wpallen@watale.UUCP (Warren P. Allen @ U of Waterloo X 2522) (11/12/85)
Can anyone explain to me (in 250 words or less) the famed 'slingshot' effect that is used to accelerate space probes? I understand this effect is used not only to change the trajectory of the craft, but also its *speed*. I know it has to do with angular momentum, but *how* is the planet's momentum transfered to the space craft? PS. keep it simple if possible.. thanx
gml@ssc-vax.UUCP (Gregory M Lobdell) (11/13/85)
> > Can anyone explain to me (in 250 words or less) the famed > 'slingshot' effect that is used to accelerate space probes? > I am told, though I haven't actually written a simulation for it that the slingshot effect is due to the fact that you are falling into a moving object, so as you fall, it pulls you along. Gregg Lobdell
carroll@uiucdcsb.CS.UIUC.EDU (11/13/85)
Very simple explanation: Suppose the space craft is traveling radially out from the sun. Now, it approaches a planet, say toward the back side (i.e. on the side away from the direction the planet is traveling). It will be attracted to the planet, and therefore gain speed in the direction the planet is moving. Because the planet is in a nearly circular orbit, it's radial velocity is about zero, so the space craft picks up radial velocity coming in and loses it going out in equal amounts. It does, however, gain some velocity perpendicular to that by being attracted to the planet as the planet moves away. So, the total velocity vector is now larger than it was originally. What the space craft gains is lost by the planet, but due to the large size difference no one notices. Actually slingshot effects are a lot worse than this, since the space craft starts with orbital motion, but that's the general idea. Alternatively, consider two objects approaching each other, just offset a little. If they attract, you could set it up so that they just go around each other a half orbit, so that each ends up moving in the opposite direction it started in.
fisher@star.DEC (Burns Fisher ZKO1-1/D42 DTN 381-1466) (11/14/85)
// I am not expert on this subject, but it was my impression that there are two different kinds of effects going on here: The first is a change of velocity, not necessarily speed. If you whip around the planet and zip off with a direction 180 degrees different (not really possible, I guess, but I can talk about that without vector notation), you have changed your velocity by -2V. Similarly with different angles. The solar polar mission coming up uses Jupitor to sling the spacecraft into an orbit which is ~90degrees to the ecliptic, nearly impossible using engines. The second, I am a bit more fuzzy on, but I have heard that if you fire your engines while you are down in the gravity well of a planet that it has a multiplier effect of some sort. That is, your final speed is higher than if you waited until you got out of the well and then fired. I guess that makes some vague sense from a conservation of energy viewpoint...the planet pulls down mass M, but only mass M-m goes back out (at a higher speed). I'd be interested in hearing clarifications and/or corrections. Burns
KFL@MIT-MC.ARPA ("Keith F. Lynch") (11/15/85)
Date: 12 Nov 85 23:53:24 GMT
From: tektronix!uw-beaver!ssc-vax!gml@ucbvax.berkeley.edu
(Gregory M Lobdell)
>
> Can anyone explain to me (in 250 words or less) the famed
> 'slingshot' effect that is used to accelerate space probes?
>
I am told, though I haven't actually written a simulation for it
that the slingshot effect is due to the fact that you are falling
into a moving object, so as you fall, it pulls you along.
(Why didn't I see the message that this is in reply to?)
When a spacecraft falls towards a planet but misses it, its
trajectory is a hyperbola. It leaves with the same velocity as it
arrived with. BUT note that this is relative to the planet! Relative
to the Sun, it looks very different, and it is possible for the
spacecraft to have accelerated from zero to twice the oribital speed
of the planet *relative to the Sun*. This is what allows the Pioneer
and Voyager probes to reach solar escape velocity (which, in the
vicinity of Jupiter is 1.414 times the orbital speed of Jupiter) with
negligible fuel consumption.
It is possible to imagine a set of neutron stars or other dense
massive objects set up to fly by the solar system and another star at
a large fraction of the speed of light. Using these, one could travel
between the stars at a large fraction of the speed of light with very
little energy consumption.
A second slingshot effect is that it is more effective to burn fuel
when passing close to a massive object. It has been pointed out that
with today's technology, we can send a probe past Jupiter in such a
way that Jupiter's slingshot effect will cancel out most of the
probe's solar orbital velocity, and will cause the probe to drop
towards the Sun (this is much more energy efficient than trying to get
to the Sun directly, since you have to cancel out earth's orbital
velocity somehow). By the time it gets near the Sun it will be moving
quite rapidly, mostly because of its long fall from Jupiter. Just
when it's closest to the Sun is when you burn all your fuel as rapidly
as possible. This will cause it to fly away from the Sun at about
1000 miles per second! At that velocity, about 100 times that of the
Voyager probes, it can reach Earth in a day, Jupiter in a week, Pluto
in 6 weeks, and Alpha Centauri in about 8 centuries. It could be
used for exploration or perhaps for energy by catching it in an
electromagnetic gun (you actually get more energy out than you put
in. The extra comes from dropping part of the Earth's mass (the fuel)
into the Sun, and from dropping Jupiter's orbit a tiny fraction of an
inch closer to the Sun.)
