- #1
prace
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Problem: Suppose that the Earth retained its present mass but was somehow compressed to half its present radius. What would be the value of g at the surface of this new, compact planet?
My work: So, this seems pretty simple, and I get the right answer, but I seem to be off by a lot of decimal places. Can anyone tell me what is wrong here with my calculations?
g = (GMe)/(Re)² where Me = mass of the Earth, and Re = radius of the Earth.
So if Re is compressed to half its present radius, then:
g = (GMe)/(Re/2)² = (6.67E-11*5.98E24)/(6370/2)² = 39344273 m/s²
The answer in my text gives 39.2 m/s².
To try and check what I was doing wrong, I tried to calculate for the known value of g = 9.81 m/s² and I got 9836068.3 m/s². So it looks as if the correct numbers are there, but I am somehow messing this up.
Thanks for any help!
My work: So, this seems pretty simple, and I get the right answer, but I seem to be off by a lot of decimal places. Can anyone tell me what is wrong here with my calculations?
g = (GMe)/(Re)² where Me = mass of the Earth, and Re = radius of the Earth.
So if Re is compressed to half its present radius, then:
g = (GMe)/(Re/2)² = (6.67E-11*5.98E24)/(6370/2)² = 39344273 m/s²
The answer in my text gives 39.2 m/s².
To try and check what I was doing wrong, I tried to calculate for the known value of g = 9.81 m/s² and I got 9836068.3 m/s². So it looks as if the correct numbers are there, but I am somehow messing this up.
Thanks for any help!