Center of gravity paradoxes

[pioneer]

The inside of the shell may show zero gravity. But if you introduce another mass, inside, the remaining empty space is still zero gravity but the mass will still have own gravity, since by the nature of mass, it has gravity. What happens, the surface needs to change its gravity field so it can compensate for the inner mass, so that the inner space is zero gravity.

 

So if we had two shells one with and one without an inner mass, both will have the zero gravity inside, but the outsides will be slightly different.

 

Here is a quote from the article suggested by BenTheMan.

 

"Something interesting to note is that when the inner sphere is introduced, the charge distribution on the outer sphere changes. The excess charge no longer lies only on the outside. The charge must redistribute itself so that E = 0 inside the conductor."

[Sisyphus]

No, if there's another mass inside the sphere, then the gravity inside is pulling towards that mass. There's still zero gravity from the shell, though.

[swansont]

The example with the electric field has the requirement that there be no field inside the conducting shell itself (i.e. the thickness of the shell), which is why the charge redistributes when an inner charge is introduced. There is no similar effect/boundary condition for the mass and gravity; there will be a field inside the thickness of the shell — you can model it as a series of thin shells.

[elas]

I am not going to join in this debate, but I am surprised that you seem to be unaware of the fact that items released in the cabin by astronauts always end up clinging to the shell fittings. (not to the astronauts or internal items).

[DrDNA]

Hey.....wasn't this on an episode of Stargate SG1...as in blatently stolen from StarTrek Next Gen (or Voyager?)....as in pilfired from the original StarTrek ?

 

If those thieves did it, it must be true...?

[swansont]

I am not going to join in this debate, but I am surprised that you seem to be unaware of the fact that items released in the cabin by astronauts always end up clinging to the shell fittings. (not to the astronauts or internal items).

 

Non sequitur. The argument does not imply that one is unaware of such things, since

 

(a) it's not gravitational attraction that's involved, since we're talking of order maybe tens of nm/sec² of acceleration (what you'd get for ~1,000 kg at 1m), which would take > a day to travel a meter if starting from rest. Residual motion from letting stuff go is responsible for objects drifting to the walls.

 

and (b) the shells of those cabins aren't spherical anyway, so the geometry isn't right for comparison.

[Quartile]

A baseball is inside a basketball.

 

If I'm following this thread correctly, the baseball experiences no gravitational effects from the basketball because the basketball acts as a shell and shells have no gravitational force inside of them.

 

First of all, isnt gravity supposed to act in a straight line? It would seem that the Earth would have to have some constant tangential acceleration in order to avoid being sucked into the Sun. Where does the Earth get that acceleration?

 

What if this basketball+baseball system is in orbit around the Earth? Where is its center of gravity?

 

On another note, would it work mathematically to model our solar system as being inside of an imaginary shell in order to calculate its gravitation on other solar systems/celestial bodies? Im thinking this could work because I imagine there is a large distance between our solar system and other solar systems, as "solar" implies the presence of a star and the nearest star to us is actually quite far away.

 

When calculating their trip to the Moon, did NASA have to consider the gravitational effects of bodies other than the Earth and the Sun?

 

What is the imaginary point that makes orbits elliptical in our solar system? Why does it exist, other than to account for elliptical orbits?

[swansont]

Orbits don't require a tangential acceleration, just the appropriate speed. An object moving in a circle feels an acceleration of v²/r, so if that's equal to the gravitational acceleration, presto, you've got a circular orbit.

[JohnB]

To see if I've got this right.

 

If we have a Galaxy inside a Dark Matter Cloud. Anything outside the cloud will feel the effect of gravity due to the mass of both the Cloud and the Galaxy. However the Galaxy will not interact gravitationally with the cloud. As in, gravitationally speaking, from the POV of the Galaxy, the Cloud isn't there.

 

Have I got that right? I hope so as it answers a question I've been wondering about.

[insane_alien]

well, if the cloud formed a shell around the galaxy then yes. but from observations the could is interspersed with the galaxy. this means that it interacts with the part of the could that is within the galaxy but that which forms the shell outside a sphere containing the galaxy doesn't affect the galaxy.

[JohnB]

Thanks, that's how I thought it must work.

