Space elevator gravity

[george7378]

Hi,

I just read two books with space elevators in them, and one suggested that the gravity would gradually decrease as you ascend until you reach geostationary altitude where you would be weightless, while the other said that you would be weightless even at LEO level. Which is right?
I believe that it is the gradually decreasing idea as the other suggests that you would be weightless standing in a tall building, and you are not in orbit if you stay above the same point at LEO altitude, but I don't really know.

Thanks.

 

[T.Neo]

If you were standing in LEO on a tower made of unobtanium, you'd definitely feel the effects of gravity. Gravity in LEO would perhaps be something like 90% of what it is at sea level.

Of course on a space elevator it'd be a combination of the effects of gravity and the centrifugal force holding up the counterweight...

 

[TSPenguin]

You are too slow at LEO to counter the gravity. You will only be weightless once you reach GSO.

 

[Pilot7893]

The first book is correct, I would assume. Just because you are out of Earth's atmosphere doesn't mean you will be weightless. Think of it this way. In a geostationary orbit position on a space elevator, the outward force created by Earth spinning cancels out the pull of gravity. Lower than that, gravity has greater force. Higher than that, the centrifugal force is greater.

 

[Izack]

The first suggestion is correct.
Objects in orbit do not experience 'zero-G' the way people think. Gravity is roughly equivalent at 300km altitude to what it is at sea level.
Objects in orbit are actually in free-fall. The only reason they don't hit the ground is that they are travelling 'sideways' so fast that they manage to fall in circles around the planet (Newton's Cannon and all that.)
A space elevator has almost no horizontal velocity component beyond that of the Earth's own rotation (not sure what the exact figure is in SI units...darned Americans ), and is therefore subject to almost all of the apparent force of Earth's gravity.

 

[george7378]

Thanks - I thought Arthur C. Clarke was right

 

[dbeachy1]

As I understand it, if you're ascending a space elevator you will not be weightless until you reach geostationary orbit (i.e, at or near the "top of the cable") because until then your orbital velocity won't be high enough to stay in orbit without the cable -- i.e., you would not be weightless yet. So as you ascend the cable you are also being accelerated into a higher-energy sub-orbit until finally you reach orbital speed at the top.

Assuming that's correct, that leads to my next question: wouldn't the energy to accelerate you to orbital speed be transferred from the Earth's rotational energy to you as you ascend the cable? (This would be in addition to any energy required to pull you up the cable, of course, although the energy required would gradually decrease until you were weightless at the top.) And then your orbital energy would be transferred back to the Earth's rotational energy when you descended the cable, correct? If we think of the cable as simply a rocket engine pushing straight up on a rocket, something has to accelerate the rocket to orbital velocity -- and since the elevator cable is attached to the earth, wouldn't the cable tend to deviate from 90 degrees as the elevator ascended? (Of course, that would assume the elevator/whatever had enough mass to make the cable deflect as the elevator was accelerated.)

 

[Fizyk]

Assuming that's correct, that leads to my next question: wouldn't the energy to accelerate you to orbital speed be transferred from the Earth's rotational energy to you as you ascend the cable?

Yeah, in a way. When you are ascending, you are increasing the moment of inertia of the Earth+you system, so by the conservation of angular momentum, the angular velocity of the Earth+you system must decrease. This means you are actually slowing the Earth's rotational movement, and you can say that's because you are stealing its energy to gain speed.

 

[dgatsoulis]

Please correct me if i'm wrong, but the only way to build a space elevator, is to get a craft to GSO orbit and then anchor the cable down to Earth, right?

But as you descend back to Earth, your orbital speed is higher, so how is it possible? Wouldn't the cable "bent" to match the Orbital speed of your altitude?

 

[tori]

It would "hang" down. At any altitude below GSO the velocity of the cable is lower than the orbital velocity at that point, and as a result nonzero gravity is perceived.

This is in essence how gravity gradient torque works.

 

[dgatsoulis]

It would "hang" down. At any altitude below GSO the velocity of the cable is lower than the orbital velocity at that point, and as a result nonzero gravity is perceived.

This is in essence how gravity gradient torque works.

So, at GSO you wouldn't feel any gravity, but lower than that, you would feel a percentage of it, right?

What happens at altitudes above GSO?

 

[Tex]

We already have a space elevator discussion which may answer some of your questions:

http://www.orbiter-forum.com/showthread.php?t=13843

In addition this may help, check the image on the right:
[ame="http://en.wikipedia.org/wiki/Space_elevator"]Space elevator - Wikipedia, the free encyclopedia[/ame]

 

[tori]

That's right. If you had a ship at GSO and managed to stick your legs out in the direction of Earth, there would be some minuscule acceleration pulling on them (about 5 nm/s² assuming your legs' CoG is one meter down of the GSO line).

Above GSO there would be a centrifugal force pulling stuff away (just like in any other orbit - that's why stuff on the ISS doesn't stay in one place but drifts on its own. I'm sure there's been a study on this already

One way to look at it is using two bodies. Body A is in a circular orbit. Now imagine you extend another body on a crane from A in the down direction. This body ("B") will now be at a lower altitude but at the same velocity as A, which is lower than the orbital velocity at this lower altitude. So as a result body B would now be in the apogee of an elliptical orbit, wanting to go down (i.e. perceiving a percentage of the gravity).

If B was extended upward (away from the planet), it would have a higher velocity than that needed for a circular velocity at this higher altitude, again forcing it into an elliptical trajectory, only this time it would be in its perigee, wanting to go up ("centripetal" force).

 

[statickid]

Please correct me if i'm wrong, but the only way to build a space elevator, is to get a craft to GSO orbit and then anchor the cable down to Earth, right?

But as you descend back to Earth, your orbital speed is higher, so how is it possible? Wouldn't the cable "bent" to match the Orbital speed of your altitude?

and a concise and to the point answer to this question is simple, the lower portions of the cable are NOT in "orbit" so no, it would not be bent and there wouldn't be an orbital speed to match.

on a similar but different subject, people interested can try this "extreme sport" in orbiter: EXTREME SPACE DIVING! get into orbit with your favorite ummu carrying, high fueled, high thrusting vessel. get into a high orbit (how high? experiment, i don't think i've gone higher than GSO) then burn retrograde until you have negated all tangential velocity to the earth. the vessel will begin to freefall towards the surface, so level the horizon and turn on the hover, then adjust it until your vertical speed is zero. another way is to point the nose at the ground and adjust retros to do the same. then drop you ummu! he/she will probably run out of 02 before hitting the ground but you can enjoy the view through the DEAD message

 

[RisingFury]

The first one is correct, assuming the elevator travels at the same velocity or very slow acceleration.