How we measure the mass of the earth?

Question

what is the system of measuring the mass of the earth?

Answer 1

There are several different ways, but perhaps the easiest is to calculate the mass of the Earth from the acceleration due to gravity at Earth's surface. If you drop something (and don't have to contend with air resistance), it accelerates at 9.81 m/s². (There are some regional variations...for example, at higher altitudes the acceleration would be slightly less, or it might be a bit more if you're standing above a huge, dense iron slab, but that's the average). You can use the acceleration due to gravity, the radius of the Earth (which was worked out pretty accurately by the ancient Greeks) and the equation:

g = GM/r²

to solve for M, the mass of the Earth in kilograms. r is the radius of the Earth in meters, and G is the universal gravitational constant, 6.67e-11 (with a big ugly unit to follow it).

Another way is to find the period of an object in orbit around the Earth:

T = 2*pi*√(a³/GM)

Where T is the period in seconds, a is the satellite's semi-major axis (the average distance between the satellite and the Earth), and M is , once again, the mass of the Earth in kilograms.

Answer 2

In 1798 Henry Cavendish determined the numerical value of the constant "big G" in the gravitational equation. To measure "big G" Cavendish designed a system which was isolated from air currents and kept at a constant temperature. Since the deflection was expected to be small, Cavendish used a device called an "optical lever". A mirror was suspended from the cable which supported the small masses . A beam of light aimed at the mirror was reflected and read on a scale which was as far away as feasible. This allowed the small twist of the supporting cable to be magnified, simply from the geometry of the triangle. He translated the angle of twist into a force, Cavendish relied upon Hooke's Law. He determined the value of G. G =6.673x10^-11 N m^2 / kg^2 Radius of earth R = 6371km. Force on 1 kg on the earth’s surface = 9.8 N~ 10 N By Newton’s law, 10 N = G M / R^2 M, the mass of earth = 10 x (6371)^2 x 10^6 / 6.673x10^-11 = 6 x 10^24 kg. Thus mass of earth is determined.

Answer 3

You can calculate the mass of a planet using the formula ,M=4 π² r³∕G T², where M is the mass of the planet, r and T are the radius of orbit and period of revolution of a satellite around the planet. G is a constant.Knowing these three values you can calculate the mass.
In the case of the earth,you can find out the values r and T of the moon and calcuate the earth's mass.

Answer 4

I thought i knew this, .....i forgot right now, but if i remember, i'll come back....sorry, bye!