How do scientists find out the mass of the Earth?

Answer 1

There are two distinct methods.

By studying a torsion balance, with two very heavy weights balanced on a bar hung from a twisting wire and attracted by two stationary weights, we can experimentally determine the value of the gravitational constant G in Newton's equation F = G * M1 * M2 / d^2. Then the Earth's observed gravitational force F on a known mass M2 can be inserted into the equation to obtain the mass M1 of the Earth.

The older method was used by the Astronomer Royal, Nevil Maskelyne, in 1774. He observed stars near the Scottish mountain Schiehallion, and determined the angle by which the gravitational vertical was deviated from the true astronomical vertical by the sideways pull of the mountain. The web site below explains the observations and calculations quite clearly. They give the ratio of the mountain's mass to the Earth's mass, and the mountain is regularly enough shaped to allow a good estimate of its mass.

Answer 2

The mass of the Earth may be determined using Newton's law of gravitation. It is given as the force (F), which is equal to the Gravitational constant multiplied by the mass of the planet and the mass of the object, divided by the square of the radius of the planet. We set this equal to the fundamental equation, force (F) equals mass (m) multiplied by acceleration (a). We know that the acceleration due to gravity is equal to 9.8 m/s2, the Gravitational constant (G) is 6.673 × 10-11 Nm2/kg2, the radius of the Earth is 6.37 × 106 m, and mass cancels out. When we rearrange the equation and plug all the numbers in, we find that the mass of the Earth is 5.96 × 1024 kg.

F = Gm1m2/r2 = ma

Gm/r2 = g

m = gr2/G

m = (9.8 m/s2)(6.37 × 106 m)2/(6.673 × 10-11 Nm2/kg2)

m = 5.96 × 1024 kg

The Earth gains mass each day, as a result of incoming debris from space. This occurs in the forms of "falling stars", or meteors, on a dark night. The actual amount of added material depends on each study, though it is estimated that 10 to the 8th power kilograms of in-falling matter accumulates every day. The seemingly large amount, however, is insignificant to the Earth's total mass. The Earth adds an estimated one quadrillionth of one percent to its weight each day.

Answer 3

By looking at how long the Moon takes to go around, given its distance.

Nowadays, we could do that with any satellite. The orbital period of a small body around a much bigger one depens solely on the Mass of the bigger body and the distance between the two bodies.