A really random but simple question about gravity.

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Which are you drawn to, the sun or the earth?

ruveyn

I find this thread entertaining. Because the question is not precise, this could go on and on. Please, continue

both, you are simply drawn more towards the earth so it overpowers the effects of the sun, if we could measure gravity precisely enough i think we could measure an increase and fall in how much earthgravity affects us druing a year.

Definitely earth.

Much weaker, definitely. The Earth is at a relatively large distance from the sun, and because gravity diminishes at the square of the distance, the Sun's gravitational field at the orbit of the Earth is dwarfed by the gravitational field of the Earth at the surface.

I got the same sort of figure by rough calculating the Earth's orbital acceleration ...

Orbital radius 93000000 miles
Orbital radius (r) 1.488E+11 metres

Orbital Period 365.25 days
Orbital Period 31557600 seconds

Orbital angular velocity (omega) 1.99102E-07 radians per second

Orbital acceleration (omega squared r) 0.005898678 metres per second per second

The Earth's orbital acceleration is due to the Sun's gravity. You don't need to know the mass of the Sun or the universal gravitational constant.

They are making it more difficult than it needs to be.

The gravitation force of one object on another is indeed given by

F=(GMm)/r^2

Notice this does not distinguish which object is which. If we said M is pulling on m, the equation is no different than it would be if we said m is pulling on M. This is because in a two object system, the force on object 1 by object 2, is the same as the force on object 2 by object 1.

One way to think of it is, the more massive object is only going to pull on the lesser object the amount it needs to to get it to move. The less massive object is going to pull on the more massive object that same amount, which is consequently as much as it can pull, and that is not enough to get the more massive object to move.

A better thing to look at would be the acceleration each object contributes to an arbitrary point in space, also known as the gravitational field at a particular point.

Since F=ma we can say F=mg and g=F/m

So for the sun we have g1=(GM)/r^2
For the Earth we have g2=(Gm)/r^2

M>>m so g1>>g2

The gravitational field at a point r, due to the sun, will always be greater than the gravitational field at some point r, due to the Earth.

Um no. It's more like this:

If we take R to be the distance from sun to that random point and r to be the distance from the Earth to that random point, we have:

for the sun: g1=GM/R^2,

for the Earth: g2=Gm/r^2.

For a point close to the Earth:

R >> r, which actually makes g1 smaller than g2 at that point. Even though M is much greater m, you will still find that if you plug in actual numbers, we still have g2 >> g1 for a point near the Earth. You forgot the distance between the Earth and any given arbitrary point in space is different from the distance from that same point to the sun.

In this case, the sun's gravity is actually weaker than the Earth's due to the inverse square law.

Are you taking into account the momentum of the earth which is directed tangentially? That is why planets trace out elliptical orbits rather than death spirals.

Also the sun is losing mass (radiating it away and coronal mass ejections). So the planets should be moving away from the Sun not toward it.

ruveyn

The r in my equations is the distance between the center of mass of the object (we are treating the object as a point source) and some point in space, and I have said let it be the same for both object, because the original poster essentially wanted to know which object had more influence.

What you have done is taken different distances, which, is not applicable to the situation I was addressing, but raises a valid point none the less, that in a two particle system you can find a point in space where the field due to the less massive object is greater than the field due to the massive object, but for difference distances.

To extend the discussion, the field in a multi-particle system at a point in space is the superposition of the fields from all of the particles.