# Mass of the earth

1. Jan 1, 2010

### hisham.i

Hello..
how can we calculate the mass of the earth?

2. Jan 1, 2010

### mgb_phys

Find the period and distance of a satelite and use Kepler's law

3. Jan 1, 2010

### sylas

By measuring the rate of gravitational acceleration at the surface. The limiting factor is the accuracy of Newton's constant G, which has been measured now to about 4 significant figures.

Cheers -- sylas

4. Jan 2, 2010

### D H

Staff Emeritus
Sylas' method is rather old school. It is confounded not only by the relative low accuracy in our knowledge of G but also by the Earth's rotation, the Earth's non-spherical shape, and local variations in g due to local variations in density. Nonetheless, that is how scientists estimated the Earth's mass prior to the space age.

The Earth's non-spherical mass plus the fact that a satellite is also subject to gravity from the Moon, the Sun, Jupiter, Venus, etc. means that a simple Keplerian model (post #2) will also give erroneous results. The current best estimate of G*Me is obtained by observing satellites over a long period of time and removing all those confounding effects. The product of G and the Earth's mass is now known to almost nine places of accuracy thanks to satellite observations. However, because the universal gravitation constant G is only known to about four decimal places, the mass of the Earth is also known to only four decimal places.

5. Jan 2, 2010

### sylas

Bah. Young people these days don't show no respect. :tongue2: That aside... you are quite correct. My old fashioned post crossed with the ever up to date mgb_phys, who is the better guide in these modern times.

Do you know how they obtain estimates for G? I'm guessing it is by measuring accelerations of known masses in a laboratory, but I've not checked.

Cheers -- sylas, who is just a tad younger than the space age

Last edited: Jan 2, 2010
6. Jan 2, 2010

### D H

Staff Emeritus
Bah right back atcha! Your parting remark ("Cheers -- sylas, who is just a tad younger than the space age") makes me my flatulence more chronologically challenged than yours.