[AR] Re: Catching Oumuamua
- From: Henry Spencer <hspencer@xxxxxxxxxxxxx>
- To: Arocket List <arocket@xxxxxxxxxxxxx>
- Date: Fri, 26 Feb 2021 19:25:06 -0500 (EST)
On Fri, 26 Feb 2021, William Claybaugh wrote:
...confirm that 60 klicks per second will catch it in about 20 years...
'Oumuamua is currently at about 3.36Gkm, doing about 27.8km/s, and it's
not going to slow down much (its Vinf is 26.33km/s). Worse, you may not
be able to launch right away, because Jupiter's got to be in the right
place and its orbital period is nearly 12 years.
Budget 4 years for build and test, 6 years waiting for Jupiter (might be
0, might be nearly 12, I'd need more work to put a number on it), 5 years
to reach Jupiter, and several more to get back down near the Sun, and
that's nearly 20 right there. 20 years from now, 'Oumuamua will be
20.4Gkm away, doing 26.65km/s. (Numbers from JPL's HORIZONS online
ephemeris generator.)
If we want a 10-year flight time from perihelion, so we reach it about 20
years after *launch*, we need to equal its velocity, plus enough extra to
make up its head start in 10 years. 20.4Gkm in 10 years is 64.6km/s
(sanity check: that's a bit over twice its velocity, which makes sense
because it will have had a bit over twice that 10 years to build up that
head start), *plus* its velocity, means the probe's average velocity has
to be about 91km/s. Ouch.
If that "about 20 years" starts at *perihelion* -- ~20 years from now --
then yeah, required average velocity is a bit under 59km/s.
...and that a plane change at Jupiter followed by a solar gravity assist
and some makeup electric propulsion would allow a flyby.
What exactly are you thinking of when you say "solar gravity assist"?
Classical gravity assists work only when the body you're passing close to
is in orbit around something bigger -- you get to swipe a bit of its
orbital momentum by swinging into and out of a *moving* gravity well.
That doesn't work for the Sun. In the absence of rocket burns, whatever
heliocentric orbit you're in when you leave the vicinity of Jupiter,
you're still in after passing close to the Sun at perihelion.
What you can do is Oberth effect: a big rocket burn at perihelion yields
a much bigger delta-V at infinity. However, to go from an ellipse with
perihelion at 50SR and aphelion at Jupiter, to a hyperbola with the same
perihelion but 50km/s of velocity at infinity, would require a burn
imparting about... 15km/s if the back of my envelope is correct. That's a
whole lot for a chemical rocket, and one constraint of the Oberth effect
is that the whole burn has to be near perihelion, so electric probably
isn't going to work for that.
Might be able to get some boost from Jupiter (as well as the plane
change), but I wouldn't want to count on it. Again, more work required to
put numbers on that.
Henry
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