A really random but simple question about gravity.

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Just a quick question: Is the sun's gravity at the Earth's average distance from the sun stronger or weaker than the Earth's gravity on the surface of the Earth?

Definitely earth's gravity, or we would all be falling towards the sun and not the earth. But maybe not, because the earth is in orbit around the sun, and we are not in orbit around the earth. Actually, I don't know. Why don't we feel ourselves weighing less during the day due to the suns gravity counteracting with the earths?

The internet says that the sun's pull on the earth is 1.55*10^16 newtons. Wait, now I'm really confusing myself. F = MG, and without a set mass, there's no way to determine how many newtons the earth pulls towards it.

I think a better question would be what is the escape velocity to get out of the solar system compared to that of the earth.

I don't really know, but I'm determined to find an answer to this.

Alright, so the internet says that the earth orbits around the sun at 29.8 km/s. This is the speed the earth must travel to maintain the same path. Now, the escape velocity for earth is 25,000 miles per hour, at the surface neglecting air resistance.

25,000mph is 11.176km/s according to Google, so now we can get a good comparison. 11.176 is less than the 29.8 of the sun's gravity at earths distance, so therefore the sun does have a stronger pull than the earth.

Why do I have fun doing this kind of stuff?

The sweet thrill of successfully completing a problem? Thanks

Much weaker. That is why we stay rooted to the ground.

ruveyn

Let's investigate: We can apply Newton's law of universal gravitation. mass of earth=5.97e24 kg mass of sun=1.99e30 kg average distance (r) between earth and sun=1.496e11

If you crunch those numbers into Newton's formula with G=6.674e-11, then you come up with 3.54e11 Newtons.

You can only measure the strength of Earth's gravity as it relates to something else, as explained by Newton's third law. You can't measure the strength of a gravitational force without two bodies of mass. Along with the mass of the Earth, the mass of an object situated on earth is needed to determine the force that earth's gravity will exert on that object.

For this second comparison of masses, we'll still use 5.97e24 kg as the mass of the earth. The mass of the unknown object we'll leave as Mx. The distance between this unknown object is just the distance to the center of the earth, which is 6.378e6 meters.

F(between unknown object and Earth)=G(mass of earth)(Mx)/(radius of earth^2)

If you set this equation equal to 3.54e11 (force between sun and earth) then you could find what mass would alter the answer in either direction, just by solving for the mass of the unknown.

The answer to your question changes depending on the mass of the unknown object. If the mass of the unknown object is under 3.61e21 kg, then the force of Earth's gravity on the object is weaker than the force between the sun and the earth (3.54e22 Newtons). If the mass of the object is over 3.61e21 kg (highly unlikely) then the force between the unknown object and the earth is greater than the force between the sun and the earth.

So to answer your question, as long as the the mass of the unknown object is under 3.61e21 kg, then the force exerted between that object and the earth is weaker than the force exerted between the earth and the sun.

Last edited by rabidmonkey4262 on 28 May 2011, 6:14 pm, edited 1 time in total.

The force of gravity from the sun at the distance of earth is stronger than the force of gravity from the centre of earth at the distance of the earth's surface.

We don't get pulled into the sun because we are in orbit.

The sun's gravitational force on the earth is much stronger than the gravitational force between a person and the Earth. Newton's Law of Universal Gravitation proves it. According to Newton, the gravitational force between a 50 kg person and the Earth is 490 Newtons. The gravitational force between the sun and Earth is 3.54e22 Newtons. That's almost 10e20 times stronger than the force between a human and the Earth. We stay rooted to the ground because the Earth is spinning. Spinning creates centripetal force. There is always a force vector pointing from every object on Earth down to the center of the Earth. If the spinning stopped, then there would be no more centripetal force and we'd go flying off. I think you're trying to view this as a "tug of war" scenario, and it's more complicated than that.

I hope you're kidding!
If the suns gravitational pull on a person were greater than that of the earth then you would fall up toward the sky and toward the sun.