[Quartile]

Orbits don't require a tangential acceleration, just the appropriate speed. An object moving in a circle feels an acceleration of v2/r, so if that's equal to the gravitational acceleration, presto, you've got a circular orbit.

 

I understand.

 

Why do planets move in circles when gravity acts between two bodies directly? Am I missing something?

[Sisyphus]

I understand.

 

Why do planets move in circles when gravity acts between two bodies directly? Am I missing something?

 

Gravity causes the planet to constantly accelerate directly towards the sun, that's true. But the planet also has a velocity at right angles to the sun, and so its inertia is carrying it in that direction while gravity is constantly pulling it sideways, so the end result is a curve (specifically, an ellipse), and the planet just ends up endlessly circling the sun.

[uncool]

Hrm...just a question on the math of it.

It seems to me that if you have a uniform sphere, then gravitational attraction will always be towards the cener. Think about it this way: Say the radius of the sphere is R. Then if you integrate the forces over each part of the ball, try integrating it by spheres around the object (not the sphere). For each spherical surface around the object until the spheres hit the wall, there is no force. However, once you hit the surface, the force drops off in one direction - so the total force for those spheres is towards the center. Therefore, since the force in each sphere is towards the center, the total force must be towards the center.

 

Even for a hollow sphere, the total force shouldn't be 0...

=Uncool-

[Quartile]

But the planet also has a velocity at right angles to the sun, and so its inertia is carrying it in that direction while gravity is constantly pulling it sideways, so the end result is a curve (specifically, an ellipse), and the planet just ends up endlessly circling the sun.

 

It is this velocity at a right angle that I am interested in. Why does it occur if gravity is the only force present between planets in the solar system? Where does this velocity come from?

 

i found this on the wiki for 'orbit':

First, [Kepler] found that the orbits of the planets in our solar system are elliptical, not circular (or epicyclic), as had previously been believed, and that the sun is not located at the center of the orbits, but rather at one focus.

 

If there is a focus other than the sun, what is it? I am assuming that the answer to this question is explained by GR?

 

If a baseball is inside a basketball and the basketball is in orbit around the Earth, do both the baseball and the basketball experience a gravitational force towards the Earth's center, or are they both accounted for as one mass with a center of gravity different than their individual centers of gravity?

[Spyman]

It is this velocity at a right angle that I am interested in. Why does it occur if gravity is the only force present between planets in the solar system? Where does this velocity come from?

The Solar System is believed to have formed according to the nebular hypothesis

...

This theory holds that 4.6 billion years ago the Solar System formed from the gravitational collapse of a giant molecular cloud.

...

The region that would become the Solar System, known as the pre-solar nebula, had a diameter of between 7000 and 20,000 AU and a mass just over that of the Sun (by between 0.1 and 0.001 solar masses).

http://en.wikipedia.org/wiki/Solar_system

 

As it collapses, three physical processes shape the nebula: it heats up, its spin increases, and it flattens. The nebula heats up because atoms move more quickly as they fall deeper into the gravitational well and become denser, colliding more frequently: gravitational potential energy is converted to kinetic energy of the atoms, or thermal energy. Second, while initially imperceptible, the solar nebula had some small amount of net rotation (angular momentum), and because angular momentum is conserved, the nebula must rotate more quickly as it shrinks in size. Finally, the nebula must also flatten into a disk, called a protoplanetary disk, as collisions and mergers of blobs of gas average out their motions in favor of the direction of the net angular momentum.

http://en.wikipedia.org/wiki/Planetary_formation

 

If there is a focus other than the sun, what is it? I am assuming that the answer to this question is explained by GR?

Kepler wrote his laws of planetary motion long before Newton, GR is not necessarily.

http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

(The picture shows the focal points.)

 

If a baseball is inside a basketball and the basketball is in orbit around the Earth, do both the baseball and the basketball experience a gravitational force towards the Earth's center, or are they both accounted for as one mass with a center of gravity different than their individual centers of gravity?

Both experience a gravitational force towards Earth. From Earths view they can be considered as one total mass.

After all, Earth is made of many small pieces and it's easier to sum them up to one total mass with a common center, than to calculate the forces for each one, but the end result is the same.

[Quartile]

Kepler wrote his laws of planetary motion long before Newton, GR is not necessarily.

http://en.wikipedia.org/wiki/Kepler%...anetary_motion

(The picture shows the focal points.)

