The weight of Earth

Isn't the Earth heavier in the US?

Originally posted by shavixmir
Isn't the Earth heavier in the US?

Yes, that's because our streets are lined with Gold.

GRANNY.

Originally posted by smw6869
Yes, that's because our streets are lined with Gold.

GRANNY.

Lined with debt, bums and gun-related deaths, you mean.

Originally posted by twhitehead
Thats nonsense. They do not lie on a straight line.

I think that the easiest way to find out the gravitational force acting on a body is to know the bodies acceleration and mass and work it out from there. The earths acceleration is almost entirely due to the sun, so I think we can quite easily ignore all the planets - and the rest of the universe too.

Don't forget that our Solar system also has some acceleration according to another reference point. Is it even possible to find a sort of unmoving point of the Universe according to which we could calculate weight? Are there any completely unmoving objects? Is that even determinable?

Eh, sorry if that sounds like nonsense, just some questions (rather philosophical though) that popped to my mind while reading this discussion.

Originally posted by kbaumen
Don't forget that our Solar system also has some acceleration according to another reference point. Is it even possible to find a sort of unmoving point of the Universe according to which we could calculate weight? Are there any completely unmoving objects? Is that even determinable?

Eh, sorry if that sounds like nonsense, just some questions (rather philosophical though) that popped to my mind while reading this discussion.

There are no fixed points in the Universe. Unless you define one.
There are no still points in the Universe. Unless you define one.

Originally posted by kbaumen
Don't forget that our Solar system also has some acceleration according to another reference point. Is it even possible to find a sort of unmoving point of the Universe according to which we could calculate weight? Are there any completely unmoving objects? Is that even determinable?

Eh, sorry if that sounds like nonsense, just some questions (rather philosophical though) that popped to my mind while reading this discussion.

You can assume any point in the universe to be immobile for the purposes of calculating acceleration. Of course, that doesn't mean that the point in question really isn't moving, it's just defined not be moving relative to its initial position.

For the purposes of calculating "weight" (i.e. the vector sum of all the gravitational forces acting on a body), the acceleration isn't needed since there's no guarantee the body in question is moving in the direction of the weight vector - even though the weight vector for the Earth points pretty much directly towards the Sun, the Earth moves perpendicular to that direction in its orbit (for the most part).

All you need to calculate the weight of the Earth is a static representation of the local gravitational forces (non-local ones don't matter much, as I found out when I calculated the gravitational pull of Alpha Centauri on the Earth to be insignificant), and a convention that tells you which end of the vector to put the arrowhead on.

Originally posted by PBE6
For the purposes of calculating "weight" (i.e. the vector sum of all the gravitational forces acting on a body), the acceleration isn't needed since there's no guarantee the body in question is moving in the direction of the weight vector - even though the weight vector for the Earth points pretty much directly towards the Sun, the Earth moves perpendicular to that direction in its orbit (for the most part).

But the earth is constantly accelerating directly towards the sun. (Velocity is not the key here but acceleration).
The earths acceleration is almost entirely due to the sun, so any other accelration can be essentially ignored. (we do the same when calculating the weight of objects on the earths surface (they always accelerate towards the earths centre and we ignore other forces such as the suns or moons gravity).
The earths weight therefore is dependant on its mass, the suns mass and the distance between the two. In fact as the earths orbit is eliptical the earths weight varies with the seasons.

Another interesting factor is that since the earth and moon are essentially one body when it comes to the earths orbit, we would have to factor the moons mass into our calculation.

Originally posted by twhitehead
But the earth is constantly accelerating directly towards the sun. (Velocity is not the key here but acceleration).
The earths acceleration is almost entirely due to the sun, so any other accelration can be essentially ignored. (we do the same when calculating the weight of objects on the earths surface (they always accelerate towards the earths centre a ...[text shortened]... when it comes to the earths orbit, we would have to factor the moons mass into our calculation.

Actually, that's right, the Earth is accelerating towards the Sun. However, not all bodies with weight accelerate in the direction of their weight vector. A rocket is a prime example - something designed to provide enough force in the opposite direction of its weight vector to overcome it and accelerate away. That's why I think all this talk about relative motion is beside the point.

The Earth's weight is dependent on its mass, the mass of all other bodies in the universe, the distance of each piece of mass from the Earth, and a constant, as per Newton's law of gravitation. However, after doing the calculation only Jupiter and the Sun really have an impact on the value of the Earth's weight, roughly 5% and 95% respectively (the Moon only contributes 2 x 10^20 N, not enough to change the sum by a significant amount).

You're also right about the weight changing with the position of the Earth in its orbit. My calculations only assume an average distance.

Originally posted by PBE6
However, not all bodies with weight accelerate in the direction of their weight vector.

They do when they are in free fall ie do not have a force acting on them other than gravity. This fact enables us to use an objects acceleration to work out its weight. In fact that is the usual method of determining mass.

However, after doing the calculation only Jupiter and the Sun really have an impact on the value of the Earth's weight, roughly 5% and 95% respectively (the Moon only contributes 2 x 10^20 N, not enough to change the sum by a significant amount).
I dispute the 5% figure for Jupiter. The main reason is that Jupiter orbit results in it being at wildly different distances from the earth that its effect would change dramatically over time, so if your 5% is its maximum effect then it is probably closer to 0 most of the time.