The Effect of Planets Rotation within its Galaxy?

[erickdt]

Hello All,

A curious person here would like to know if a planet gains gravitational force as it rotates around the center of its galaxy. From what I understand this speed is quite impressive (the speed at which we travel around the center of our galaxy) so I'm wondering if the sheer mass of our planet (or sun), traveling at that velocity, would have the effect of amplifying Earth's (or the suns) gravitational force.

Thanks in advance for any explanation!

E

 

[Simon Bridge]

Welcome to PF;
I'm guessing you are thinking that energy is mass so a high kinetic energy would result in a higher "mass" which means extra gravity compared to if it is still.

I think the short answer is "yes and no".
The generator of the gravitational field is the stress-energy-momentum tensor $T^{\mu\nu}$ whose components are energy $T^{00}$, co-momentum $T^{0,j}$ and co-stress $T^{ij}$.

Anything with a non-zero T^μν will feel gravity. In the non-relativistic limit co-momentum and co-stress vanish and energy reduces to mc², which explains why masses appear in a non-relativistic description of gravity.

Kinetic energy contributes to gravity, mainly in the energy and co-momentum parts.

A quick calculation should show you how fast the Sun would have to be going to give it additional energy similar enough to it's mass-energy, and so show up as additional gravity that you'd notice. Even so - the Earth moves with the Sun, so the Sun is not going all that fast wrt us... and it is relative speeds that count here.

You also seem to be asking if overall gravity increases due to motion - I think the best answer here is "no", after a circuit of the galaxy, the Solar system has the same gravity that it started with.

Introduction to general relativity.
http://preposterousuniverse.com/grnotes/grtinypdf.pdf

 

[erickdt]

Hello Simon,

Thanks for your response! It looks as though I have some more reading to do!

I guess what I'm wondering is whether or not the gravitational pull or stars on their respective orbiting planets is in some part due to the velocity at which they orbit the center of our galaxy.

Our sun for example orbits the center of the Milky way at about 139 MPS. Pretty darn fast! Let's say it wasn't orbiting anything at all, just standing "still" in space. Would its gravitational pull be less than it currently is moving at its impressive speed?

Along these same lines, would an object that rotates around the center of the Milky Way have less gravitational force than the same object rotating around the outer extents of the Milky Way (assuming their moving at the same RPM)? The object that is further out from the center would be going faster since it would have to be covering more space to maintain the same RPMs as the inner object.

Thanks again for your help! I really appreciate it!

E

 

[Simon Bridge]

I guess what I'm wondering is whether or not the gravitational pull or stars on their respective orbiting planets is in some part due to the velocity at which they orbit the center of our galaxy.

No. But it is in some small part due to their velocity with respect to their planets.

would an object that rotates around the center of the Milky Way have less gravitational force than the same object rotating around the outer extents of the Milky Way (assuming their moving at the same RPM)? The object that is further out from the center would be going faster since it would have to be covering more space to maintain the same RPMs as the inner object.

The short answer is "no".
The gravitational force in question is the same both ways - the relative velocity contributes a component.
There is no absolute frame for velocity, so at each instant, the outer object is the fast one in the frame of the inner object and the inner object is the fast one in the frame of the outer one.

There are complications due to the large distances and the fact that rotating frames are non-inertial.
We are also dangerously close to mixing up the models too much.

BTW: properly, something that goes around another is said to be circling or orbiting - not rotating.
The term "rotating" is reserved for objects that turn about their own axis. So the Earth rotates (on it's axis) as it orbits the Sun: two different motions.