# How to determine earth's weight!

## Main Question or Discussion Point

Pls,
I'm thinking about weight according to w=mg. In this case g is earth's gravitational constant. When I think about earth's weight, how to reference about g, for example . from sun?, from moon? . Pls think about this and help me to learn about this. Thank's alot

## Answers and Replies

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arildno
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Well, the classical way of doing this was by a Cavendish-like experiment, the aim of which is to measure big G in Newton's general law of gravitation.

Once big G is known (approximately), and the radius r of the Earth is known, then the mass of the Earth is readily obtainable from little g, big G and r.

You might wish to look up on the Cavendish experiments.

Today, I'm sure there are other ways of "weighing" the Earth.

what you surely want to find out is Earth's mass? If not, the question of Earth's 'weight' doesn't really seem to make sense from most points of view. Weight is something that happens to a mass when it's 'exposed' to a gravitational field.

Thus, in any system, a body has a value of 'weight' due to any other body in that system. The final result for Earth as a local body in our solar system is a summation of the effects from each of the other planets/sun etc. (So Earth has a weight from each individual body, you can calculate the effect from whichever one you want by choosing the effective 'g' from that planet)

Otherwise, there are various experiments you can use to calculate the mass of the Earth.

arildno
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a) With "weighing an object" we colloquially mean "calculate the mass of the object" (typically by means of a weight instrument)
b) Similarly, Cavendish himself said he was "weighing the Earth"

Now, this colloqualism, albeit as imprecise as most colloquialisms are, is so common that we won't get rid of it anyhow, so we might as well quit quibbling about it.

I do see, however, that the OP is probably more confused about the distinction between "weight" and "mass" than I thought by a cursory first reading.
So your post seems very appropriate nonetheless..

how to reference about g, for example . from sun?, from moon?
Valid method. Measuring the orbit (with respect to the stars) should tell the mass of the earth (in units of the mass of the moon). Arildno is suggesting a different valid method to tell the mass of the earth (in units of the mass of a paperweight).

Thank's for your generosity.

rbj
Valid method. Measuring the orbit (with respect to the stars) should tell the mass of the earth (in units of the mass of the moon). Arildno is suggesting a different valid method to tell the mass of the earth (in units of the mass of a paperweight).
it seems to me, that if we can measure the distance to satellites (moon and artificial) accurately(in terms of cesium radiation and the speed of light, the SI meter) and measure the periods of orbits (against the stars) over the long term (in terms of cesium radiation, the SI second) and taking consideration of the Earth's movement around the Sun, then we oughta be able to measure GM quite accurately. is that the case? then, if we could make an independent measure of M from knowledge of its size, spherical shape, and composition, we oughta have a pretty good measure of G, better than the 4 or 5 significant digits we have from the best of the Cavendish-like experiments that humans have done to date.

i dunno. just a thought. maybe we don't know the composition of most of the Earth's volume as well as i am assuming.

it seems to me, that if we can measure the distance to satellites (moon and artificial) accurately(in terms of cesium radiation and the speed of light, the SI meter) and measure the periods of orbits (against the stars) over the long term (in terms of cesium radiation, the SI second) and taking consideration of the Earth's movement around the Sun, then we oughta be able to measure GM quite accurately. is that the case? then, if we could make an independent measure of M from knowledge of its size, spherical shape, and composition, we oughta have a pretty good measure of G, better than the 4 or 5 significant digits we have from the best of the Cavendish-like experiments that humans have done to date.

i dunno. just a thought. maybe we don't know the composition of most of the Earth's volume as well as i am assuming.
I've always been intrigued by the fact that modern experiments that are done to determine G are not appreciably different from Cavendish's original experiment. These days, it seems that the gravitational force that twists the rod (from which the two masses are suspended) is balanced by a magnetic field, since the torsion in the apparatus can actually oppose the gravitational force and skew the results. But in essence, it's the same experiment. In fact, I'm told that G is one of the least accurately known of all physical constants.

rbj
I'm told that G is one of the least accurately known of all physical constants.
well, you don't have to take the word of whomever told you that, it's shown clearly at NIST.

i think we do measure the GM product pretty accurately, but they don't have a decent independent measure of the mass of the Earth (or the mass of the Sun or the mass of any other massive celestial object that we see other objects orbiting). without an accurate independent measure of the Earth's mass (or similar object) relative to the prototype kg (or some other known standard), i dunno if they can get a good value for G.