Orbiter missions with no (or little) fuel usage for deceleration, Target planet capturing the spacecraft w/o extensive fuel usage Options

[Anton Martynov]

I was involved in a casual conversation recently about the exploration of bodies in Solar System, in particular about fly-by approach vs. orbiter approach. In particular, I was saying that the main challenge with orbiter missions is that either you have to decelerate once you reach your target (requires tons of fuel on board), or you have to travel along the trajectory that would take an unreasonable amount of time to reach the target. As an example of the latter, I said that you could launch a spacecraft into a trajectory that would be a part of an elliptical orbit around the Sun with the perihelion around Earth and the aphelion around the destination. That way, when the spacecraft reaches its target, its speed relative to the planet will be slow enough for it to be "picked up" by the planet's gravity, and it will start orbiting the planet.

The other person in the conversation pointed out that it's been shown that when two bodies pass each other and influence each other gravitationally, it's not possible for them to start orbiting each other (or, in the case of one object being much more massive than the other (planet vs. spacecraft), simply "one orbiting another"). He said that either the more massive object will simply alter the trajectory of the passing smaller object, but not capture it, or the smaller object will crash into the bigger one.

And this is something that, to me, "intuitively" shouldn't be right, but I don't have enough expertise to prove that it's wrong. My counter-arguments are:

- Some of the natural satellites in the Solar System are believed to be captured by the planet as they were passing by (true, these are mainly hypotheses, but people wouldn't make such hypotheses if this wouldn't be possible?).

- If the object is passing by the planet at the speed less than what is required to enter the orbit, then it will crash down onto the planet. If the object is passing at the speed greater than the escape velocity, then it will continue flying without being captured by the planet. Surely if the object's speed is between these two values, it has to start orbiting the planet? (Not necessarily in a perfect circular orbit of course).

As further proof for the second point, I calculated the elliptical orbit with the perihelion at Earth (1 AU) and aphelion at Uranus (19.2 AU). Sure, it would take 16 years to get to Uranus, but the required takeoff speed would be 41.1 km/s (relative to Earth, that would be 11.3 km/s, so just barely above Earth's escape velocity, so we're good here), and the spacecraft's speed when it arrives to Uranus would be 2.1 km/s relative to Sun, and -4.6 km/s relative to Uranus. This 4.6 km/s speed happens to be the speed of a circular orbit at 266000 km from the center of Uranus.

So, in my understanding, we can launch the spacecraft from Earth at 11.3 km/s into the elliptical orbit, and then some 16 years later it will pass by Uranus and be captured by it. If we make some small course corrections along the way so that it passes 266000 km from Uranus, it will even be a circular orbit.

... but, like I said, maybe I'm missing something that won't allow the spacecraft to be captured by the planet's gravity? My whole point was that in this scenario you don't have to use fuel for anything else other than takeoff. Of course, some course corrections would be inevitable, but at least you won't have to try to decelerate from New Horizons-like speeds.

[Explorer1]

I'm pretty sure the above is correct; in a simple two body situation it is not possible to get 'in-between' escape velocity and a collision. It will either be a hyperbolic/parabolic 'orbit' or an impact trajectory. One cannot get an ellipse without intervention, either by firing thrusters or a flyby of something; that's how all those natural moons got captured; they were in the right positions to exchange a bit of momentum and slow something down to remain in the SOI, but even then it doesn't always work.
Compare Triton with Shoemaker-Levy 9; both were captured, but one lasted a single orbit of a few years around Jupiter before impact and the other has lasted for many millions of orbits around Neptune.
Sometimes visuals are better than words (select generate proto disc): http://www.nowykurier.com/toys/gravity/gravity.html Notice how often moons show up around the 'planets', and how often they are unstable.
Maybe Cassini could have been captured with a Titan flyby alone, but it was obviously a much easier engineering feat to just fire the engines for capture and use Titan later for adjustments

I had the same question a long time ago, but a few hours of Kerbal Space Program will also suffice to demonstrate this.

[Anton Martynov]

Sometimes visuals are better than words (select generate proto disc): http://www.nowykurier.com/toys/gravity/gravity.html Notice how often moons show up around the 'planets', and how often they are unstable.

I remember having made a "gravity simulator" like this one a few years ago as well. It wasn't a web app, but a standalone program instead (all calculations were on CPU); I left it pretty underdeveloped, but I remember running into the precision problem pretty quickly. With a fixed time step, very elongated elliptical orbits (and in general any orbits that have a high velocity at some point) become extremely inprecise. When the planet "curves" around the sun at a very high speed, it's very important to have a smaller time step there, otherwise the orbit becomes very approximate.