 

I understand that there is a focus other than the Sun and that it is needed for elliptical orbits to make mathematical sense. What I dont understand is why this focus exists in physical terms, i.e., what is it and why does it exert gravitational force on planets?

[Sisyphus]

I understand that there is a focus other than the Sun and that it is needed for elliptical orbits to make mathematical sense. What I dont understand is why this focus exists in physical terms, i.e., what is it and why does it exert gravitational force on planets?

 

The other focus is nothing. It doesn't exert any force on anything. The math just works out that if you exert a force (gravity) on an object that decreases with the square of the distance, it will go in an ellipse around you, where you are at one of the foci of that ellipse. It has nothing to do with GR, and the math is not that complicated - you only need basic calculus (like Newton used).

 

As for where that perpendicular velocity comes from, it is still there from the formation of the solar system (once you have velocity, you don't need an additional cause to keep having velocity, it's just inertia). If you think about it, there's almost guaranteed to be a perpendicular velocity of some kind, just because the only way there wouldn't be was if two objects happened to be heading exactly towards one another. Anything else has a perpendicular velocity, and thus they end up orbiting on another.

[Spyman]

I understand that there is a focus other than the Sun and that it is needed for elliptical orbits to make mathematical sense. What I dont understand is why this focus exists in physical terms, i.e., what is it and why does it exert gravitational force on planets?

The focal points are just coordinates in space they don't exert gravitational force.

 

An Ellipse is characterized by its two focal points:

In mathematics, an ellipse is the locus of points on a plane where the sum of the distances from any point on the curve to two fixed points is constant. The two fixed points are called foci (plural of focus).

http://en.wikipedia.org/wiki/Ellipse

[Quartile]

I understood that GR is not needed for this.

 

The focal points are just coordinates in space they don't exert gravitational force.

 

At least one focal point does exert gravitational force because it is the center of gravity of the sun. I understand that the other point doesnt exert gravitational force because there is no mass there to account for it, but at the same time it would seem like it does exert gravitational force because the orbit of planets is elliptical! As little as I understand about physics, I have the tendency to assume that an orbit with one focus, the sun, should tend to be circular rather than elliptical. Can the elliptical orbit of Earth be accounted for by summing the vector components of gravitational force acting on it not only from the sun but from other planets?

 

I have checked over my logic several times to make sure im not being a retard and it looks good so please help!

[D H]

I understand that the other point doesnt exert gravitational force because there is no mass there to account for it, but at the same time it would seem like it does exert gravitational force because the orbit of planets is elliptical! As little as I understand about physics, I have the tendency to assume that an orbit with one focus, the sun, should tend to be circular rather than elliptical. Can the elliptical orbit of Earth be accounted for by summing the vector components of gravitational force acting on it not only from the sun but from other planets?

 

The elliptical orbit arises in the two body problem (e.g., a universe that comprises the Sun and the Earth and nothing else.) The general solution of the two body problem is a conic section: a hyperbola, a parabola, an ellipse, or a circle. A truly circular orbit is essentially impossible to achieve. Everything has to be just right for an orbit to be circular.

 

As soon as you add in influences other than the Sun, the planets no longer follow truly elliptical paths. The paths are close to elliptical because the Sun dominates over even Juputer by three orders of magnitude.

[Spyman]

I have the tendency to assume that an orbit with one focus, the sun, should tend to be circular rather than elliptical.

A circular orbit requires a constant orbital speed, maybe that's the key point here ?

 

The planets travels faster while close to the Sun and slows down when they are farther from the Sun.

[CanadaAotS]

Hm.

 

When the planets were created from the gobbledy-gook that was the solar system, they ALL had an angular momentum of some kind. Anything that didn't was sucked into the sun.

 

The thing to realize too is that the 1st focii isn't centered on the sun, it's centered on the gravitational centre between the sun and the orbitting body... it just so happens that the sun is so gravitationally dominant so this point is very close to the sun's centre.

 

The 2nd focii's placement is placed by what the obitting body's initial velocity was when it was caught by the sun's gravity.

 

 

 

Btw, gobbledy-gook is a scientific term, I swear.

[Quartile]

Thanks!