How did we weigh the mass of the Earth?

Question

How did we weigh the mass of the Earth?

Answer 1

I would have to agree with the first answer.  Weight and mass are not similar.  Mass measures how big something is, not how much something weighs.  You just use some simple mathematics and get the diamater of the earth around the equator and mulitiply it times Pi I believe.

Answer 2

Newton determined how much force would be exerted on an object when he came up with his formula for gravity:

Force = Massofobject 1 * Massofobject2 * SomeConstant / Distance ^2

Since we know how small objects around us are, and how far from the center of the Earth we are, and what the force on objects in Earth's gravity are (that is, enough to accelerate them at 32 ft/sec^2 or 9.8m/s^2,) finding the mass of the Earth simply required determining the absolute strength of gravity.   In other words, finding out what that constant in Newton's equation was.

In the 1790's an experimenter named Henry Cavendish  placed a small metal sphere next to a large metal sphere and measured the tiny gravitational force between them.  (He did this by figuring out how much force it required to twist a thin metal wire- coming up with a device called a torsion balance.)   Because he knew the masses of the objects in question, he was able to determine the absolute force of gravity.   (Cavendish, in fact, skipped determination of the force of G and went straight on to figure out the mass of the Earth, but this was, in effect, the same thing.)

Once the absolute strength of gravity was determined, scientists could use what they knew to be the acceleration of objects towards the Earth, deduce the force that the Earth imparted on objects and, thus, figure out the mass of our planet.

Answer 3

mss and weight have nothing to do woth each other

Answer 4

it's impossible. you'd have to weigh all ppls accurately.. (cough cough ;; impossible) + land mass/water

Answer 5

It's easy to get the mass of the Earth, provided you know Newton's constant, G, because the period of the Moon's orbit depends only on the distance to the Moon (obtainable by parallax measurements from different places on Earth), G, and the mass of the Earth.  You can use any other satellite instead of the Moon.

The only real problem is getting G.  That's a difficult laboratory experiment, since gravity is so weak, but it can be done with the right experimental apperatus.

Answer 6

The simplest way is to calculate the volume of the Earth and the density of the Earth, which is mostly iron and nickle.

Mass equals volume times density.

Answer 7

You would get the mass of Earth the same way as an oblong sphere.  Since we have the dimension of Earth, we can calculate the approximate density.

You also have to realize our planet's mass is changing on an hourly basis with meteor impacts.  Even if it doesn't become a meteorite by striking the surface, the meteor's mass is calculated into the equation through our atmosphere's mass.

Also remember that matter is never created or destroyed.  So if our planet were to be isolated from everything, the mass would never change.

Answer 8

calculations.

Answer 9

This may be more understandable for this forum:

<<Correct way would use barycenters and take into account all possible conical orbits>>

Just assume orbits are circular.

Mass of "central object"= 4[(pi)^2] K/G

G= Newton's gravitational constant

K= Kepler's constant = (R^3)/(T^2)

R= distance from the center of  the "central object" to the center of the "orbiting object"

T= period of the "orbitting object" around the "central object"

M={4[(pi)^2][R^3]}/{G[T^2]}

For the Earth's mass just plug in the distance to the Moon from the Earth for 'R' and the Moon's period around the Earth for 'T'.  Watch your units!

Answer 10

science is cool.

you start with what you CAN measure directly, use it to measure something indirectly, use that to measure a third thing... on and on...

errors accumulate and sometimes you just gotta take a guess (like the distance to Polaris), but mostly you get an answer that seems reasonable.

I remember showing my Dad about 20 years ago, just using some tables from the CRC how to figure out the mass of the Moon.

(he wasn't impressed)

Answer 11

Just find the average density of the composition of Earth and multiply by the volume.

This is how you would calculate the mass.  The weight takes gravity into consideration which wouldn't apply in this calculation.

Answer 12

What a cool question!  Calculations of some sort...but I'm not sure.

Answer 13

by its gravity.

Answer 14

I think...Density=mass over volume. So, Mass=density * volume. To check the volume 2 * pi * the radius of earth, and density of land and water. I don't know....maybe..

Answer 15

Wow, big scale......very big scale.

John

http://www.spotlighttees.com

Answer 16

Isaac Newton determined that the gravitational attraction between two masses is F=GmM/r^2 where G is a constant, m and M are the masses, and r^2 is the square of the distance between their centers of mass.

Eratosthenes determined the value of r.

Henry Cavendish determined the value of G.

So if you know F (your weight), m (your mass), G and r, it's possible to solve for M (the earth's mass). 6.0x10^24 kg.

Answer 17

Brad gets my vote as the correct explaination.