[AR] Re: Catching Oumuamua

From: William Claybaugh <wclaybaugh2@xxxxxxxxx>
To: arocket@xxxxxxxxxxxxx
Date: Mon, 1 Mar 2021 08:04:32 -0700

Ivan:

20 km / sec of required delta-v is 2.5 times that required to reach earth
orbit.  The only way I know to “cheaply” get that sort of velociy change
would be electric propulsion, which would not be an impulse maneuver.

I remain concerned that this mission requires understanding momentum
transfer from the Sun’s orbit around the galaxy.  That must have occurred
during the Oumuamua encounter and—despite starting with a Solar velocity
vector because it originates in the Solar System—a probe may be effected by
such momentum transfer, possibly positively.  That said, I note that the
Sun’s orbital acceleration around the galaxy is order 10^-8 cm/sec^2.

Does extending the mission time by five or ten years lower the delta-v
required at the Sun?

Bill

On Mon, Mar 1, 2021 at 6:29 AM Ivan Vuletich <ivan.vuletich@xxxxxxxxxxxx>
wrote:

This may not be what you are looking for. But I decided to try and model
the trajectory using NASA's GMAT tool.

So far the trajectory model consists of an impulsive burn at Jupiter to
kick the probe towards the Sun with a periapsis at 50 solar radii and the
inclination of Oumuamua. Than another impulse burn to fling the probe out
to the distance of Oumuamua 20 years after periapsis.

I haven't put Oumuamua into the model or tried to aim the probe at
Oumuamua at this stage. And I've used a Jupiter flyby in 2025, which
corresponds to an initial starting state approaching Jupiter that I was
able to find online.

If I haven't screwed something up (quite likely considering my limited
GMAT skills). Then for a Jupiter flyby in 2025, the Jupiter burn is about
3.8km/s and the Solar periapsis burn is about 20 km/s.

On 27/02/2021 11:25, Henry Spencer wrote:

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

References:
- [AR] Re: Catching Oumuamua
  - From: Ivan Vuletich

[AR] Re: Catching Oumuamua

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