PDA

View Full Version : Dropping balls from a space elevator



Tucson_Tim
2009-Apr-19, 11:05 PM
Let's assume a fully operational space elevator, attached at the equator, where the center of mass is at the geosynchronous orbit altitude (approx 22,000 miles), with a large counterbalancing mass (space station?) at the top. For my question, let's also ignore the Earth's atmosphere and its effects. If you like, the space elevator can be on the Moon or Mars. Please see the following link:

http://en.wikipedia.org/wiki/Space_elevator

My question evolves from reading the Clarke novel Fountains of Paradise:

http://en.wikipedia.org/wiki/Fountains_of_Paradise

Question: Let's say on our trip up the elevator we stop every 20 miles or so and drop a ball from a "window". We don't give the ball any other velocity -- we just drop it straight down. Now, in Clarke's novel, Morgan is able to free an auxillary battery and it drops. He states that at the current altitude, which is 405 km, that it will land 10 km directly east of the base of the elevator. I believe the dropped balls (at every 20 miles of altitude) will follow parabolic curves to the ground. We continue to do this till we get to the geosnychronous altititude of 22,000 km. Now at 22,000 miles, the ball will not fall but will just float along next to the elevator -- in geosynch orbit. I have several questions now:

1) For balls dropped from under the geosynch point, are the falling paths indeed parabolic? The balls don't have enough radial speed to be in these orbits.

2) Are there points nearing the geosynch point where the balls will fall but miss the Earth and end up in some elliptical orbit?

3) What will be the path of balls dropped from above the 22,000 mile geosych orbit? Say from the space station at the top? The balls have too much radial speed to be in these orbits.

grant hutchison
2009-Apr-19, 11:16 PM
Every dropped ball follows an orbit corresponding to one of the usual conic curves. Those below geosynch will follow elliptical orbits inwards towards a perigee point. Balls released low on the elevator will enter orbits that intersect the Earth's atmosphere, or the surface of the Earth. But those higher up will enter stable elliptical orbits, assuming they don't hit the tower when they return.
Those released above geosynch move outwards towards apogee. If the tetherweight is high enough to allow you to move sufficiently far outwards, you'll eventually start releasing balls into parabolic or hyperbolic orbits.

The apparent path of the ball is complicated by the rotation of the Earth and elevator. Balls dropped from low on the elevator tower will seem to fall more or less vertically initially, and then will gradually pull away eastwards as their orbit takes them lower and faster.

Grant Hutchison

George
2009-Apr-19, 11:41 PM
The ball will only have the elevator's tangential velocity, which is much less than the orbital velocity until you get close to the geosynchronous orbit point.

This elevator speed is simply 2*pi*r/24 hrs. The circular orbtial speed required is very close to (mu/r)0.5*3600, where mu for Earth = 398,600 and r is in km.

This graph should help some, and I think I did it right.

Tucson_Tim
2009-Apr-19, 11:46 PM
Thank you Grant and George. Cool graph - did you make that just now?

George
2009-Apr-20, 12:08 AM
Yep. You asked such an interesting question, I thought I'd take a shot at it and, as usual, learned much in the process.

Tucson_Tim
2009-Apr-20, 12:24 AM
Yep. You asked such an interesting question, I thought I'd take a shot at it and, as usual, learned much in the process.

When I first read it in Clarke's novel I thought "What?! That can't be right. When I drop something from a tall building it falls straight down." But then I realized that if there was no atmosphere on the Earth, an object dropped from a tall building would drift to the East due to its slightly higher initial tangential velocity than a point on the ground. It may even be measureable at heights of the new record-setting buildings (if there was no air).

George
2009-Apr-20, 04:30 AM
When I first read it in Clarke's novel I thought "What?! That can't be right. When I drop something from a tall building it falls straight down." But then I realized that if there was no atmosphere on the Earth, an object dropped from a tall building would drift to the East due to its slightly higher initial tangential velocity than a point on the ground. It may even be measureable at heights of the new record-setting buildings (if there was no air). Wind would be the big issue. Try calculating the difference in rotational speed between land and 1 km up the elevator. Ignoring wind and air resistance, you should find that the ball will land only ~ 1 meter away to the east.