...Keithmcdaniel@uiucdcsb.CS.UIUC.EDU (11/17/85)
Could someone please post the EQUATIONS for the slingshot effect?!? It's hard to figure ( :-) ) how it works, given only text.
carroll@uiucdcsb.CS.UIUC.EDU (11/18/85)
Isn't it control of direction that is more efficient deep in a gravity well? I.e., if you want to make a course correction, it's a lot cheaper to do it close to a large mass (as exemplified by the Solar Polar Mission doing it's course change next to Jupiter). I would suppose that it is easier since you can dump your momentum into a huge momentum sink (in effect, using the planet as reaction mass).
slerner@sesame.UUCP (Simcha-Yitzchak Lerner) (11/19/85)
> > Can anyone explain to me (in 250 words or less) the famed > 'slingshot' effect that is used to accelerate space probes? I am not going to go into full detail, but it has to due with the loss of mass from doing an engine burn in the gravity well. You gain speed from falling, loose mass from the burn, and loose less speed going out than coming in (assuming you stay out of atmosphere) since your mass is down. 'nuff said! -- Opinions expressed are public domain, and do not belong to Lotus Development Corp. ---------------------------------------------------------------- Simcha-Yitzchak Lerner {genrad|ihnp4|ima}!wjh12!talcott!sesame!slerner {cbosgd|harvard}!talcott!sesame!slerner talcott!sesame!slerner@harvard.ARPA
crimmin@tle.DEC (DTN 1-2015) (11/19/85)
> When a spacecraft falls towards a planet but misses it, > its trajectory is a hyperbola. It leaves with the same > velocity as it arrived with. BUT note that this is > relative to the planet! Relative to the Sun, it looks very > different, and it is possible for the spacecraft to have > accelerated from zero to twice the orbital speed of the > planet *relative to the Sun*. Queries: [Assume a probe using the slingshot effect around Jupiter] Is the trajectory a hyperbola while the probe is en route to Jupiter, or only after it misses? Watching from Jupiter, the probe approaches and departs at the same velocity. Does the probe perceive a faster velocity in relation to Jupiter? to the Sun? What is the meaning of *zero* the orbital speed of the planet relative to the Sun? Does it mean that the probe is moving at the same orbital speed as Jupiter? If so, how does the probe catch up and swing (sling?) around the planet. Is this correct? From the Sun, the probe appears to accelerate to a speed twice that of Jupiter in its orbit of the Sun. But from Jupiter, the probe appears to come and go at a constant velocity. Can you descibe how this works? Piter (New Hampshire)
space@ucbvax.UUCP (11/21/85)
Outstanding! Yours was the first explanation of the slingshot effect that truly made sense to me. No, I am not the poster of the original question, just an interested evesdropper. --Brian M. Godfrey
eugene@ames.UUCP (Eugene Miya) (11/21/85)
> You > gain speed from falling, loose mass from the burn, and loose less > speed going out than coming in (assuming you stay out of atmosphere) > since your mass is down. > What?! WRONG! Neither Voyager nor Pioneer "burned" into the Jovian or Saturn systems. No significant mass loss. From the Rock of Ages Home for Retired Hackers: --eugene miya NASA Ames Research Center {hplabs,ihnp4,dual,hao,decwrl,allegra}!ames!aurora!eugene emiya@ames-vmsb.ARPA
KFL@MIT-MC.ARPA ("Keith F. Lynch") (11/21/85)
Date: 19 Nov 85 20:00:07 GMT
From: decwrl!dec-rhea!dec-tle!crimmin@ucbvax.berkeley.edu (DTN 1-2015)
Subject: slingshot effect
Is the trajectory a hyperbola while the probe is en route
to Jupiter, or only after it misses?
The trajectory isn't really a simple curve, since it is influenced
by both the Sun and Jupiter. At first, you can regard it as being an
ellipse about the Sun. If Jupiter didn't get in the way, it would
continue to orbit the Sun in an elliptical orbit with perihelion near
Earth's orbit and a aphelion near Jupiter's orbit. Eventually, it
would get close enough to either Jupiter or Earth that its orbit would
be perturbed (or it would crash into one of those planets, or perhaps
into an asteroid - not into Mars though, it passes above or below
Mars' orbit).
But of course the elliptical orbit is so designed that Jupiter will
be at the apogee when the probe is there, so it never completes even
one full elliptical orbit of the Sun. This, by the way, is called a
Hohmann minimum energy orbit - the least energy way to get from here
to Jupiter.
