# Mass of the Earth

1. Aug 21, 2010

### hasan_researc

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*108)m/s
= 1.4*1011m.
[ 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.

2. Aug 21, 2010

### Tusike

You're idea seems good, but I don't think that's what the problem wants you to do.
For the radius of Earth, I suggest using how 1km was defined in the old days as the circumference at the equator / 40000. The google the average density of Earth... I don't know what it is, but my guess would be near 4g/cm3. From there all you need to use is m = V*q.

3. Aug 21, 2010

### hasan_researc

You're asking me to google the average density of the earth, but can't we get that value based alone on logical arguments.

4. Aug 22, 2010

### Jobrag

I'm not sure why you are concerned with the radius of Earth's orbit round the sun.
If you have a value for G (universal gravitational constant) and an approximation of the earths radius just plug the values into g=MG/R*R.

5. Aug 22, 2010

### Tusike

@Jobrag: how could he use that he doesn't know the mass of Earth, M...

@OP: here's a logical argument: the density probably isn't higher x*10^2. I would say that could be a "rough idea" or "knowledge". Seeing as you have a real precise value for the radius of the Earth, and so it's volume (from the post I've given above), the order of magnitude you'll get for Earth using either q=x*10^0 or q=x*10 will only have an error range of two magnitudes, much less than your original answer (since m=q*V).

6. Aug 22, 2010

### theJorge551

Jobrag is correct. If you have a somewhat accurate number for the radius of Earth, and you know the mass of something that falls at an average 9.8 m/s2, you then plug it into the equation here and should come out with a good estimation of Earth's mass.

7. Aug 22, 2010

### Tusike

@theJorge551, @Jobrag: Sorry, from the way I read the post I just thought he was trying to get the radius of Earth, not it's mass:) And yeah that would work as well, I was just trying to incorporate the density as the problem asked.