Perpetual Motion In The Gravitational Field

gabbagabbahey

Quote by izemabdo

we conventionaly take this constant equal 0 constant=0
due to this even r--->infinity; U=0
or U=GMm/r +constant .....r-->infiity
we conclude constant=0

You are missing a negative sign. U=-GMm/r + constant. Taking the constant to be zero, U is a negative number that approaches zero, as r goes to infinity. The potential increases with distance.

izemabdo

Quote by GarageDweller

The constant makes no physical difference due to F=-Grad(U)

yes, true but according to this question maybe he or she wanna understand how can make to an object motion around the earth....is in it??????,

Vorde

Quote by izemabdo

yes, true but according to this question maybe he or she wanna understand how can make to an object motion around the earth....is in it??????,

You're not making any sense, and it doesn't seem like the OP is currently online.

izemabdo

Quote by gabbagabbahey

You are missing a negative sign. U=-GMm/r + constant. Taking the constant to be zero, U is a negative number that approaches zero, as r goes to infinity. The potential increases with distance.

no sign -

the primitive of -1/r² are 1/r !!!!!

GarageDweller

Comedy gold
Perhaps we should change the flat space interval to dxdtdydz=ds^2 just for kicks too

davenn

Quote by GarageDweller

Comedy gold

isnt it !!! LOL

will some one please just link to a factual www site with the correct formula and put every one at ease

Dave

gabbagabbahey

Quote by izemabdo

no sign -

the primitive of -1/r² are 1/r !!!!!

[tex]\mathbf{F}=-\mathbf{ \nabla } U = - \mathbf{ \nabla } \left( -\frac{GMm}{r} \right) = -\frac{GMm}{r^2}\hat{r}[/tex]

The force of gravity is pointed radially inward toward the Earth. The negative sign is necessary.

Vorde

Quote by davenn

isnt it !!! LOL

will some one please just link to a factual www site with the correct formula and put every one at ease

Dave

No need, gabby's said it a couple times, he's just not listening.

GarageDweller

Quote by gabbagabbahey

[tex]\mathbf{F}=-\mathbf{ \nabla } U = - \mathbf{ \nabla } \left( -\frac{GMm}{r} \right) = -\frac{GMm}{r^2}\hat{r}[/tex]

The force of gravity is pointed radially inward toward the Earth. The negative sign is necessary.

Thank you, i wanted to put it this way but did not know how to type that

izemabdo

Quote by davenn

isnt it !!! LOL

will some one please just link to a factual www site with the correct formula and put every one at ease

Dave

sorry for this language accent, but i used to speak french well

physio

Quote by Vorde

Okay, let's define potential energy.

If you have a region with a massive body, every object in the region will be attracted to that body with an acceleration depending on how far away from that body the object is (gravity).

If you put an object at a certain distance away from the body without any starting kinetic energy (i.e. motionless), it will gain motion (and gain kinetic energy) and start moving towards the body (because of gravity). Obviously kinetic energy is not conserved or this would be impossible.

So what we do is add in another type of energy, called potential energy. If you put the object right next to the body, it won't move (akin to being on the surface of the earth), if you move the object away from the body you would have to exert energy to move it away from the source of gravity (because it's being pulled in the opposite direction).

The potential energy of an object a certain distance away from a source of gravity is defined as the amount of energy it takes to bring the object to that distance when you start with the object right at the source of gravity (actually it's defined as the work required in lifting the object not the energy required in the lifting the object, but if you don't know what work is then thinking of it as energy is fine).

If you understand that, realize that no matter how little the acceleration from the massive body is (i.e. how far away you are from the source of gravity), it will always take some energy to move further away from the body: meaning that potential energy will always increase with distance.

Okay...so if I have an object the size of Earth and another object taken from the planet and I leave the object in space (considering no other objects in space), then will it start directly falling towards the larger object and vice versa with an initial low velocity and then as the distance decreases the velocity increases?

Am I right in saying so? Have I understood??

I have further 2 questions..

1) Why do you say it's the work required and not the energy required? Are they both not mathematically the same?

2) Can I safely generalize that force (any of the fundamental forces) is the prime reason for potential energy then?

voko

Quote by physio

Okay...so if I have an object the size of Earth and another object taken from the planet and I leave the object in space (considering no other objects in space), then will it start directly falling towards the larger object and vice versa with an initial low velocity and then as the distance decreases the velocity increases?

If the initial velocities of the two objects are zero relative to each other, then yes, they will move toward one another with ever increasing velocity. If we treat both objects as point masses, then we even get infinite velocities at the impact time; this, of course, will not happen with real objects.

If, however, the mutual velocity is not zero, and it is not directed along the line between the two objects, then they will orbit about their mutual center of mass. Again, this is completely true only for point masses. Real objects may collide if the orbits are not well separated. The separation depends on the initial position and velocities. If the separation is adequate, they will move "perpetually" if nothing else acts on them and we assume that the objects do not undergo any changes.

physio

I don't know why I am digressing but (and this is completely off topic) if in the universe everything attracts everything then shouldn't the universe sorta collapse i.e everything will come together and smash us into extinction....How is it expanding? Also if the universe is expanding, then it is expanding into what??? A big thanks to everyone whoever has helped me understand the concept of P.E.

Vorde

I'd start a new topic. There's lots of stuff to explain.

sophiecentaur

Quote by GarageDweller

I'd grab a book

I totally agree. Half of this thread has consisted of telling the OP what he could have found in a basic Physics text book. Trying to learn something from scratch in a series of mis-directed questions, followed by answers that are then mis-construed is not the best way to get to know a formal subject like Physics.
It doesn't even need to involved spending money on a text book. There are dozens of .edu web pages that have all the information, well described and accurate - for free! It just requires a bit of time and effort to take it on board.

physio

I am reading lectures on physics by r.feynman as for the .edu web pages I think you are right...:)

Vorde

Quote by physio

I am reading lectures on physics by r.feynman as for the .edu web pages I think you are right...:)

People might totally disagree with me here, but I wouldn't say that's the best place to start. The Feynman Lectures are much more mathematical and rigorous than a everyday physics book, but less so than a real textbook. I find that his lectures are fantastic (the best, really) for review, but not the best for learning stuff (remember the lectures are based off of a freshman physics course designed by him that was a self-admitted failure).

I'd start with some of the physics-orientated books for the everyman that are all around if you want to just know what goes on in the world. If you are more serious and care about the mathematics I'd get a real textbook (there are free ones online) or try to find a class you can take in introductory physics (that's vague, but I don't know your age).

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GarageDweller	Comedy gold Perhaps we should change the flat space interval to dxdtdydz=ds^2 just for kicks too

physio	I don't know why I am digressing but (and this is completely off topic) if in the universe everything attracts everything then shouldn't the universe sorta collapse i.e everything will come together and smash us into extinction....How is it expanding? Also if the universe is expanding, then it is expanding into what??? A big thanks to everyone whoever has helped me understand the concept of P.E.

Vorde Recognitions: Gold Member	I'd start a new topic. There's lots of stuff to explain.