In this simulation, I can see the same problem with the time step being too big in some cases. Look at elongated elliptical orbits and examine parts of them that are near the massive star - you'll see that the curve is a noticeably polygonal chain. In my old implementation that I mentioned above, elongated elliptical orbits exhibited the same instability as in this implementation, but the smaller (= more precise) the time step was, the more stable the orbits were.

I don't want to jump to conclusions, and please don't take my words as a criticism of the implementation you linked to: I certainly don't say that it is bad (and it's definitely better in so many aspects than mine was), but I just wanted to point out that at least some of the instability / "rotation" of elongated orbits is because of not having enough precision during close approaches.

I remember that I wanted to implement individual time steps for every object as an attempt to fix this, but never really got around to doing it. The idea was to choose the time step for an object based on its current velocity (faster object = smaller time step needed) instead of having a fixed time step for all of them.

In fact, even when I used to input "perfect" parameters for objects (as in, spawn a planet at these coordinates with this speed, which should have given the planet this or that type of "perfect", circular or elliptical, orbit), lack of precision was slowly but surely accumumating and resulting in the orbit deteriorating over time.

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To everyone: If we "somehow" spawn an object at distance N from the planet with the speed that an object going in a circular orbit at this distance should have, would that object get into this orbit? To extend this question, what if a spacecraft flies at this particular speed into this particular point of space (with the help of some small course corrections beforehand), will it get into this orbit? And if not, why? I understand that the general consensus says "no, it won't start orbiting the planet", but I want to understand what I'm missing (what will prevent this, so to say).

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In a two body interaction, in vacuum with point masses, etc., can't we say that what happens after closest approach has to be symmetric with what happened before closest approach? The relative approach velocity of the smaller object should accelerate until closest approach and then decelerate with an identical time/distance profile, so if the smaller object wasn't in orbit before the approach, it won't end up in orbit afterwards either. Caveat: there may be some relativistic effects to consider for the accretion disks "orbiting" black holes, but in a planetary-scale Newtonian universe, symmetry should rule out getting into orbit.

I agree with this approach, but I'm not sure if we can extrapolate orbits (not just some particular types of orbits, but orbits in general) into the past. Is it possible that for some location and speed of the object, there are multiple variants of how this object got here and got this speed?

Also as a counter-argument for this particular "symmetry" argument: in the frame of reference of the planet, "before" and "after" closest approach situations are not exactly the same. The Sun - the thing that got the spacecraft into the necessary point in space - is somewhere else now in this frame of reference. (Of course, with the Sun being there and influencing stuff, it's no longer a two-body problem).

[djellison]

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To everyone: If we "somehow" spawn an object at distance N from the planet with the speed that an object going in a circular orbit at this distance should have, would that object get into this orbit?

Yes - obviously.

To extend this question, what if a spacecraft flies at this particular speed into this particular point of space (with the help of some small course corrections beforehand), will it get into this orbit? And if not, why? I understand that the general consensus says "no, it won't start orbiting the planet", but I want to understand what I'm missing (what will prevent this, so to say).

The part you're missing is that by the time you are at that point, the spacecraft has been falling thru the planets gravity well to a speed greater than that of the orbital velocity you want, and so you're doing a flyby.

Not to put too fine a point on it - but if orbital capture were this easy.....everyone would be doing it. Galileo's orbit insertion was 630m/sec - Cassini's was 626m/sec - MESSENGER, after putting itself thru many gravity assists still needed 800m/sec+ for it's orbit insertion burn. A Uranus orbiter is expected to need around 800m/sec. Mars orbiters often have burn of 1 km/sec to go into orbit.

Another way of thinking of the problem..... say you are in an orbit with a Perihelion of 1AU and Aphelion of, say, Saturn orbit. When you are aphelion, you are travelling significantly slower than Saturn. Assuming you time it right and you arrive at that point as Saturn does - Saturn is now catching you up - so when you enter it's gravity well you are now falling towards Saturn...thus, in the solar frame of reference...you're slowing down. Your orbit around the sun is now LESS Saturn like than when you arrived.

[HSchirmer]

... Not to put too fine a point on it - but if orbital capture were this easy.....everyone would be doing it...

Good way to put it.

There is an asterisk to that though. There. is a distinction between orbital capture, and a quasi-stable orbit.
Getting a stable circular orbit around an outer planet it energy intensive.
But, there are lots of energy cheap unstable orbits around interesting destinations.
Orbits that are only stable for a century or so, then the space craft gets ejected from the system.
Generally, not a problem for this situation.

