How accurately do we know the mass of the Earth and how is the measurement or calculation performed?

Answer 1

rent the series 'A short history of nearly everything'...it tells the story of this and other scientific endeavors...very interesting.

Answer 2

The other links talk about the _basic_ way that the mass is determined. Another way is to use the orbits of _all_ the planets and their effect on the Earth's orbit, and vice versa. This comes up with a value of 5.9736 x 10^24 kg. The accuracy is about +/- 2 in the last digit, I think.

The old value, 5.9742 x 10^24, is from the early 1990's, but is still widely reported

Answer 3

Mass of the earth is: 5.9742 x 1024 kilograms.

We calculate Earth’s mass as follows:

Everything pulls on everything else in a simple way that involves only mass and distance. Newton said every body attracts every other body with a force that, for any two bodies, is directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance separating them.

The equation, expressing Newton’s statement, is

(1) F = G (m1) (m2) / d²

where G is the gravitational constant.

Newton also said that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.

The equation, expressing this statement, is

(2) a = F / m.

We substitute Earth’s mass (me) and Earth’s radius (r) in Equation (1) to get the force that Earth attracts a body of mass (m) on the surface of Earth.

(3) F = G (me)(m) / r²

We substitute the acceleration (g) due to gravity in Equation (2) to get the force that the object of mass (m) resists the acceleration due to gravity

(4) F = mg

To calculate Earth’s mass, we equate the forces given by Equations (3) and (4) and solve for (me). We get

(5) me = g r² / G

where the constants are given by G = 6.67300 x 10-11m³/(kg s²),

g = 9.8 m/s²,

and r = 6.378 x 106m.

Plugging the values of the constants in Equation (5) we get the mass of Earth:

me = 5.9742 x 1024 kilograms.

Answer 4

We know the mass by how strong gravity is and how large it is. You need to know the size of the Earth because it is the distance from the center of mass and not the distance from the surface that determines how strong gravity is. You know how strong gravity is by either weighing a known mass or timing how long something takes to fall when dropped from a known height.

It is known to an accuracy of about 1 part in 7,000.

Answer 5

Bill Bryson reviews this briefly in A Short History of Nearly Everything, cd #1 -- Cavendish carries out the experiments in 1797 using equipment bequeathed due to death of John Mitchell(?), came out to around 5 billion metric tons, and hasn't been much improved upon since, even with modern measrmts and equipment.

Answer 6

Didn't you see in Monty Python, they put the Earth on a big scale...

Answer 7

Here's a pretty basic and cool site which will answer your question...