I am quite fascinated by this site. You can drag the rotating globe to any position you want and watch the earth turn below you. Now, I’ve heard of geostationary orbits, but those only work over the equator. Is it possible to move a spacecraft to an arbitrary position above earth and keep it there? I assume that with today’s technology, the answer is “no”, otherwise we wouldn’t need tricks like Molniya orbits. But is that merely a technical problem (in terms of propulsive power, fuel capacity or the like), or is it physically impossible? Why?
If you postulate enough propulsive power, you can hold any position for as long as your energy source holds out.
To say that you can achieve a certain position & trajectory but not stay there seems equivalent to saying that the displacing force somehow becomes unlimited.
“Free” or ballistic orbits of an object are maintained by two balanced forces; the graviational force of the massive body (i.e. planet) being orbitted, and the inertial force of the object due to its existing momentum. This balance of forces ensures a closed elliptical orbit for any object that is moving at less than escape speed of the massive body and in a trajectory that does not intersect the body (including its atmosphere). The period of this orbit depends only the eccentricity and semi-major axis, although four additional parameters or “elements” are required to fully describe an orbit, and though these can be stated in various ways, the traditional Keplerian desciption of them is inclination, argument of periapsis, longitude of the ascending note, and mean anomaly at epoch. All closed free orbits are in a planar ellipse have a focus at the center of mass of the massive body, although they can have perturbations that cause them to oscillate above and below the plane (one type of nutation).
A very special case of the free orbita is a geostationary orbit, in which not only is the orbital plane be conincident with the equatorial (latitude of 0 degrees), but the orbital period is the same as the rotational period of the body. For the Earth, this is at an orbit that is about 22,200 miles above the surface and with a period of one sidereal day. In order to have a geostationary orbit at any other latitude, the orbital plane of the object would have to be parallel to but offset from the equatorial plane. This would require energy to hold it up there as it would not be a free orbit. This is called a powered or lofted orbit, as it requires an external source of propulsion.
Obviously, a spacecraft having to expend propellant constantly to stay in orbit wouldn’t remain there very long because the amount of propellent that can be reasonbly carried is very small (tens to a couple hundred kilograms). However, schemes have been proposed to use solar light pressure or tethers to provide propulsion that could maintain an object in a non-free orbit, including a stationary polar orbit where the satellite would just hover directly above a pole. None of these have been demonstrated to date, but they are physically feasible.
Stranger
Any earth orbit will have the earth’s centre of mass within the plane of the orbit. If the inclination is zero, the satellite will remain directly above the equator. A non-zero inclination will mean that the satellite will oscillate between latitude +x and latitude -x once per orbit.
Any attempt to force the satellite to remain at a non-zero latitude would require constant application of reactive force, and you would (very) quickly run out of reactive mass.
So the answer is somewhere between “impossible” and “impossible with current (or currently conceivable) technology”.
Great answers, thank you very much!
Hmm, yes. I hadn’t thought of it that way before, but that makes sense.
Thank for your comprehensive and clear explanation of orbits, Stranger. How do powered orbits work? Is the spacecraft basically hovering over a point on the surface - kinda like this, only thousands of miles higher up? So, in other words, do you need to constantly apply downward thrust to match escape velocity, if that makes any sense?
Ah, hadn’t thought about reactive mass. Good point.
Could you use an ion thruster for this? As I understand it, reactive mass is less of an issue with those.
Ion thrusters are very efficient, in some senses, but they also produce extremely low thrust. You can run one for a very long time, but trying to hover in any reasonable orbit with one would be like trying to fly by spitting at the ground really hard.
That depends on where you’re trying to do it. Directly over one of the poles, it would exactly be hovering. Directly over the equator at the right height, it’s exactly an orbit, no rocket needed. Anywhere in between, it’s a mixture of orbiting and hovering, and your nozzle won’t be pointed straight down. Escape velocity isn’t relevant to this, since you’re not trying to escape, and you’re continually thrusting.
Specifically, ion thrusters are propulsively efficient–that is to say, they obtain a high specific impulse compared to chemical engines for a given propellant mass–but they are highly energy inefficient, wasting most of the energy on heating the propellant to very high temperature that is not translated into momentum. They are also, as Chronos notes, of low thrust and generally speaking cannot be scaled up to produce higher thrust. As such, they are useful for low thrust applications such as stationkeeping and continuous impulse trajectory change for interplanetary spacecraft, but are not of adequate thrust to counteract any significant gravity field. And at any rate, they would still require propellant which would be a finite resource for the orbiting spacecraft.
A powered orbit is any orbit that is not purely ballistic; that is, an orbit that does not obey Keplerian mechanics (as modified by external influences and general relativity, of course).
Stranger
I find that the simplest way to answer these sort of questions is by taking an extreme example, or an almost-extreme example.
In this case, the extreme example would be choosing to move one’s spacecraft to a point above the north pole, and stay there. In such a case, he would not really be moving (relative to the earth) at all, merely hovering. This could be done, of course, but only with an incredible use of power. That is to say, no, it can’t be done. At least not for a significant length of time.
The almost-extreme example would be to choose a point some distance from the pole, say 100 miles, or even 1000 miles. I don’t think one needs much physics knowledge to understand that this would not really be a free-ride orbit at all, but would require enormous amounts of steering and propellant. Again, not possible, at least not for a significant time.
I think that regardless of latitude, firing your rockets directly towards the equatorial plane would be the “best” option, in the sense of requiring the least amount of force from your rockets.
You might be right about that. I certainly can’t come up with any counterexamples.
Would such a thing be possible by using a light sail with a ground based laser to provide propulsion?
Hypothetically, yes. In reality, the same problems that have made ground-based (and even aircraft-based) lasers unsuited for ballistic missile defense also render them unsuited to a propulsion scheme that you suggest. Beyond that, high energy chemical, gas dynamic, or free electron lasers are hugely inefficient just coming out of the output coupler even before atmospheric and divergence losses. The high transient power throughput makes the desireable for military applications but the could not be sustained over periods of tens of seconds using any existing technology.
Stranger
I’ve also seen proposals that are held in place by light pressure from the Sun. Like anything that depends on light pressure from the Sun, the practicality is limited by the mass to area ratio required.
The word for such an object is “statite”, coined by Dr Robert L Forward. The wiki link mentions solar sails, but magnetic sails and an electrodynamic tether have also been suggested as means to keep the statite in position indefinitely.
I clicked a random point on the Earth and it said Leningrad. Where did they get the map?
If you click on northern Virginia and find Kruschevgrad just to the west of Andropolis (Home of the Red Banner Western Fleet Naval Academy) you may have reversed the polarity on your matter digitizer.
Stranger