Jeff Root
2009-Apr-20, 05:29 AM
I found that pennies tend to glide rather than fall straight down, over a
vertical distance of a hundred feet or so.

-- Jeff, in Minneapolis

Jeff Root
2009-Apr-20, 05:31 AM
If you find a dartboard lying flat on the ground close to a tall building, run!

-- Jeff, in Minneapolis

Tucson_Tim
2009-Apr-20, 01:42 PM
Try calculating the difference in rotational speed between land and 1 km up the elevator. Ignoring wind and air resistance, you should find that the ball will land only ~ 1 meter away to the east.

I assume that is calculated at the equator. The further you get from the equator the lower the tangential velocity and the direction changes to something more north or south of due east.

gfellow
2009-Apr-20, 01:44 PM
For my question, let's also ignore the Earth's atmosphere and its effects...

Forgive a slight detour, some might consider this nit-picking, but in the spirit of Eddington, sometimes it is minor discrepancies (Mercury's orbit, eclipse displacement of stars) that make for new directions...

What if we were not to ignore Earth's atmosphere and its effects?
Galileo's rolling balls work fine, but over distance drag from air resistance would mean that the larger, more massive ball arrives first.
The famous Ball and Feather on the Moon demonstration works fine, but dropped from an altitude of 300 miles, the feather would be subject to interference from solar wind and would arrive after the ball.

Even in the thinnest intergalactic space, any given cubic centimeter is awash in activity. Virtual particles spontaneously come into existence, then blink out again. Radiation permeates this thinnest of space. Whole atoms, unhindered, reach such high velocities that a plethora of them pass through a given cubic centimeter at any given time.
ALL space appears to be a fabric of interference, so the laws of pressure are just as relevant in outer space as within the boundaries of our own atmosphere, just on a much bigger scale.

...so my question - in the strictest sense - is there a problem with our present reasoning about the behavior of mass and motion, if the experiments upon which we base our reasoning shows discrepancies? Or am I just being too nit-picky?

Tucson_Tim
2009-Apr-20, 01:49 PM
...so my question - in the strictest sense - is there a problem with our present reasoning about the behavior of mass and motion, if the experiments upon which we base our reasoning shows discrepancies? Or am I just being too nit-picky?

gfellow, you probably have a valid question here but why don't you start a new thread with this question, since it doesn't really answer my questions in this thread. Your question won't be given the consideration it deserves buried here in this thread. And welcome to the forum -- hope you like it here.

George
2009-Apr-20, 02:09 PM
...so my question - in the strictest sense - is there a problem with our present reasoning about the behavior of mass and motion, if the experiments upon which we base our reasoning shows discrepancies? Or am I just being too nit-picky? Discrepancies often lie within the margin of error. Solar wind, magnetic fields, etc. will play a minor role in trajectory, but if the discrepancy exceeds all these effects, then something new and exciting could be happening. There is a thread regarding a space probe that seems to be behaving oddly, though it is likely it really is not.

[This is another topic, so you might want to go here (http://www.bautforum.com/astronomy/70997-nasa-baffled-unexplained-force-acting-space-probes.html), which is the space probe thread.]

gfellow
2009-Apr-20, 02:17 PM
For sure Tucson Tim. Sorry for my spontaneous mis-posting. Your comment popped up in my keywords of Google Alerts and I appear to have trod without grace. Thanks for the welcome, though. Great forum!

Tucson_Tim
2009-Apr-20, 02:19 PM
. . . and I appear to have trod without grace. Thanks for the welcome, though. Great forum! (my bold)

Not at all! Your question will be seen if it is in a new thread and you WILL get replies.

George
2009-Apr-20, 02:21 PM
BTW, gfellow, welcome aboard. :clap: Your type of question tells me you will indeed enjoy this forum.