Maximum safe mass of an asteroid in geostationary orbit

[caladin]

Summary:: What is the maximum safe mass of an asteroid in geostationary orbit before it causes problems?

Hello everyone,

If there was an asteroid in geostationary orbit around the Earth, over the Pacific Ocean, what would be the highest mass it could have before it would start having detrimental effects on the Moon and Earth, such as the orbit of the Moon or noticeable tidal effects?

I initially thought it would be fairly easy to calculate a mass that would shift the moon by a predetermined amount and leave it there, but I'm sure there are a number of variables I'm not considering.

 

[anorlunda]

That's a curious question. Maybe others can give you an answer. But I'm curious as to the reason for your question. Are you working on a SF story?

 

[caladin]

Yes it's for SF and relating to a space elevator construction, I am figuring out the optimal size for the story. The asteroid has construction on it and I am figuring out the relevant possibilities.

I am also simply interested in knowing as I've not imagined this before and enjoy this kind of problem.

 

[russ_watters]

The tidal effects question you can answer easily enough by plugging some numbers into the tidal acceleration equation (and establishing a criteria for the boundary of "detrimental effects").

 

[snorkack]

The thing is, low mass geostationary satellites are actually inherently unstable. The minimum mass for a geostationary satellite to be stable can be computed.

 

[sophiecentaur]

Yes it's for SF

I don't know how 'responsible' you attitude is to the possible long term effects of proposed major fictional structures but the word "safe' would imply the possibility of long term global effects. A large orbiting object could produce strange night time illumination around the operational base. GSO is a long way away so the illumination could be irrelevant but the brightness of the object could be around 100 times that (per m²) of the Moon (ignoring albedo effects); very visible when compared with, say the ISS. That could be disruptive for nocturnal animals in unpredictable ways.
That light could be in the same place in the sky for almost 24 hours a day. Would people pay money to live away (or near) that effect?

 

[eachus]

Don't let others get you wrapped around the axle. Choose an asteroid suitable for your project, say Apophis, and go with it. Assuming you are building a space elevator, there are three options. First build up and down at the same time, and part of the engineering will be to keep the orbit correct. Once the space elevator is completed, it will keep the asteroid in place.

The second option is to just build down. The asteroid will end up being the counterweight. Depending on how much mass is in the elevator, during construction the asteroid will move outward, and when the elevator is connected to the earth, it will need to yank the asteroid back into position--not a good plan--or the asteroid can be given a fairly massive kick by rockets or a nuclear explosion. (Fat chance of getting that authorized in our universe.)

The third option is probably the best. Build a thin elevator and enough of a counterweight to balance it. Then add strands to the elevator. Corrections to the asteroid's orbit will happen. But gently.

Oh, one other thing I hope you will get right. Space elevators are pictured connected to the Earth or some other planet--they work well on Mars and the Moon--without any thought given to the fact that the elevator will need miles of slack to allow for expansion and contraction. A much better design is to end the elevator portion about 200 kilometers up, and have multiple anchor cables going a few hundred kilometers in say six directions. These can be constantly adjusted for tension, and the equivalent of cable ski lifts take passengers and freight to the junction outside the atmosphere.

 

[Melbourne Guy]

I plugged a reasonably massive asteroid - 6.8e19 kg and 180 km diameter - at geosynchronous orbit into a simulation app and it stayed in place for the few decades I ran it forward. However, that's not say it will persist, I've often seen moons stripped away by gravitational effects, and it can happen really quickly (within centuries), but they are larger bodies than this one, and usually orbiting further out.

More massive asteroids will either shift Earth's orbit or move it out of its orbit entirely, but I only saw that at e22 km range and above, which is not a solar system object we're going to be moving around any time soon. Think our Moon, Io, Titan, etc. as that's where you start to see problems emerge.

Note that tidal effects are not modeled in my app, that would be a complicated problem to solve...at least for me

In terms of a novel, unless you're going to make it really technical, I'd do as @eachus suggests and just pick a small one and use it with some handwavium to put it in place and assume it stays there. Unless your novel is about bad outcomes from a space elevator?

 

[sophiecentaur]

pick a small one and use it with some handwavium to put it in place and assume it stays there.

If you have the energy to spare to put it there then you will have energy to maintain its place.

 

[Melbourne Guy]

If you have the energy to spare to put it there then you will have energy to maintain its place.

Possibly. But it's more presumptive science fiction, because there are many stories where the remnants of space elevators litter the planet. Alternatively, I can imagine competing commercial interests moving asteroid masses too close to each other - inadvertently or deliberately - and dislodging the asteroid. There's a huge technological difference being able to carefully nudging something that large into orbit and being able to direct it like a space ship!

 

[sophiecentaur]

There's a huge technological difference being able to carefully nudging something that large into orbit and being able to direct it like a space ship!

I can't see any inherent difference unless the object has beeb subjected to a collision. But, even then, if we had the technology to set up the original situation, we would have the technology to predict and to deal with a collision before it occurred.

The problem with SciFi discussion is that both sides of any argument can play wildcards at any time and make the goalposts move. There is no valid source to resolve a fiction vs fiction argument.

In any case, if the book is written well and the characters are believable then small technical details are not worth worrying over. Asimov is full of absolute technical rubbish but that doesn't detract from the worth of the Foundation Trilogy.

 

[Melbourne Guy]

The problem with SciFi discussion is that both sides of any argument can play wildcards at any time and make the goalposts move. There is no valid source to resolve a fiction vs fiction argument.

