Problem: Suppose that the Earth retained its present mass but was somehow compressed to half its present radius. What would be the value of(adsbygoogle = window.adsbygoogle || []).push({}); gat 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 ofg= 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!

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# Force of gravity if the Earth's radius, r = r/2

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