I working on a story, and there is a space elevator. I know that moon and sun have a gravitational effect on bodies in orbit. And if a heavy asteroid was used for counterweight, wouldn't it require a massive amount of propellant (or power depending on propulsion) to keep the north-south station keeping? Anyway, what I want to ask is if anyone knows how much influence would moon and sun be on the counterweight. Same, more or less or than on a large unanchored station in geostationary orbit.
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$\begingroup$ Welcome to Worldbuilding! Please be sure to take the tour and read through the FAQ. This is a good first question, IMO, and I need to think about an answer. $\endgroup$– Zeiss IkonAug 17, 2022 at 19:01
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$\begingroup$ Fundamentally, this seems like an ordinary physics question, but not enough of the question has been described clearly to start filling in enough variables to make it answerable. $\endgroup$– user535733Aug 17, 2022 at 19:08
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$\begingroup$ About the same as to station, because counterweight is pretty close to the geostationary orbit, and gravity acceleration does not depend on the recipient mass, while it's way less than the other body's. Here you speak about asteroid as counterweight, they still have way less mass than Moon or Earth or Sun, so count them as "big stations on the same orbit" $\endgroup$– VesperAug 17, 2022 at 19:19
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I don't have the math or orbital mechanics to prove it (despite playing hundreds or hours of Kerbal Space Program), but I'm inclined to think that if your ground anchor is smack on the equator, in one of the ground locations corresponding to the most stable points in GEO (the reason Taprobane -- essentially a fictional Sri Lanka but on the equator -- was chosen in Fountains of Paradise), station keeping for the counterweight could be nearly zero.
First, a geostationary satellite over one of these stable locations needs almost none to begin with, because these locations are potential wells in the geosynchronous environment -- and secondly, the counterweight is, in terms of forces, hanging from the ground anchor. Any perturbation by the Moon or Sun, forward, backward, north or south, will create a restoring force that wants to return the tether to a vertical position. This will, of course, result in some pendulum effect, but it should be possible to damp this (especially in the fore-and-aft plane) by timing transits of mass up and down the tether (momentum to bring those to orbital velocity is also supplied by the ground anchor through the tether).
In the end, I would suppose that having the ability to actually build a Beanstalk tends to presuppose the ability to stabilize it.
answered Aug 17, 2022 at 19:13
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3$\begingroup$ If the 'weight' of the station is 'hanging' from the planet, you have done something very, very wrong. The counterweight station needs enough mass out beyond the geosynchronous point to counter the mass of the cable from the geosynchronous point to the ground. The beanstalk is being held up by the counterweight. The counterweight is not being held in place by the connection to the ground. $\endgroup$ Aug 17, 2022 at 19:28
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$\begingroup$ Siri Lanka was moved for Fountains of Paradise. It isn't actually on the equator. $\endgroup$ Aug 17, 2022 at 20:08
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1$\begingroup$ @MichaelRichardson, you want to keep the cable under tension, which means your counterweight isn't quite a perfect balance for the rest of the system. $\endgroup$– MarkAug 18, 2022 at 2:47
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$\begingroup$ @JohnDallman It's been quite some time since I read that, but wasn't the terminus in a fictional country that if you squinted, kinda looked like Sri Lanka, but wasn't? $\endgroup$ Aug 18, 2022 at 13:39
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$\begingroup$ Yep, Taprobane (says a quick search). I haven't read it since the year it came out, either. Clarke called it "90% congruent with Sri Lanka" but further south. $\endgroup$ Aug 18, 2022 at 13:59