What is the weight of the Earth?

Answer 1

Weight of the EarthThe Earth is in orbit around the Sun, or in freefall, so technically its weight is zero.

Weight depends on measuring the attraction between two objects, such as a person

and the Earth. It is actually a mutual attraction between their masses. The mass of

the Earth, however, can be calculated from its gravity.

Mass of the EarthNewton showed that, for spherical objects, you can make the simplifying assumption

that all of the object's mass is concentrated at the center of the sphere. The following

equation expresses the gravitational attraction that two spherical objects have on one another:

F = G * M1 * M2 / R2

R is the distance separating the two objects.

G is a constant that is 6.67259x10-11m3/s2 kg.

M1 and M2 are the two masses that are attracting each other.

F is the force of attraction between them.

Assume that Earth is one of the masses (M1) and a 1-kg sphere is the other (M2).

The force between them is 9.8 kg*m/s2 -- we can calculate this force by dropping

the 1-kg sphere and measuring the acceleration that the Earth's gravitational field

applies to it (9.8 m/s2).

The radius of the Earth is 6,400,000 meters (6,999,125 yards). If you plug all of these

values in and solve for M1, you find that the mass of the Earth is 6,000,000,000,000,000,000,000,000 kilograms (6 x 1024 kilograms), or

6 quintillion metric tons (6 x 1021 tonnes).

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As odd as it sounds, the weight of Earth is exactly zero, because the Earth is in

orbit around the sun, and as such, the Earth is free falling in space around the

sun.1 Any object in free fall in space, including an object in orbit, is weightless.

That is why astronauts are weightless when in orbit around the Earth.

Weight is a characteristic of an object as it relates to the gravitational field it is

resting in. You would have to take the earth to a much more massive world, like

Jupiter, and ignoring the difficulties caused by the gaseous make up of the

planet, put the Earth on a rather large scale to see what the Earth "weighs"

there. Of course, its weight would change based on its distance from the center

of gravity of the attracting object. On Earth, weight changes negligibly at any

altitude within the atmosphere.

The mass of the earth is another matter. The mass of the earth is 5.9736×1024 kg,

or about 5,973,600,000,000,000,000,000,000 Kg.

1 An orbit is a special case of a free fall condition. As the orbiting object falls downwards, it

also travels transversely (sideways) at such a rate that its falling trajectory projects a curve

that always remains the same distance from the planet's surface.

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From a different perspective:

The following experient was performed. Gravitational forces always occur in pairs,

between the centers of two masses, and the two forces are equal, so that the

force between me and the earth is what I call my "weight". If this is generally

correct, then the weight of any object depends on the other object to which

it is gravitationally attracted at the moment, and if that's true, then I can weigh

the earth on me.

In my laboratory, I placed a tiny mirror on the floor. I then took a bathroom scale

out of a cabinet, inverted it, and placed it top-down on the floor, with its digital

display visible in the tiny mirror. I then alighted upon the scale, placing my full

body upon the surface that is normally the bottom of the scale ... the surface

with the label, the rubber feet, and the battery door on it. In this way, I was

able to weigh the earth in my gravitational field, and (just as Sir Isaac might

have predicted) it was precisely equal to myweight when measured in the

earth's gravitational field.

It would seem that in order to accurately quote the earth's weight, the question

must specify the other object to which the earth is being gravitationally attracted,

and must also specify the other object's mass, and the distance between the

centers of mass of the earth and the other object. As any of these details

changes, so too does the earth's 'weight' change!