# Gravitacional Field and momentum conservation

#### Littlepig

1. Homework Statement
So imagine we have Earth and Moon, and there is a tird body(A), equidistant from moon circular tragectory in one point, from Earth. whoever, that body haven't enought graviticional Force to pull moon from his orbital around the Earth.
Whoever too, that gravitacional force provokes positive linear aceleration when moon is aproching the equidistant point(somewhat like a comet aproxing the sun, provoking increase of velocity), and provokes negative linear aceleration when the moon is moving away from that equidistant point(like when a spaceshutlle is tring to move away from Earth): as aceleration has the same direction when the moon is aproching that point, and have opposite direction when the moon is moving away from that point).

So, we can say the moons momentun is conserved, as in a complete rotation, the moon's velocity is the same.

Now, hypoteticly Imagine Human already can transform all mass in energy, by Emc^2.
So, when the moon was moving away from the equidistant point, Human would transform all the (A) mass in energy, what would happen to the gravitational Field of (A)?? would the gravitational field disappear??

2. Homework Equations
P=mv(just the concept)
E=mc^2(just the concept)
Pf=Pi(momentum conservation)

3. The Attempt at a Solution

So, my real point is, if gravitational field disappear, the moon, instead of losing the velocity by (A) graviticional aceleration, it won't, what makes the moon to have highter momentum than in the begining of the process...
if we would transform that energy in mass again when the moon was aproaching the point again(after semi period), the moon would get positive aceleration again...
Where is the logical error here(if there is), has there is no momentum conservation. what can't be true has there are no dissipative forces included here...

Regards, Littlepig

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#### Hootenanny

Staff Emeritus
Gold Member
Where to begin. Firstly in relativity classical momentum is not a conserved quantity; however, energy and momentum must be conserved. Secondly, in general relativity the gravitational 'force' is produced by the curvature of space-time (as you have probably heard). Now, not only does mass curve space time; but energy also causes space-time to curve (momentum also curves space time). Therefore, if 'somehow' we could convert the mass of this mysterious body into energy, the gravitational field would not disappear.

I think that'll do for starters. (Btw is this a homework question - interesting course if it is)

#### Littlepig

Where to begin. Firstly in relativity classical momentum is not a conserved quantity; however, energy and momentum must be conserved.
yeh, I understood the concept not the detail, has you said, even in relativity must be a conservation, and that thing was missing me in this question...

Secondly, in general relativity the gravitational 'force' is produced by the curvature of space-time (as you have probably heard).
well, but i prefered to use the classical mecanics in gravity has i'm not quite known about general relativity(has you said, "heard" about)

Now, not only does mass curve space time; but energy also causes space-time to curve (momentum also curves space time).
that is waht i didn't know... and that was mistake...:P (always learning)

I think that'll do for starters. (Btw is this a homework question - interesting course if it is)
i'm 17years old, not have relativity still, but was in classroom when i putted this question to myself(so i can say is a homework right?)...to don't put a post so basic like this in the general forum, i prefered to put it here, in a "lower degree" #### Hootenanny

Staff Emeritus
Gold Member
that is waht i didn't know... and that was mistake...:P (always learning)
Learning it good, its when we stop learning that's the problem... i'm 17years old, not have relativity still, but was in classroom when i putted this question to myself(so i can say is a homework right?)...to don't put a post so basic like this in the general forum, i prefered to put it here, in a "lower degree" Never be scared of asking a question, if you have an inquisitive mind, you'll not go far wrong with your studies. (And who says that homework forums are at a "lower degree" that the general forums, you should see some of the posts in there :rofl: )
It was a pleasure 