Mar 16 2008, 06:47 PM
I wondered how today's scientists and engineers design the trajectories for their missions. After all, there is a fixed ∆V-budget, but the time we arrive at the target is usually not that important in unmanned spaceflight.
In an old book I read about the patched two-body approximation - this means, we always just calculate the gravitational forces between the probe and the celestial body which acts most strongly upon it. But certainly this is not up to date any more, and i doubt that the Cassini mission design could have been done this way. After all, there is not only the gravitational slingshot at jupiter (I think that would still be possible with the old approach), but the trajectory for the many moon flybies. Is this done numerically, and what techniques are used? Is the commercial software for doing this, i.e. you specify your targets and the timeframe and get the minimum ∆V needed? Are we close to the mathematically optimum solution, or is there still room for improvements?
It would be quite interesting if anyone could give me a rough picture of how this stuff is done nowadays.
Mar 17 2008, 03:45 AM
It depends tremendously on the mission. Usually, there are one or two guiding constraints that are all-important, and everything else is shoehorned to make that work. For example, New Horizons was to get to Pluto as fast as possible, and to arrive with Charon in a particular orbital configuration. With Charon's orbital period so tiny compared to the lengthy cruise, it became easy to reduce everything to getting the right gravity assist from Jupiter. That's why the flyby distance was so sub-optimal for Galilean science, and they couldn't even time the flyby to get a great closeup of Callisto that might have occurred serendipitously.
For a Venus/Mars mission, they're just trying to minimize energy.
For something like the Cassini tour, the guiding rules were:
1) The orbital inclinations were to vary throughout the mission.
2) Only Titan can provide gravity assists, so the orbit has to always provide close return trips to Titan with minimal delta-V.
3) Because the other moons have tiny gravitational effects, flybys of them can be targeted without worrying about their effect on the future trajectory.
4) Time it so that there was a Phoebe flyby on the way in.
It is not possible to program a very large number of constraints and force them to happen. It is also not possible to perform an exhaustive examination of all possible trajectories for something like Cassini. So they hand-develop several options, and in planning meetings choose among the options and in post-launch planning look for opportunistic alterations that are cheap in delta-v.
Mar 17 2008, 11:32 AM
Great info, thank you. I also did some more websearching and found some interesting papers and websites:New methods in celestial mechanics and mission design
This is a rather theoretical article, i.e. they don't tell you how they worked on a technical level - how they hack the stuff together. But hey, it's the American Mathematical Society Implementation of a Low-Thrust Trajectory Optimization Algorithm for Preliminary Design
This shows a tool for once, but of course it's far from a complete solution - it's rather a niche tool for optimizing your trajectory using continiously firing low-thrust engines (read ion thrusters).Continuous Low-Thrust Trajectory Optimization: Techniques and Applications
With a title similar to the previous one, this is a lot longer and more comprehensive (it's a dissertation, not just an article). This drops some names of software packages:
The global search for optimal trajectories was performed using the STOUR (Satellite Tour Design Program) software package; the GALLOP (Gravity-Assist Low-thrust Local Optimization Program) optimization tool was used for the local search. The algorithm was compared to SEPTOP (Solar Electric Propulsion Trajectory Optimization Program, developed by Carl Sauer of JPL) a software package based on indirect methods. Both optimization packages showed comparable performance characteristics and to be in good agreement with respect to propellant consumption and overall mission time.NASA Solar System Simulator
With this web version it is not possible to try and design a custom trajectory for a probe, but the underlying data for the NASA probes and celestial bodies seem to be very exact, so I guess there exist other front-ends to take advantage of this.
I'd really like to try and design a trajectory for something, just for fun, but I guess it's not easy to do. I guess I'll have to stick to Hohmann and bi-elliptic transfer orbits
I found another good presentation, which basically elaborates on what you said:Some Methods for Global Trajectory Optimisation used in the First ACT Competition on Global Trajectory Optimisation
Website of the GTOCGlobal Trajectory Optimisation Competition
Accompanying UMSF threadAsteroid Grand Tour
Mar 17 2008, 06:09 PM
And keep in mind, as any hypothetical Saturn orbiting probe approaches Titan, there is a 360 degree target around Titan and an almost infinite gradation of fly by altitudes possible. Each and every path leading somewhere different.
Most combinations don't return to Titan, but many do, and of the ones that do, a certain tiny percentage manage to do something interesting in the interim. Also, there would be trajectories that would eventually return to Titan, but perhaps after 1, 2, or more revolutions about Saturn. Also, maybe your next encounter with Titan might be as you rise away from Saturn rather than while you plunge towards it. I note usually for the pretty elliptical orbits we see for Cassini, the inbound and outbounds are ~90 degrees apart.
I don't think any one has ever said, and perhaps the orbital tour software automatically rejects paths like this, but there are probably many interesting trajectories that can't be flown because somewhere along the orbit it intersects a portion of the Saturnian rings we don't want to fly through. Also, we can't get too close to Titan as it's puffy atmosphere might interfere with our craft.
