barb and the planet is 354,999 N

We see that the force exerted by the Planet on Barb is much greater than the force exerted by the planet on Dustin. Assuming that the mass of Dustin and Barb is similar, then we can say that the magnitude of the force of gravity depends mainly on the distance:

And since the force is inversely proportional to the square of the distance, this means that the distance between Dustin and the planet is larger than the distance between Barb and the planet.