"From your rough ideas or knowledge of the density and radius of the earth, estimate its mass to an order of magnitude. "
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*108)m/s
[ 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/R2, where g = 9.8 m/s2, M = mass of the earth and R = radius of the earth.
R = 106 implies M = 1.5*1023.
R = 105 implies M = 1.5*1021.
R = 104 implies M = 1.5*1019.
R = 103 implies M = 1.5*1017.
[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?