Gravity problem

[steppjr78]

Me and a buddy from work got in this extremely stupid argument about gravity. So here it is!

If you took the earth and some how removed half the planet by some unknown means, would the rest of the planet slingshot out from the sun or fall into the sun? I say it will fly away from the sun because the mass is not half and if you plug the new numbers into the gravity equation the force will be less then it was before and there will not be enough gravitational force to hold the mass in orbit, thus flying away from the sun. He says you have to also account for the spinning of the earth but I don?t see why. Centrifugal force would have no effect on gravity.

So what does everyone else think? can any one prove either side right?

 

[deveraux]

Well, from what I've learnt, there is actually no such thing as a centrifugal force. A centrifugal force is always a resultant of several other forces which happens to cause a circular motion. But anyway, back to the question, firstly, Earth's orbit is not circular, but elliptical and hence, if you were to remove part/half of the mass, it will being to sprial outward.

The only way to stop it spiralling would probably cause another change in mass or some other form of force on the system to enter it into a new elliptical orbit. I could be wrong though, this is just speculation. I haven't done elliptical orbits in over a year and I wasn't even that good at it when I was doing it (hated that topic really).

 

[PunDogg]

i know I prob, shouldn't be posting in Highly Tech. but what about Jupitors Gravity. I mean Jupitor and saturn work together with the Sun to keep the Solar system free from comets and such, but would that have an effect on Earths motion if it lost have its mass.

Also could the Earth go and be pulled into Jupitors gravitional field and become another Moon??

These are prob really stupid ideas but just thought i would post them

Dogg

 

[DaTT]

I have a similar question......If you were to dig a hole in your back yard directly to the otherside of the earth and then jumped in feet first, would you fall through the hole and exit feet first?

 

[YOyoYOhowsDAjello]

Originally posted by: DaTT
I have a similar question......If you were to dig a hole in your back yard directly to the otherside of the earth and then jumped in feet first, would you fall through the hole and exit feet first?

this one i know for sure, you would fall past the center of the earth by a little ways and then come back the other way less and so forth until you eventually stop at the center of the earth.

 

[YOyoYOhowsDAjello]

Is this what we're looking for?

"Consequently, for a given orbit, a satellite with a large mass has exactly the same orbital speed as a satellite with a small mass."

So, if the speed remains the same, it will keep the same distance?

source

 

[DaTT]

Originally posted by: YOyoYOhowsDAjello

Originally posted by: DaTT
I have a similar question......If you were to dig a hole in your back yard directly to the otherside of the earth and then jumped in feet first, would you fall through the hole and exit feet first?

this one i know for sure, you would fall past the center of the earth by a little ways and then come back the other way less and so forth until you eventually stop at the center of the earth.

You have just ruined me dreams of falling to china feet first all jacky Chan like.

 

[YOyoYOhowsDAjello]

Well, I don't think anyone has acutally ever tried this, so maybe all of physics is wrong

You should try it and see what really happens.

Just make sure you post results here after you try it.

 

[Calin]

All the forces that keeps Earth on its orbit are dependant on mass. So, any change of mass will have nil effect.

 

[YOyoYOhowsDAjello]

Originally posted by: Calin
All the forces that keeps Earth on its orbit are dependant on mass. So, any change of mass will have nil effect.

can you explain that again?

I'm reading it as

The Earth's orbit is dependant on mass, but a change in mass doesn't effect it.

I don't get it.

 

[MisterPants]

F=GmM/r^2 where m is the mass of the earth, M is the mass of the sun, G is a constant, and r is the distance between the earth and the sun. This is exerted on the sun and the earth in the same magnitude and opposite direction.

For the earth's motion: F=ma. Thus: ma=GmM/r^2 --> a=GM/r^2, so the earth's acceleration is dependent only on the mass M of the sun. There would be an effect on the sun's acceleration but since the force the earth exerts on the sun is negligible given its mass, very little will change.

 

[Calin]

The orbit of a celestial mass can be uniquely determined from its position and speed at a certain moment (any moment). It does not depends on mass, as long as the mass is negligible in regards to the mass of the sun (or whatever other gravity source there is).
By example, the Moon "rotates" around the Earth. If an satellite (1 ton of mass) would be at that distance, it would rotate around the center of the Earth (or more specifically the center of rotation would be between the center of the Earth and the satellite, so the fraction of the mass is inverse to the fraction of the distances. For Earth, mass is some 6x10^24 kg, satellite is 1x10^3 kg, the total distance would be 384x10^6 m - let's say 4x10^8 m. The Earth would move around a rotation center 10^-10m from its center.
Put the moon into equation and you will get: Earth's mass 6x10^24, Moon's mass 7x10^22 kg - total distance 4x10^8 m, the mass fraction is somewhere 1:100, so the rotation center is at some 4x10^6m from Earth's center. That is 4 000 km, adn Earth radius is 6378.137km. You can certainly say that Moon rotates around Earth.

