Orbital math question

[GIThruster]

ISS has an orbit inclined at 51*. It weighs 450 metric tons. So here's the question: how much constant force (thrust) is required to move it from its current orbit to an equatorial orbit in 3 years time?

Gold stars for showing your work. I know there must be a delta V equation for orbital maneuvers but I can't find it.

[hanelyp]

A couple off the cuff thoughts:

- Total delta V somewhat greater than if a single short burn was used. I believe the point where the start and desired end orbit intersect is optimal for application of thrust. Since this is a much easier figure to compute, it can be used as a sanity check against the more complete calculation.

- The thrust for a slow change in orbital inclination won't be a constant direction.

- This can be looked at as turning a gyroscope by applying thrust to the rim. Thrust in some parts of the orbit will be more effective, and at some points in the orbit unproductive.

[GIThruster]

Yes well, there's little reason to thrust as the orbit crosses the equator, and thrust at the extremes of the orbit farthest from the equator are the most efficient, but one would suppose there is a single equation that can be used to do this sort of calculation. Orbital mechanics are a little trickier than one would guess. I know NASA has some computational tools for this but I am not competent to use them.

[paperburn1]

45 m /s to keep it where its atover one year soooo let me look some more

[hanelyp]

Yes well, there's little reason to thrust as the orbit crosses the equator, and thrust at the extremes of the orbit farthest from the equator are the most efficient. ...

That's backwards. You want to thrust as you cross the equator, and have the most velocity not parallel to your desired final vector. To reduce orbital inclination you need to cancel poleward velocity, and add to equatorial velocity.

[Aero]

Yes well, there's little reason to thrust as the orbit crosses the equator, and thrust at the extremes of the orbit farthest from the equator are the most efficient. ...

That's backwards. You want to thrust as you cross the equator, and have the most velocity not parallel to your desired final vector. To reduce orbital inclination you need to cancel poleward velocity, and add to equatorial velocity.

the question: how much constant force (thrust) is required to move it from its current orbit to an equatorial orbit in 3 years time?

Orbital mechanics is tricky and you would not want to do it this way, but this should give you an idea.

The ISS orbital velocity is 7.66 km/s crossing the equator at a 51.65 degree angle. You want to achieve an orbital velocity of 7.66 km/s crossing the equator at a 0 (zero) degree angle. Assume a flat earth then pick a point above the equator and subtract the two velocity vectors. That will give you the delta V difference between the start of the maneuver and the end of the maneuver. That is, at the start, Vx = 4.7527515 km/s and Vz = 6.007241728 km/s. (x is along the equator, x is toward the pole.) Now, at the end, Vx = 7.66 km/s and Vz = 0 km/s so the difference, delta V = 6.673758088 km/s.

If you used the brute force method to rotate to orbital plane you would need to be very careful that your orbital velocity always remained 7.66 km/s, you don't want to drop out of orbit after all. So always thrust in a direction perpendicular to your velocity vector and perpendicular to your radius vector, always reducing the magnitude of Vz and increasing the magnitude of Vx. The orbital plane could be changed this way but you may not be able to tolerate a constant thrust magnitude and it certainly would need to change thrust directions north to south or south to north each time you cross the equator. On average, over 3 years = 94.608E6 seconds, you need a delta V of 2.1162E-07 m/s. Delta V = a*t and F = ma, so thrust, F = ~95 mN.

That should be doable, but notice that orbital velocity plus delta V = 7.66 + 6.67 = 14.33 km/s which exceeds escape velocity from an impulsive burn. This is why plane changes are so hard. But because the thrust is so small the impulsive burn assumption inherent in most orbital mechanics equations is not valid so escape wouldn't happen anyway. See the comments on low thrust here. http://en.wikipedia.org/wiki/Delta-v_bu ... low_thrust From Wikipedia you see that the delta V would likely only reach geostationary altitude if applied over 3 years.

I'm out of my depth talking about low thrust considerations so I'll stop now.

[paperburn1]

I thought I was doing it wrong but yes it looks like would be easier to go to the moon than change your orbital inclination from the current altitude to geosynchronous equatorial orbit

[zapkitty]

I thought I was doing it wrong but yes it looks like would be easier to go to the moon than change your orbital inclination from the current altitude to geosynchronous equatorial orbit

In all the times I've seen the concept of shoving ISS around brought up I've never heard a different answer.

Usually the only reasonable application where this comes up is in discussion of electrodynamic tethers. As with ME units such tethers require no propellant.

And the usual upshot of such discussions have been "You theoretically could do it with a tether but it'd be far faster and cheaper to deploy an ISS-class station on the exact orbit that you want..."

... and that was before Bigalow started talking up their BA 2100 idea.

Is this for an ME demo kind of idea?

ME + BA modules = cislunar all-you-can-eat buffet.

[paperburn1]

I beleive Arthur clarke wrote a book called "The Promise of space". It it it have a large section entitled halfway to anywhere. it was all about all the delta V required to do certain missions.
A very interesting read and as relevant today as when it was written over twenty years ago.
I also think Issac Asimov did a similar one. as well as From A Step Farther Out by Jerry Pournelle

[GIThruster]

Is this for an ME demo kind of idea?

Not really a demo but M-E related. I'm looking at a DARPA grant proposal and the proposal process requires all the history for TRL-1-5, the TRL6 phase 1 project plan with detail, the TRL7 phase 2 plan with detail, the TRL8 manufacturing methods and expertise plan and the TRL9 market plan.

