# Perpetual Motion In The Gravitational Field

1. Aug 10, 2012

### physio

Can perpetual motion be possible in a gravitational field? If I take an object and into space from earth, the potential energy increases but as we go further away from the earth the forces which contribute in the work done decreases, thus it seems to me as if energy is destroyed. Because the kinetic energy of the object is directly supplied by me, the potential energy mgh starts to decrease as we move away from the ground, thus it seems that potential energy is decreasing. Please explain why this reasoning is wrong. Thanks!!!

2. Aug 10, 2012

### Vorde

Because potential energy increases as distance from the potential increases. Think about it, what happens if you double h in mgh.

3. Aug 10, 2012

### physio

But acceleration due to gravity is 0 for an object not under the influence of earth's gravity. Hence mgh=0.

4. Aug 10, 2012

### Vorde

You'll have to rephrase, I don't really understand. The gravitational field is infinite in reach.

5. Aug 10, 2012

### physio

Assume the object is at a height of 5 metres, the potential energy is mgh=5mg. Now I give it sufficient kinetic energy such that it starts ascending. As it is moving up the potential energy decreases and also the height is increasing from a reference position, but at a certain stage it escapes earth's gravitational field and now there is no acceleration due to gravity thus potential energy has been made 0. Also the object is moving because I have supplied the kinetic energy hence it seems to me that the potential energy has been destroyed. There is some flaw in this argument which I cannot discern.....

6. Aug 10, 2012

### fedaykin

I don't understand what relation your other questions have to perpetual motion. If you take an object and place it some distance away from Earth in space, and no other forces change the objects motion, the object will have kinetic energy equal to the work you did to move it when it returns to the point you started moving it, e.g. the surface of the Earth.

http://physics.info/gravitation-energy/ might give you some insight.

It is true that the potential energy per unit distance decreases as you get farther away from the Earth's center of mass, but you'll never be able to completely leave the influence of Earth's gravity in a finite amount of time. Note that any mass still has an escape velocity where an object will never return. An object that leaves the surface at escape velocity would only hit zero velocity after an infinite amount of time. The flaw in your argument seems to be the idea that you can escape Earth's gravity well.

If you're thinking of astronauts in microgravity as having escape Earth's gravity well, they have not. They are merely in freefall, but moving tangentially at an equal rate. Since all the objects around them are also falling, they are not pushed upward as we are by the surface of the Earth. You can experience a little bit of freewall in an elevator by jumping shortly before the car begins descending. Be careful though.

7. Aug 10, 2012

### Vorde

Acceleration due to gravity is never zero. It gets exponentially smaller and approaches zero but never reaches it. Just think mathematically, graph mgh where mg is a constant and h is a variable and see what happens as h (distance from ground) goes to infinity. (Hint: potential energy also goes to infinity)

8. Aug 10, 2012

### physio

What I have understood is that when you take an object to a certain height it's potential energy increases because of the acceleration i.e. the velocity of the object is greater at the lowest point when dropped from a height h2 than the velocity of the object when dropped from height h1 where h2>h1. So what I am driving at is this: can we move the object in a closed path in such a way that the object's velocity increases in short can we obtain perpetual motion in a gravitational field?

Also if we have given an object sufficient energy to break away from the earth's gravitational field then what happens to it's potential energy because now according to my understanding it cannot "fall" back in an elliptical fashion or directly since there is no "sufficient" force acting on the object to bring about the change.

9. Aug 10, 2012

### Vorde

But its potential force is still rising. It doesn't matter how fast the object is going (i.e. if it will ever return). Potential Energy is strictly a function of distance, therefore and distance increases potential energy will increse without regard to acceleration and velocity.

10. Aug 11, 2012

### physio

which formula are you using?

11. Aug 11, 2012

### Staff: Mentor

Sounds like you are describing escape velocity. If an object is traveling above escape velocity, it will continue to travel away from earth forever. All this means is that it has enough kinetic energy that it will never be able to trade all of that for gravitational potential energy.

12. Aug 11, 2012

### Vorde

The same formula you've been using the whole time. But it would work with any formula.

13. Aug 11, 2012

### physio

So you mean to say potential energy keeps on increasing as we move the mass from the earth's surface into space? But I thought the value of g kept on decreasing...

14. Aug 11, 2012

### izemabdo

HI!!! to request this (PHYSIO) look....there s no perepetual motion as you expected..but all depend on launching speed....so we got three cases
first in this speed are weak it can undergo a free fall
second if this, are so important , the object in space will search an equilibre position due to attractive forces applied by other planet..etc
here if we want a perpetuel motion we have ( as done in launching fusil) to communicate to this object a very important speed over space (after launching from earth)in other terms ,at space the object receive another speed (from a capsule for example that re fixe in space)..consequently , our object gonna do an elliptical trajectory which the earth occupates one of this pole.....i guess it s clear for you ...else you can contact me on my account facebook or in my gmail just to make things right

Last edited by a moderator: May 6, 2017
15. Aug 11, 2012

### gabbagabbahey

The formula $U=mgh$ is only valid relatively close to the Earth's surface. It is a first-order (linear) approximation of $U=-\frac{GMm}{r}$ (where $r$ is the distance from the centre of mass of the Earth - assuming that the Earth is a sphere, this is just its centre).

Clearly, as the distance from the center of the Earth increases, so does the potential energy (its absolute value decreases, but since it is negative, its signed value increases)

16. Aug 11, 2012

### izemabdo

gabbagabbahey ,right but don't forget other forces applied by other planets.....in space there is a solar system ..

17. Aug 11, 2012

### GarageDweller

Perpetual motion is impossible only in a more realistic context, if you approximate everything in central force problems, you can have non-physical perpetual motion.
For example, the orbits calculated using the effective potential continue until infinity. This is because we have approximated the system and ignored the rest of the universe
To be honest i find the idea very ill defined, motion is only meaningful when it is measured with respect to some observer, it is always possible to choose a frame in which an object is in motion.

18. Aug 11, 2012

### Vorde

You're complicating a simple situation. You're right, of course, but considering outside forces makes the mathematics much more annoying and yields the same end result.

19. Aug 11, 2012

### izemabdo

great, in reality all physics are approximations...& pereptuel motion in reallity doesn't exist
but according to our approximations we expect the possible motion.

20. Aug 11, 2012

### GarageDweller

The original poster is obviously not famaliar with taylor series, this will just confuse him more