(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

"From your rough ideas or knowledge of the density and radius of the earth, estimate its mass to an order of magnitude. "

2. Relevant equations

I don't know the density or the radius of the earth, but I do know that it takes 8 minutes for light from the Sun to reach the earth.

3. The attempt at a solution

So, the radius of the earth's orbit around the sun = (8*60)s * (3*10^{8})m/s

= 1.4*10^{11}m.

[ My estimate of the time is crude, so I've kept the radius to one s.f.]

Assuming that the radius of the earth << the radius of its orbit around the sun, I am estimating the radius to be on an order of magnitude of 3 to 6. Is this reasonable?

Next, let's estimate the mass of the Earth. According to the theories of classical mechanics,

g = GM/R^{2}, where g = 9.8 m/s^{2}, M = mass of the earth and R = radius of the earth.

R = 10^{6}implies M = 1.5*10^{23}.

R = 10^{5}implies M = 1.5*10^{21}.

R = 10^{4}implies M = 1.5*10^{19}.

R = 10^{3}implies M = 1.5*10^{17}.

[All estimates are in SI units.]

But I have not used density to find my answer. Moreover, my answer has a very large error range.

Can anyone help, please?

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# Homework Help: Mass of the Earth

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