clj@ksr.com (Chris Jones) (11/05/90)
In article <1990Nov2.173226.19955@cbnewsl.att.com>, sw@cbnewsl (Stuart Warmink) writes: > >I assumed that velocity w.r.t. to Sun meant *away* from the Sun. No, I think it means as measured from the Sun's frame of reference. Earth has a velocity w.r.t. the Sun of about 66000 mph. Ulysses' speed w.r.t. the Sun immediately after launch did look like that velocity added to 30000mph plus, which is what you would have expected the result to be. I still have seen no explanation of how Ulysses gained velocity in the period after the boost, but I'm almost certain it didn't, and that there was an error in one of the velocity reports. -- Chris Jones clj@ksr.com {world,uunet,harvard}!ksr!clj
davew@sputnik.mit.edu (dave warkentin) (11/07/90)
In article <883@ksr.com>, clj@ksr.com (Chris Jones) writes: > In article <1990Nov2.173226.19955@cbnewsl.att.com>, sw@cbnewsl (Stuart Warmink) writes: > > > >I assumed that velocity w.r.t. to Sun meant *away* from the Sun. > > No, I think it means as measured from the Sun's frame of reference. Earth has > a velocity w.r.t. the Sun of about 66000 mph. Ulysses' speed w.r.t. the Sun > immediately after launch did look like that velocity added to 30000mph plus, > which is what you would have expected the result to be. I still have seen no > explanation of how Ulysses gained velocity in the period after the boost, but > I'm almost certain it didn't, and that there was an error in one of the > velocity reports. > -- > Chris Jones clj@ksr.com {world,uunet,harvard}!ksr!clj ------------------------------------- I doubt it was merely a numerical reporting error, since I seem to recall a specific statement about the speeding up in one of the updates (sorry, I can't refer to the exact message.) At the risk of wasting bandwidth, I'm reposting a followup to an earlier comment on the peculiarities of Ulysses's orbit (I suspect the followup wasn't properly transmitted due to server problems): ------------------------------------- In article <484@hal.CSS.GOV>, stevem@hal.CSS.GOV (Steve Masters) writes: > sw@cbnewsl.att.com (Stuart Warmink) writes: > > >Assume that Ulysses was boosted out of Earth orbit in such a direction > >that it was originally at a tangent to the Earth's orbit - not an > >unusual direction for a boost to the outer planets. If started of in such > >a direction its velocity w.r.t. the Sun would be 0. As Ulysses gained > ^^^ > ...not unless it were launched directly against the earth's orbital velocity > at the earth's orbital speed...Ulysses, upon leaving earth's orbit, was almost > certainly moving close to the earth's orbital velocity (about 18.5 mi/sec, > I think) relative to the sun. > > This doesn't explain an increase in sun-relative speed...are we sure there isn't > a typo? Unless there is a gravity assist from Venus, there is no way to get > to Jupiter by dropping closer to the sun (I don't think, anyway :) ) > > Steve Masters stevem@hal.CSS.GOV > ENSCO, Inc. > Melbourne, FL 32940 USA I too was puzzled by Ulysses's increase in speed, so I performed a few calculations to see if I couldn't come up with an answer (in the absence of more authoritative pronouncements :-). First of all, the most obvious transfer orbit from Earth to Jupiter is the ever-popular Hohmann transfer - the 1/2 ellipse which is tangent to Earth's orbit at perihelion and to Jupiter's at aphelion. Event schedules have been posted for Ulysses which give the launch date as 10/6/90 and the Jupiter encounter date as 2/8/92 for a time of flight of 490 days. The TOF (in years) in the Hohmann orbit, though, is .5*(a^1.5), where a is the semi-major axis in AU. Jupiter averages 5.2 AU and Earth about 1 AU, so a for the transfer would be .5*(1+5.2)=3.1 and the TOF is 2.73 years, or 997 days! Clearly the Hohmann transfer is not being used. Presumably the mission planners wanted to a) shorten the flight time and b) have more speed for the Jupiter gravity assist, so they launched from Earth with a velocity greater than that needed for the Hohmann. It still seems reasonable to assume (as Stuart did above) that Ulysses leaves on a path tangent to Earth's orbit, in order to take fullest advantage of Earth's orbital velocity. So now we need to find an orbit which leaves Earth on a certain date tangent to Earth's orbit and which arrives at Jupiter on another specified date. According to my home-made ephemeris program, Earth was 1.000 AU from the Sun at launch and Jupiter will be 5.401 AU from the Sun at encounter, and the angle between these two points is 145.2 degrees (just using heliocentric longitude and ignoring Jupiter's latitude at encounter, which I think is about 1 degree). It turns out, though, that a Keplerian orbit satisfying all these conditions does not exist! The one which connects these two points and is tangent to Earth's orbit takes 558 days. Assuming no really major mid-course corrections, we have to through out the assumption that the departure is tangent to Earth's orbit. After some trial and error, I found that if you assume that Ulysses actually does move closer to the Sun before heading out to Jupiter, you can make the transfer orbit satisfy the conditions. This means transfer orbit perihelion doesn't occur at launch, but some 6.24 days (8.445 degrees true anomaly) _after_ launch, and so at first speeds up with respect to the Sun before moving away and slowing down. Using this assumption, I find that Ulysses reaches Jupiter with enough energy to perform a hyperbolic fly-by gravity assist maneuver to redirect its velocity vector so than as it leaves Jupiter's sphere of influence it can be in an orbit with aphelion at 5.401 AU, perihelion at 1.374 AU, a period of 6.235 years, and an inclination to the ecliptic plane of 83 degrees. This looks fairly good, since previous postings have mentioned a perihelion of 1.4 AU (signif. digit?) on 2/5/95 (period of just under 6 years). A couple of questions remain. First of all, why didn't they launch tangent to Earth's orbit? My tentative answer - that was the nominal trajectory, but it just so happened that they got it off in the first half of the launch window, so they adjusted injection conditions so as not to throw everything else off schedule. Sky and Telescope (Nov. '90, p.498) mentions a 19-day launch window starting on Oct. 5, so the mid-point would have been Oct. 14-15. Thus it could well be that they launched a few days early, thus producing the 6.2 day time to perihelion. More importantly - why didn't they put it in a higher inclination? Perihelion of the solar orbit is 1.4 (maybe 1.374) AU - why didn't they trade some of that energy to reach a higher angle? And perhaps most important of all - what does this imply for the question of when Ulysses was closest to the Sun? Unfortunately, not much - I calculate the perihelion distance of the transfer orbit to be .9949 AU, as opposed to the Earth's .9836, so it was still closer to the Sun on Earth than it ever was/will be in orbit. (N.B. It occurs to me that in the above arguments about the transfer not being tangent to Earth's orbit I haven't taken Earth's non-zero flight path angle into account, but I believe this effect is minor and doesn't substantially affect the calculations. A good reference for would-be space cadets: Fundamentals of Astrodynamics by Bate, Mueller, and White : ISBN 0-486-60061-0 It is (or was) the USAF Academy textbook on the subject. It's a Dover publication, and cost me $5.50 about 10-12 years ago, so it probably costs a bit more now.) For those who actually read this far, thanks for letting me put my $.02 in. Maybe someone with more info can correct/supplement these wild computations. -- Dave Warkentin davew@sputnik.mit.edu