Absolutely! I moved 356791 Lompoc into LEO in a story, with nary a hint as to how it might have been done. And I like your conclusion, 'well written' trumps everything else. Unless the science is appallingly done - and I've read many books where it is - readers are generally happy to overlook 'technical rubbish'

 

[snorkack]

I plugged a reasonably massive asteroid - 6.8e19 kg and 180 km diameter - at geosynchronous orbit into a simulation app and it stayed in place for the few decades I ran it forward. However, that's not say it will persist, I've often seen moons stripped away by gravitational effects, and it can happen really quickly (within centuries), but they are larger bodies than this one, and usually orbiting further out.

More massive asteroids will either shift Earth's orbit or move it out of its orbit entirely, but I only saw that at e22 km range and above, which is not a solar system object we're going to be moving around any time soon. Think our Moon, Io, Titan, etc. as that's where you start to see problems emerge.

Note that tidal effects are not modeled in my app, that would be a complicated problem to solve...at least for me

For me, that´s the easy part to model.
Deimos orbits near areostationary orbit. It is inherently unstable because of tidal effects. The reason is thai if Deimos orbits slightly outside areostationary orbit, the tides would accelerate Deimos, which would cause Deimos to get further from areostationary orbit, which would cause the tides to get stronger. Likewise, if Deimos orbited slightly inside areostationary orbit, it would be slowed down and spiral in increasingly... which has happened to Phobos.

The more massive the satellite is, the less stable the stationary orbit would be, until...

Moon would not be stable in geostationary orbit. But a satellite slightly more massive than Moon would be stable - like Charon is.

The reason is that a low mass satellite which is accelerated by tides to a higher orbit (like Deimos) is thereby slowed down, but due to low mass of Deimos, the effects on rotation of Mars are minor.
A massive satellite displaced above stationary orbit would spiral out, but it would slow down the planet, so the rotation and orbital period would converge.
I think the stability condition is easy to calculate from here.

 

[Melbourne Guy]

I think the stability condition is easy to calculate from here.

I use AstroGrav for my empirical approach because I don't have the orbital math, and I've now run the space elevator asteroid I mentioned above 1,000 years into the future, and it's stable. I also also added another space elevator asteroid of the same mass and dimensions about 1/3 around the globe another 2,000 years out and both remained in stable orbits.

The more massive the satellite is, the less stable the stationary orbit would be, until...

Until? You seem to be suggesting, @snorkack, that the orbit will decay and a collision occur. But that's not what I've seen. The more massive it is, the more the Earth starts to move in its orbit, until, when the 'asteroid' is considerably more massive than Earth, Earth is ejected from its orbit.

 

[snorkack]

Until? You seem to be suggesting, @snorkack, that the orbit will decay and a collision occur.

Only if the orbit is inside the stationary orbit, or retrograde.
No, what happens is that if satellite is low mass, it will spiral out. The tides will weaken, but the outspiral will go on at a slower rate, as it is doing with Moon.
When the satellite is massive enough, however, the primary´s rotation slows down during the outspiral - enough to make primary´s rotation speed equal to satellite´s orbital speed if they are not equal already.
This is easy to calculate because for tidal forces, the total angular momentum of primary´s rotation and satellite´s orbit is constant.

 

[Melbourne Guy]

No, what happens is...

Aha, thanks, @snorkack, that's my limitation of watching the simulation without completely understanding what's driving the simulation

So, I've learned a few things from this thread, which is pretty much what I always find in PF!

 

[stefan r]

...

Oh, one other thing I hope you will get right. Space elevators are pictured connected to the Earth or some other planet--they work well on Mars and the Moon--without any thought given to the fact that the elevator will need miles of slack to allow for expansion and contraction. A much better design is to end the elevator portion about 200 kilometers up, and have multiple anchor cables going a few hundred kilometers in say six directions. These can be constantly adjusted for tension, and the equivalent of cable ski lifts take passengers and freight to the junction outside the atmosphere.

On Mars the elevator is going to be very close to or beyond limits of what can be done. Hop's blog (not peer reviewed link) goes into very nice detail. His Lower Phobos tether using Zylon looks particularly believable IMO. If you want to use better material like graphene you could get away with an elevator. A skyhook is a much faster way to travel. Given the presence of Phobos a passive support orbital ring is fairly easy.

If you have a Mars elevator then it connects at Pavonis Mons. The southern edge of the caldera is exactly at the equator. Expansion and contraction would be a thing but the tether itself does a lot of that. A Mars elevator has to split in order to avoid Phobos. Springs and/or shock absorbers add weight. At higher altitude there is less Martian gravity and the spring material will rotate faster which lowers tension.

On Luna the A-frame is much easier. The cable sags so at 45 degree or so it is running horizontal along ground towers instead of elevating. I do not see much advantage over just grounding the climber and switching to trains or cars. Angling out 10 or 20 degrees might have enough advantage to be worthwhile.

On Luna there is no air drag and on Mars drag is tiny. That allows for very fast ground transport. The limits will be set by the hoop stress on the wheels or flection heating. Improvements in tether material engineering will tend to improve wheel material too. The climber will also be dealing with wheels. It is likely to be much simpler and faster to just drive to the space port at Pavonis or Sinus Medii.

 

[sophiecentaur]

Expansion and contraction would be a thing but the tether itself does a lot of that.

I've always assumed that the tether would naturally lag more or less, to keep the tethered mass at the right speed. There would be a 'restoring force' in the appropriate sense to make things stable. Even if that doesn't work perfectly, the adjusting force at the bottom of the tether would be small as the maximum tension is at the top end (supporting the whole weight of the string).