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## Homework Statement

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

## Homework 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.

## 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?