We have other threads here that discuss possibly using Titan's atmosphere to brake (or help brake) into orbit about Saturn. Such a flight path would be very interesting, recall the Pioneer Venus bus experiments as it skimmed the Venusian atmosphere.
IIRC, decels in the range of 40g are possible during an atmosphere graze. Done right you save fuel, and perhaps have an opprotunity to maneuver during the braking and wind up somewhere more interesting than you could have otherwise.
Mar 17 2008, 06:21 PM
Since SOI, the rings haven't been much of a worry because periapsis is well outside the major rings. It would actually take a lot of energy to get down to them, the same way it takes a lot of energy to get to Mercury from Earth/Venus. That's why ring imaging was so important during the initial approach in 2004 -- we'll never get that close again (unless in the XXM/endgame).
Cloudtop distance, mimimum:
Pioneer 11: 20,000 km
Voyager 1: 124,000 km
Voyager 2: 100,800 km
Cassini: 18,000 km around the time of SOI
more like 400,000 km since then (varying)
Mar 18 2008, 09:22 AM
For End-Of-Mission scenarios, I've wondered.... How much can an optimized Titan flyby drop periapsis? Could it be dropped to a "nearly safe" (end of mission risk levels permitted) zone near the F-ring or the Keeler Gap? Are there gaps that appear wide enough and empty enough to give a decent chance of a successfull ring passage? Could they intercept such a gap, do a Titan flyby, and drop periapsis inside of the D-ring or into a C or D-ring gap that seems "nearly safe"
The ring science and particles and fields Saturn-geophysics science bonanza from such possible trajectories could equal the entire rest of the mission in many most-important regards.
Mar 18 2008, 02:30 PM
How much can an optimized Titan flyby drop periapsis? Could it be dropped to a "nearly safe" (end of mission risk levels permitted) zone near the F-ring or the Keeler Gap?
As the current periapsis is already down to 163000 km, it should definately be possible to bring that down using Titan gravity assists. The (very) theoretical maximum for ∆V on a single Titan gravity assist is about 11 km/s (twice its orbital speed), but realistically it is much lower than that, due to the extensive atmosphere.
JPL document they say that
Note that a Titan flyby at an altitude of 950 km imparts an equivalent ∆V of about 800 m/s to the spacecraft
So, what would this do:
Periapsis: 163000 km
Apoapsis: 1300000 km
-> Semi-major axis: a = 731500km
-> Specific orbital energy = -GM/2a = -25 930 739.8 (m/s)^2
-> Speed at Apoapsis: 2.550 km/s
∆V at Apoapsis: 0.8 km/s -> New speed 1,75 km/s
-> New semi-major axis: a = 685 995 km
-> New Periapsis: 2a - 1300000km = 71 990 km
Which is coincidentally just inside the D ring. So I think it is well possible that we can aim for a specific spot inside the rings for our Periapsis. It is really the question how safe these trajectories are.
Mar 19 2008, 02:24 AM
Dropping Cassini thru a ring gap near EOM had always appealed to me. The problem is getting direct from instruments to Earth transmission instead of thru the tape recorder in order to get some data back in case it doesn't make it thru. I don't recall reading whether this mode was possible.
"These ships weren't made for shooting the rapids." A line or something similar from Silent Running.
Mar 19 2008, 10:08 AM
" It is really the question how safe these trajectories are. "
Cassini's going to run out of trajectory adjustment propellant, and ultimately (I don't know how long a zero-encounter mission could last) momentum-wheel-despinning attitude control propoellant.
It's really a question of a really long, boring, senile "distended" mission, (possibly following a 1 or 2 year reduced activity second extended mission), or going out in a blaze of heroic (and far more scientifically valuable) glory.
Mar 20 2008, 01:20 AM
Please don't overestimate the scientific value of most of the 'abrupt' mission ends.
Mar 20 2008, 01:45 AM
Think that mchan has it right, though; any sort of extremely risky EOM scenario has to rely on DTE comm, otherwise what's the point if the spacecraft may not survive?
With respect to detailed ring studies, this means that waiting as long as possible would be best since we're approaching ring-plane crossing as seen from Earth (Sept 2009).
Mar 20 2008, 11:33 AM
Extended mission is 2 years. INCLUDING the equinix. Scientific objectives and orbital inclination/viewing angles are picked out as I understand it; detailed science planning in development.
As I understand, there's expected to be hydrazine left for a second extended mission, which can be some combination of "Active but short" or "Avoid encouinters, minimize delta-v-using orbit maneuvers, and live long". If we do "more of the same" that we've been doing till the hydrazine runs out, it's unlikely we'll have dramatically new science. Dito for a long, boring retirement.
Some figure of merit might be arm-wavingly invented (and quantified for end of mission scenario selection) goes like this....
1.) The more new science, the better - squared
2.) The more new data, the better - NOT squared.
3.) For every 50% reduction in remaining hydrazine, you can double spacecraft risk after that to expected hydrazine depletion. I.E., If you expect to run dry on the next orbit, you can take a pretty big risk.
4.) You can't let it hit Titan or Enceladus after the End Of Mission, even many decades later.
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