What is the weight of the Earth?
Weight of the Earth
The 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 Earth
Newton showed that, for spherical objects, you can make the
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
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
6 quintillion metric tons (6 x 1021
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
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
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
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 my
weight 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
and must also specify the other object's mass, and the distance
centers of mass of the earth and the other object. As any of
changes, so too does the earth's 'weight' change!