NASA currently spends $500M/year lifting propellant to ISS and replacing the current chemical thrusters with METs would save an enormous amount of money given a commercial grade FOM thruster (which is what we're looking at.) So the question is, if you have that sort of thrust, what then can you do with it? From the answer here, obviously you could reposition ISS into a more useful orbit and with the Russians pulling out in 2015, there's no reason to not sell MET development predicated on the notion of making our $150B investment in ISS more useful.

Even if ISS could be moved to the Moon more easily, it would not be useful there as it does not have adequate rad hardening to go outside the Van Allen Belt. It would be useful for cislunar expeditions if it were on equatorial orbit which seems pretty doable. In fact, seems like it could be managed in much less than a year from these figures. This is a huge selling point for DARPA, one of 6 specific programs I am proposing as early application TRL9 market examples.

BTW, I am still putting together the team for the UHF MET grant. Anyone interested should write me. There is room on the team. I already have the thruster manufacturer picked out and the methods necessary, which is by far the hardest part of the task. We will likely have to build our own lab and I need 3 people to run it, including at least one accomplished EE. The power system is also going to be shopped out however, so the real lab work is in characterizing the test items and since they're intended for commercial use, this will be under very diverse conditions including large temperature bandwidth.

Looking for good people both part and full time and still looking for a part time graphic artist.

[Aero]

I looked a little further. ISS orbital decay compensation will be needed. Orbital decay is 2 km/month which is 7.716E-07 m/s and requires a constant thrust of 0.35 N. That's about 4 times more thrust than my earlier number calculated to change the inclination.

http://en.wikipedia.org/wiki/Internatio ... ce_Station

Speaking of inclination change, why are you considering equatorial orbit? That is easily reached from an equatorial launch site, but not so easily from Cape Canaveral. I think a 23 degree inclination orbit is easy from the cape and of course changing the orbit inclination only half as much is easier.

[GIThruster]

As a waypoint to deep space, equatorial makes good sense. When on the way to the Moon, Mars or even most GEO and Lagrange points, ISS is out of the way. That orbit was only chosen so it would fly over Russian monitoring sites and if the Russians really leave in 2015 as they've been saying the past couple years, we'd be free to reposition and retask the station. If you want a construction or refueling point for deep space activities, equatorial LEO is the best choice, IIUC. I'm not suggesting ISS as a refueling depot, but it could be used to support such a depot, which would certainly be useful at least until we have yet higher FOM MET's such as microwave, which is much harder to do than UHF.

So for instance, if NASA wants to build a fleet of Nautilus X type craft and do some serious space exploration, constructing them by ISS and replacing crews could more safely and cheaply be done from ISS than by building another station. While I'm all for building more on orbit, I would prefer it sit next to ISS, for many reasons.

[Aero]

As a waypoint to deep space, equatorial makes good sense. When on the way to the Moon, Mars or even most GEO and Lagrange points, ISS is out of the way. That orbit was only chosen so it would fly over Russian monitoring sites and if the Russians really leave in 2015 as they've been saying the past couple years, we'd be free to reposition and retask the station. If you want a construction or refueling point for deep space activities, equatorial LEO is the best choice, IIUC. I'm not suggesting ISS as a refueling depot, but it could be used to support such a depot, which would certainly be useful at least until we have yet higher FOM MET's such as microwave, which is much harder to do than UHF.

So for instance, if NASA wants to build a fleet of Nautilus X type craft and do some serious space exploration, constructing them by ISS and replacing crews could more safely and cheaply be done from ISS than by building another station. While I'm all for building more on orbit, I would prefer it sit next to ISS, for many reasons.

I understand your point of moving the ISS to a more suitable orbit. I'm just suggesting that a 23 degree inclination LEO orbit for the ISS would save over an equatorial LEO orbit for what you propose. Check with an expert but here's my thoughts on the matter.

First, a caveat. I assume that there would be a number of launches to the ISS and that NASA would launch most of them from the cape. A 23 degree orbit is natural from the cape while an equatorial orbit from the cape requires a 23 degree plane change for each launch. The plane change must be done over the equator either in LEO or higher orbit and either of these requires a substantial additional propellant expenditure over the launch to the 23 degree orbit.

Construct the BEO vehicle at the ISS in 23 degree orbit. Once a BEO vehicle leaves the 23 degree LEO orbit it can perform the plane change at much higher altitude with a quite low expenditure of propellant. It would now be in equatorial orbit or on an equatorial escape trajectory heading to its destination. The total amount of prop required to be launched from earth would be significantly less.

Again, check with an expert, don't take my word alone for it, but do check.

[GIThruster]

I appreciate this but I'm not going to try to sell a particular plan to NASA. They'll have their own ideas. From the maths shared here, looks to me we only need to install a few Newtons thrust to the entire station, to be able to reposition it in a few weeks. So NASA doesn't even need to settle for one solution. The point is, this astonishing outcome you have when you can't run out of propellant. We can do all these extraordinary things, even with low thrust/mass and thrust/power FOM's. So if NASA pays to upgrade ISS's stationkeeping ability, what they automatically get is the ability to reposition it in very useful ways. That's the TRL9 bargaining chip I needed for that program. There are 5 other such programs I want to pitch that are at least as compelling, such as a NautilusX style deep space explorer fleet, enabled by UFG MET's. Your trip time to Titan will vary, but it is going to be weeks rather than years.

Combined with the proprietary radiation hardening technology I hope we'll develop either first or simultaneously, should get us off this rock pretty quickly.

[krenshala]

I know this is an old topic, but I thought I'd throw out some useful info for you to chew on GIThruster.

While inclination changes are expensive in delta-v, they get cheaper the larger your orbit. Depending on the exact plane change you are going for, it might actually take less delta-v to expand the orbit, change inclinations when you pass the next ascending or descending node (while at your apoapsis), then move back to the original orbit. Options options options.