Actually, that could be a blessing in disguise.
The US military recently asked for ideas about how to use decomissioned spy satellites.
As I understand it, US intelligence agencies had a bunch of Hubble sized telescopes in orbit, but pointed DOWN to keep an eye on things.
Next generation drones are cheaper / better / less predictable than spy satellites, thus triggering the US orbital telescope garage sale.

I suggest taking one or two of the decomissioned keyhole (IIRC) spy satellites, drag them down to ISS, polish them up,
drop in a state of the art CPU, add a giant antenna, top off the volatiles, bolt on some sunshields and a Dawn style ion engine.
Then give them a swift kick out to L2 Earth-Sun and then start pushing them through the "Interplanetary Transportation Network"
While it is on the way to Mars, the "mobile Hubble" could do the usual "stars/galaxy/cluster" style astronomy.
Then, when it gets close to something local and interesting, say asteroid or comet, it observes that for several months.
Then back to stars and galaxies.
Next, a tour through the Jovian system, orbit for several months or a few years, get the Galilean worlds, then out.
Stars and planets for a few years, then Saturn.
Repeat for Uranus, and Neptune, and Pluto.

[djellison]

Getting a stable circular orbit around an outer planet it energy intensive.

Indeed. The examples I cited ( MRO, Cassini, Galileo, MESSENGER, Uranus orbiter ) almost all end in exceptionally eccentric orbits - they are pretty much the minimum delta V you could possibly use whilst remaining gravitationally bound to the spacecraft. MESSENGER wasn't hugely excentric - but far from circular. It's already highly energy intensive to get into ANY orbit - let alone a circular one.

in the case of Cassini and Galileo, multiple gravity assists from moons were used to manipulate the orbit thereafter.

In the case of MRO - it's aerobraking that makes up the difference.


The spare NRO hardware equates to enough hardware for one telescope. It's to be used as the basis for the proposed WFIRST mission. Getting a spacecraft that massive ( >11 tons ) into some sort of orbital tour of Mars, asteroids and the outer solar system would require extraordinary amounts of Delta V that would pretty much require next gen solar-electric prop ( which obviously isn't going to work beyond Jovian like distances )

[HSchirmer]

Getting a spacecraft that massive ( >11 tons ) into some sort of orbital tour of Mars, asteroids and the outer solar system
would require extraordinary amounts of Delta V that would pretty much require next gen solar-electric prop

Correct. Except when it isn't.

The beauty of chaotic orbits that require little to no delta-v is that 0 x anything = 0
Zero x 350kg craft = zero thrust.
Zero x 11 ton craft = zero thrust.

http://www2.esm.vt.edu/~sdross/talks/ross-csulb-2003.pdf
http://forum.nasaspaceflight.com/index.php?topic=26217.0

Idea is, old spy satellite and icbm components could be reporposed into a group of space telescopes.
If we aren't using them to spy on each other, might as well send them out to get pictures of other planets and moons.

Take a spy satellite telescope, add a Dawn style ion engine powered by a RTG, and a big antenna to transmit back to earth.
Send it out to Earth's L2 point, then let it traverse the roughly zero-delta-v chaotic orbit pathways from earth's L2 out to the gas giants and beyond.
While it is in-between planets, telescope could look at stars and galaxies just like hubble.
But when it closes in on planetary sytems, we get great images of planets, moons etc.
That takes lots of time, but, if the telescope does science on the way out, who cares as long as our kids and grand-kids get great photos?

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[djellison]

Zero x 350kg craft = zero thrust.
Zero x 11 ton craft = zero thrust.

You say zero thrust - then talk about an RTG powered Dawn Thruster.

Dawn's thrusters require approx 10x the output of a typical RTG. Also - assuming you could apply every ounce of Delta V that Dawn has generated and apply it to a Hubble sized payload, the total Delta-V it would impart would drop from approx 10km/sec to 1.4 or so.

Exploring the Earth-Moon region with little Delta-V is easy. It's been done time and again. That Scientific American article is somewhat disingenuous to talk about the '300 million miles' that Genesis traveled....when it actually just went to L1 and back, via L2... in an geocentric frame, a few million miles, not hundreds of millions. It also negates the fact that getting from LEO to L1 requires >3.5km/sec in the first place.

Getting out to Mars, Jupiter, Saturn and beyond....I see no reference to the zero Delta-V trajectories in either of the papers you cite.

I'd be delighted to see a realistic trajectory that gets 11 tons from LEO or even L1 to Mars, Jupiter and beyond with zero delta V in a time frame realistic for the lifetime of a spacecraft. Say, 10-20 years.