Calin

 

[Calin]

And let's take into account the Sun-Jupiter situation: Sun's mass is 1.99×10^30, Jupiter's mass is 1.9×10^27 - a 1:1000 fraction. The distance between Sun and Jupiter is 778,330,000 km, and Sun's equatorial radius is 695 000km. The center of rotation would be at 777 552 km from the Sun's center, so Jupiter is not orbiting around the Sun but around a rotation center, and also Sun is orbiting around a rotation center outside of its surface.

 

[rocketPack]

Originally posted by: YOyoYOhowsDAjello

Originally posted by: DaTT
I have a similar question......If you were to dig a hole in your back yard directly to the otherside of the earth and then jumped in feet first, would you fall through the hole and exit feet first?

this one i know for sure, you would fall past the center of the earth by a little ways and then come back the other way less and so forth until you eventually stop at the center of the earth.

Make sure you wear some PPE when you take the final plunge, I hear it gets warm around the middle.

 

[DaTT]

I'll have on some shorts and a Tee

 

[sao123]

Because the orbital center is inside the sun, a reduction of mass of earth will not affect the orbit (assuming that its velocity is unchanged.)

However what will happen is the orbital point of the earth moon system will move from inside the earth to somewhere between the earth & moon, and they will have a newly defined orbit.

also, if the mass removal is uneven, the earths rotation will develop a severe wobble. At the instant of the mass loss, this wobble would cause a net displacement of the earths position (imagine a spinning top flying apart.) But this should not significantly affect the earth - sun orbit. -- I believe this is what your friend was referring to.

 

[RelaxTheMind]

Originally posted by: YOyoYOhowsDAjello

Originally posted by: DaTT
I have a similar question......If you were to dig a hole in your back yard directly to the otherside of the earth and then jumped in feet first, would you fall through the hole and exit feet first?

this one i know for sure, you would fall past the center of the earth by a little ways and then come back the other way less and so forth until you eventually stop at the center of the earth.

This my friend sounds like fun. How about if you made a big hole through and through and dumped a couple million gallons of water? would you get a huge shperical hot tub?

 

[YOyoYOhowsDAjello]

If you could overcome all the things trying to destroy it (heat, pressure, entire weight of the earth) then yeah, I think so

Of course all those things would also prevent you from actually making the hole in the first place hehe.

 

[WaxHaX0rS]

Originally posted by: RelaxTheMind

Originally posted by: YOyoYOhowsDAjello

Originally posted by: DaTT
I have a similar question......If you were to dig a hole in your back yard directly to the otherside of the earth and then jumped in feet first, would you fall through the hole and exit feet first?

this one i know for sure, you would fall past the center of the earth by a little ways and then come back the other way less and so forth until you eventually stop at the center of the earth.

This my friend sounds like fun. How about if you made a big hole through and through and dumped a couple million gallons of water? would you get a huge shperical hot tub?

You could jump in and then drown because you would be stuck in the center of it all.

 

[YOyoYOhowsDAjello]

Originally posted by: WaxHaX0rS

Originally posted by: RelaxTheMind

Originally posted by: YOyoYOhowsDAjello

Originally posted by: DaTT
I have a similar question......If you were to dig a hole in your back yard directly to the otherside of the earth and then jumped in feet first, would you fall through the hole and exit feet first?

this one i know for sure, you would fall past the center of the earth by a little ways and then come back the other way less and so forth until you eventually stop at the center of the earth.

This my friend sounds like fun. How about if you made a big hole through and through and dumped a couple million gallons of water? would you get a huge shperical hot tub?

You could jump in and then drown because you would be stuck in the center of it all.

Would it be any different than just swimming in a pool on the surface? Couldn't you just swim to the surface?

You're weightless in the exact center, right?

Gravity gets weaker the closer you get to the center of the earth, right? Isn't it stongest at the surface?

 

[Viven]

I agree with sao123's wobble statement. but i feel since the whole question of instantaneous mass reduction is conceptual , we can safely assume uniform mass reduction. Gravity is not the only cause of the orbital motion. As MisterPants says, the whole orbital motion is the result of two forces : 1) Gravity 2) Inertia . These two are perpendicular to each other as the instantaneous direction of inertia is along the tangent.Vector addition of these two forces gives the resultant force and direction of motion. If gravity reduces due to loss of earth mass, inertia also reduces proportionately (gravity = GMm/ r^2 inertia = 1/2 * mv^2/r ) so if m changes to m/2 resultant direction of revolution remains the same.

 

[Calin]

I disagree about the wobble statement - this is not a thing that is having a fixed center of rotation. We are talking about a mass that rotates "at will" around its center of mass. That its center of mass will change, that is certain. And maybe (if you leave a cilindric part) it will rotate like a pipe thrown in the air.
Removing parts of the Earth so that it would resemble a thumbtack will make its rotation much more visible.

Calin