There is a small centripedal force from the earth spinning but if it were indeed stronger than the earth's gravity it would throw you OFF the earth and not keep you on the earth.

If you lived in a cylinder shaped space ship that rotated at the right speed then centripel force would hold your feet to the space ship's inner surface and would in effect serve as artificial gravity. But the same force would hurl you away if you tried to walk on this big beer can's outer surface.

The astronauts on the moon did not fall off the moon toward the earth, nor did they fall from the earth moon system toward the sun.

Lets say you're an astronaut on the surface of the moon. For simplicity lets forget about the sun for a moment.

The gravitational pull of a body is proportional to its mass times the square of its distance.

So for a moon astronaut its a tug of war between the center of the moon (1000 miles beneath your feet), and the center of the earth (about a quarter million miles above your head). The moon has a mass of one and the earth has a mass of 80 ( since its 80 times as massive as the moon). But the ratio in distances is 250 to one. Two fifty squared is in the tens of thousands (call it 64000-dont have a calculator). Eighty into 64000 is 1/800. So the pull of the earth on a moon walking astronaut is one eighthundreth of the pull of the moon on the same astronaut. Thats why buzz aldrin did not fall back to earth from the surface of the moon. Do the same math for you, the earth, and the sun, and you will get a similiar story.

Nonsense.

If the earth stopped its forward motion then it would stop orbiting and start plunging toward the sun. But you and I would not fall from the earth toward the sun. We would be stuck like glue to the earth as it and us all plunge into the sun ( except at the last moments tidal forces might tear us from the earth in the last few miles to the sun surface).

I'm not kidding. If you wanna use a moon-earth comparison, that's fine, but then we'd be talking about the force between the earth and the moon (1.998e20 N) versus the force between the astronaut and the moon (81.4 N). We're not talking about the comparison of the force between an astronaut and the moon (81.4 N) versus the force between the astronaut and the earth (only 0.135 N). That's not what the OP was asking. Like I said earlier, this is not a tug of war scenario, but it's easy to make that assumption. I made the mistake of doing that at first, but if you use Newton's Law of Universal Gravitation like I did in my first post, you'll see my reasoning. If we did make it a tug of war scenario with a human in the middle, then the Earth would obviously "win" seeing as we're still standing here. The Earth exerts a force of 490 N on a human, and the sun would only exert a force of 0.297 N.

As a matter of fact, you could probably think of it as a tug of war between a human and the sun, with the Earth in the middle. The human and the Earth exert a force of 490 Newtons on each other, but the sun and the earth exert a force of 3.54e22 Newtons on each other. The sun wins. That's why the Earth orbits around the sun and not us. If someone could construct a mass greater than 3.61e21 kg, then that mass would "win" and the Earth would orbit around that mass instead of the sun.

Last edited by rabidmonkey4262 on 28 May 2011, 8:06 pm, edited 3 times in total.

The earth is not going forward. The earth is going in an elliptical motion. Any type of forward/backward motion is irrelevant to a spherical object. If the Earth stopped it's orbit, that would only be because the object that it is supposed to orbit around (the sun) disappeared. In which case we'd go shooting off into space, not into a non-existent sun. You just need to look at a force vector diagram of centripetal motion to understand that. The vector pointing to the center (the sun) would disappear and we're only left with the vector pointing out.

The earth is much more massive than a person. The suns gravitational force on a person is MUCH smaller than the earths gravitational force on a person. While what you say is true, it is a pointless comparison.

No. If not for gravity, inertial forces would fling us off the spinning earth. Haven't you seen how water flings off spinning tires or how kids fling off those spinning merry-go-round things on playgrounds? The centripetal force that holds us on the spinning earth is from gravity.

It's not a pointless comparison because it was the question that the OP had explicitly asked. Also, this has nothing to do with the sun's gravitational force on a person. It was the force between a human and earth vs the force between the sun and earth. If you look at the section of mine that you quoted, I didn't mention anything about the sun's gravitational force on a person. I did mention the sun's gravitational force on a person in another post, but that was to explain to someone else how he misinterpreted the original question.

