Gravity and increase and decrease of orbit

[princess]

So, I was thinking about gravity. Now, I know how gravity works. But my question is this.

 

The further away you get from an object, the less the gravity is apon it. Also, I know about the orbit or w.e thing.

 

So if you are 100 miles off the earth, going at the exact velocity to keep you in geostationary orbit; if you raise the height of your orbit 1 more meter, your speed is no longer fast enough to keep you in geostationary orbit, since you would need a faster speed due to the increased circumference. What isn't added into this thought is the of the decrease in gravity's effect apon the satelite.

 

This means that not only would you be going 1/10th slower than the speed required to stay in geostationary orbit, but you now have 1/10th less gravity pulling you down.

 

So, if your speed stayed the same, would you just fall back into the correct orbit? Also, what about momentum? If your momentum was going downward due to insufficient speed to stay in geostationary orbit, would your inertia actually result in putting you further below your starting point, meaning you would be going faster than circumference allows, and therefor, would the satellite go back up?

 

 

If this is the case, then it would seem to me that all one would need to do is throw a satellite into orbit, and let it find it's own height in which it wants to stay?

 

 

Am I missing some variables?

 

P.S. im asking this because I just thought of it at the top of my head, and if it's true, would make a fascinating essay for my teacher!

[cuttergirl]

 

I did a little research, and I came up with this answer. Please correct me if I'm wrong guys!

 

We know that the circumference of the earth is 24,934 miles. We also know that gravity at sea level is 9.81 meters per second. Every meter above sea level you increase, gravity decreases by .0003086 cm squared.. I think. Also, if you are at an altitude of 100 miles above earth, that would mean that the circumference is now 25,214 miles.

 

So, (25,214 x 100) / 24,934 = 1.123% more circumference distance that the satellite is traveling than it would be if it were on the surface of Earth.

 

If we were to increase this height by 1 meter, then we are increasing the height 1/1609.344ths of a single mile. This would mean that 25,214 would turn into 25,214.2 about. 1.124% So we can say that increasing the height of the satellite by one meter would increase it by 1 thousandths of a percent in circumference.

 

Now for gravitational pull~

 

If gravity is 9.81 meters per second at sea level, and it decreases by .3 x 10^-3cm, than we can say that; Gravity at 100 meters above sea level would be 9.81 - (160,934.4 x .000003)

 

This means that the force of gravity at 100 miles above sea level is 9.3271968.

 

If we increase the height of the satellite by 1 meter, than the equation would become: 9.81 - (160,935.4 x .000003)

 

So the force of gravity 100miles + 1 meter above sea level is 9.3271938.

 

(9.3271938 x 100) / 9.3271968 = .000043

 

This means that Gravity would have went down .000043% due to the height increase of the satellite by 1 meter. or 4 billionths of a meter.

 

 

 

 

wow... lots of math. Break time. Brb, food.

[ajb]

The escape velocity is the initial speed (without extra propulsion) that is required to escape the gravitational potential (i.e. never get pulled back).

 

So, an object can be initially thrown out above the escape velocity, but still be captured in an orbit. (By orbit, I mean some curved path. )

 

For geostationary orbits you can show that the radius (distance from centre of the Earth) cubed is proportional to one over the angular speed squared,

 

[math]r^{3} = \frac{GM}{\omega^{2}}[/math]

 

where [math]G[/math] is Newton's constant, [math]M[/math] is the mass of the Earth and [math]\omega[/math] is the angular speed.

 

So from the above you can investigate how speed changes the hight.

 

 

 

By momentum, as we have objects moving in circles, it makes sense to talk about angular momentum.

 

The (magnitude of the) angular momentum of the satellite is

 

[math]L = m r^{2}\omega[/math],

 

where [math]m[/math] is the mass of the satellite.

 

 

Technically the angular speed should be a vector called the angular velocity and the angular momentum is also a vector. If you look at cuttergirl's picture these vectors point up or down. Note they are not along the radius.

[swansont]

For geostationary orbits you can show that the radius (distance from centre of the Earth) cubed is proportional to one over the angular speed squared,

 

[math]r^{3} = \frac{GM}{\omega^{2}}[/math]

 

where [math]G[/math] is Newton's constant, [math]M[/math] is the mass of the Earth and [math]\omega[/math] is the angular speed.

 

Surely you don't mean geostationary here (it is also mistakenly used in the OP) — this is the general orbit equation one can derive by setting the centripetal force equal to the gravitational force. A geostationary orbit has the added requirements that the orbital period be a day and that the orbit be equatorial.

 

i.e. there is only one solution for r for a geostationary orbit.

[ajb]

Surely you don't mean geostationary here (it is also mistakenly used in the OP) — this is the general orbit equation one can derive by setting the centripetal force equal to the gravitational force. A geostationary orbit has the added requirements that the orbital period be a day and that the orbit be equatorial.

 

i.e. there is only one solution for r for a geostationary orbit.

 

Indeed you are correct, an oversight on my part.

[infinitesolid2]

How do communication satalites float in space without crashing to earth.

Why does the moon not fly off?

Is there somoething else other than gravity?

 

Objects fall to earth at the same speed, all this does not make sense.

 

Gafferuk. Bristol.

[DJBruce]

The satellite is falling to the Earth the same rate the curve of the Earth is falling away from the satellite thus an orbit is formed.

[infinitesolid2]

The satellite is falling to the Earth the same rate the curve of the Earth is falling away from the satellite thus an orbit is formed.

 

 

Does not make sence. This orbit & gravity is a little bit strange.

 

I don't even believe the universe is expanding. Pictures is taken of distant galaxys over many days, where the blur from expanding universe?

 

Gafferuk, Bristol.

Edited August 15, 2009 by infinitesolid2

[iNow]

Reality has no requirement to act in a way which makes sense to you, nor does your belief have anything whatsoever to do with the way nature operates.

 

The satellites don't "float." They are placed at such a height and travel at such a speed that they fall down to the earth at the same rate that the earth curves away from them... Precisely as DJBruce already indicated above.

 

As for expansion, the light reaching us is red shifted, which in some ways could be considered a blur if you really want to look at it in such a manner.

[Klaynos]

Off topic posts moved to This Thread, could we please keep to the subject of orbits.

 

Things in orbit are continually falling but because they are also moving tangentially to the earth they just keep missing the surface, if they're in a steady circular orbit they keep missing by exactly the same height.... Gravity constantly accelerates them so their velocity remains tangentially to it.

Edited August 15, 2009 by Klaynos
Consecutive posts merged.

[infinitesolid2]

Off topic posts moved to This Thread, could we please keep to the subject of orbits.

 

Things in orbit are continually falling but because they are also moving tangentially to the earth they just keep missing the surface, if they're in a steady circular orbit they keep missing by exactly the same height.... Gravity constantly accelerates them so their velocity remains tangentially to it.

 

Theres rubbish floating in space left by us. why does this stuff not fall to earth between earth and the moon?

[insane_alien]

Theres rubbish floating in space left by us. why does this stuff not fall to earth between earth and the moon?

 

perhaps because there is no earth between the earth and the moon?

 

but on a more serious note, the debris leftover will not come out of orbit until it either hits something else and slows down or is slowed down by drag with the tenuous and extremely thin atmosphere present at that altitude.

[Klaynos]

Because the stuff we left there was in a stable orbit, it will eventually fall to earth though due to losing energy due to friction.