HW Question, very simple. mass/gravity

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If a planet is half the size of Earth but has the same gravitational pull, its mass must be four times greater than that of Earth. This conclusion stems from the relationship between mass, radius, and gravity, where the gravitational force is proportional to mass and inversely proportional to the square of the radius. Therefore, if the radius is halved, the mass must increase by a factor of four to maintain the same gravitational acceleration. The discussion clarifies the mathematical relationship underlying these concepts. Understanding this relationship is crucial for grasping how mass and gravity interact in planetary bodies.
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If a planet is 1/2 of earth, gravitational is the same of earth, what does that tell you about the mass?
 
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ek378996 said:
If a planet is 1/2 of earth

half the size?

anyhow...What is mass affected by?
 
yes, half the size. Nothing, just trying to find out if the mass of the planets is 2 or 4 times larger/smaller than earth.

basically if a planet is half the size of the earth, and gravitation is the same as earth, what would the planets mass have to be? 2 or 4 times larger than earth?
 
Last edited:
Greetings:

If acceleration due to gravity is equal for both the Earth and another planet, then,

Gme / re2 = Gmp / rp2.
==> me = (re / rp)2 mp
==> me = (2rp / rp)2 (given re = 2rp)
==> me = 4mp

Regards,

Rich B.
rmath4u2@aol.com
 

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