On the second point, we would go flying off if the centripetal motion of the Earth stopped. I remember that clearly from my physics class, or pretty much any physics class in high school or college. The atmosphere wouldn't stop spinning, so you get a Newton's first law scenario. I did over-simplify it, but yeah you're right. The attraction of two masses (us and the Earth) is what keeps us grounded, at least according to Newton. Otherwise it would be like letting go of a spinning carousel.

The earth IS trying to move in a straight line at 40 thousand miles an hour. The sun is trying to pull the earth towards itself through the force of gravity. The gravity and momentum balance out so the earth moves in an orbit around the sun. Thats the whole reason we are in orbit around the sun in the first place!

If you somehow applied brakes to the earth so it stopped its linear motion then there would be nothing to balance the gravitational pull of the sun and the earth would fall into the sun.
And we would stay on its surface for most of the ride and would not fall seperately into the sun.

Thanks for reiterating the very point im making!

But actually something just occured to me- for the wrong reason you might be right.

Okay: on one hand:

The sun is 240,000 times the mass of the earth, but the center of the sun is 25 thousand times farther away from a person on earth than is the center of the earth. Twenty five thousand squared is 625 million.
Divide that number into the 240thousand and you'll find that the pull of the sun on your body is about 1/2500th as strong as that of the earth on your body by that newtonian equation.

But on the other hand:

In its orbit around the Sun the Earth is moving about 40thousand miles an hour. That means that escape velocity from the Sun in our neighborhood of the solar sytem must be slightly more than that speed .
But escape velocity from the earth isself is only 25 thousand miles an hour. So I gotta admit that now Im confused too! Maybe you're right.

One things for sure. The spinningof the earth is irrelevent. But maybe not the orbit of the earth. Like Sarah Palin says "Ill have to get back to you on that". I know that the earth pulls on you more than does the sun, but apparently a rocket has to go faster to move to the outer planets than it has to to just get off the earth. Its a conundrum.

There seems to be allot of confusion in what the original question asked was. The way i read it you are comparing object-earth and object-sun gravity when the object is located at the earth's surface.

object-earth gravity is significantly stronger.

The best way to look at this issue is using the earth's sphere of influence (AKA hill sphere). Picture a sphere around the earth with a radius of 1,500,000 km, anything that is inside this sphere, the gravity of the earth is significant and the gravity of the Sun can be considered negligible/zero. Everything within this sphere can be thought of as orbiting the earth, but it all moves with the earth as the earth orbits the sun. Outside this sphere, the gravity of the sun is significant and the gravity of the earth can be considered negligible/zero.

This is the method that astrophysicists use to solve for the orbits of interplanetary spacecraft, before doing more accurate simulations, called the reduced three body problem.

The escape velocity to exit earth's orbit is significantly lower than the escape velocity for the sun's orbit. At earth escape velocity you have too much kinetic energy for the earth to hold you in it's orbit, and you shoot of in a random direction leaving the earth's sphere of influence.

You still remain stuck in the gravity of the sun, because the sun has a much larger mass and it's gravity acts across much larger distances than that of the earth. Even if it pulls you with a lower force than the gravity from earth once did, it will continue to pull you into it's orbit for a significantly longer time than the earth can.

Last edited by huntedman on 28 May 2011, 10:06 pm, edited 1 time in total.

That's definitely a mis-interpretation of the original question. " Is the sun's gravity at the Earth's average distance from the sun stronger or weaker than the Earth's gravity on the surface of the Earth?

Clearly the first part is asking for the gravitational force between the sun and the Earth. The second part is asking about the gravitational pull of an object actually on Earth. People are creating their own question, and then answering it. There is nothing that says anything about object-sun gravitational pull. If that was the question, then the answer would be obvious and quite easy, seeing as we're still on Earth and not flying towards the sun.