The probe does not quite hit Jupiter, but it does pass so close that
Jupiter's effect on the probe greatly overwhelms the Sun's effect. If
we now switch to a frame of reference in which Jupiter is stationary
(we were in a frame of reference in which the Sun was stationary), we
see the probe coming almost directly towards Jupiter in nearly a
straight line. As the probe gets closer it speeds up and curves
towards Jupiter. It swings past, the path straightens out in a new
direction, and it slows down. Once more it is in a nearly straight
line, going almost directly away from Jupiter, and is going at the
same speed it came in at. Note that since it 'fell' to Jupiter from a
great altitude, it had more than Jupiter-escape-velocity at every
distance from Jupiter, so it could not possibly have become a
satellite of Jupiter. No matter how it was aimed, unless it hit
Jupiter it had to leave the vicinity of Jupiter as fast as it came in.
In the vicinity of Jupiter and in the reference frame in which Jupiter
is stationary, the path of the probe was a hyperbola with Jupiter at
one focus.
Switching back to a Sun centered reference frame we see that the
velocity is not the same as it was. After passing by Jupiter the
probe is now going much faster. Once it becomes distant enough from
Jupiter that the Sun's gravity is the only significant force on the
probe, the path of the probe is a hyperbola with the Sun at one focus.
If nothing gets in the way, the probe will continue out of the solar
system and into interstellar space to wander among the stars for
countless eons. The chances of it ever running into a star or a
planet in another solar system are vanishingly small, even though it
will be roaming entirely within our galaxy - it doesn't have galactic
escape velocity. It is an interesting exercise to imagine how one
would go about detecting a Voyager/Pioneer type probe in interstellar
space, even assuming there are several in each cubic light year
(launched by other civilizations).
Watching from Jupiter, the probe approaches and departs at
the same velocity.
Right.
Does the probe perceive a faster velocity in relation to Jupiter?
to the Sun?
After leaving the vicinity of Jupiter, the probe is going faster
relative to the Sun than relative to Jupiter. A few years later, when
Jupiter is on the other side of the Sun, the probe is going faster
relative to Jupiter than to the Sun, not that that is especially
relevant.
What is the meaning of *zero* the orbital speed of the
planet relative to the Sun?
I meant that if the probe was in the vicinity of Jupiter and was at
rest relative to the Sun, Jupiter could accelerate the probe to twice
Jupiter's orbital velocity, relative to the Sun. That alone is faster
than solar escape velocity.
The Voyager and Pioneer probes were not at rest relative to the Sun,
however their velocity relative to the Sun in the vicinity of Jupiter
WAS less than Jupiter's, i.e. Jupiter overtook the probes.
It's kind of confusing. One could, in principly, go anywhere simply
by aiming your rocket in the right direction. But we don't have
anywhere near enough energy to do it that way. So it is done in the
most energy efficient way possible, hence the various Hohmann orbits
and slingshot effects.
Is this correct? From the Sun, the probe appears to
accelerate to a speed twice that of Jupiter in its orbit
of the Sun. But from Jupiter, the probe appears to come
and go at a constant velocity.
Right. Not really twice Jupiter's speed, that is the theoretical
maximum. Anyway, you don't really want to go that fast if you want to
get to Saturn and to pass both Jupiter and Saturn as SLOWLY as
possible, to have lots of time for observations.
Also (in the Jupiter frame), the probe does come and go at the SAME
velocity, but it isn't really a CONSTANT velocity. It increases to a
maximum at the closest point to Jupiter and then decreases back to the
original value.
I think there is an out-of-ecliptic-plane probe being planned, that
will pass underneath Jupiter so as to rise up out of the plane which
all the planets travel around the Sun. This will give us the first
clear view of the Sun's north and south poles. It is ironic that a
probe meant to study the Sun has to go past Jupiter first, since
Jupiter is four times further than the Sun, and in the opposite
direction. But it is the most energy efficient way to get a probe out
of the ecliptic plane. It would be done in the same way if the probe
was to drop straight into the Sun. In space it is just as hard to
lose velocity as to gain it, and any probe to the Sun has to lose the
Earth's orbital velocity about the Sun or it will just continue to
orbit the Sun in the vicinity of Earth.
Hope this answers your question.
...Keithcarroll@uiucdcsb.CS.UIUC.EDU (11/23/85)
The zero factor on the orbital velocity means that the probe is moving in
a purely radial direction, i.e. straght out from the Sun. The planet, however,
sees it as moving at orbital speed away. After slinging around, it is moving
at the same SPEED with a different VECTOR. So, from the planet's point of view
it comes in one way and goes out the opposite. From the Sun's point of view,
it goes in with no orbital and come out with 2 times the planets orbital
velocity.
<- +++++++++++++++++
+
(Jupiter's Orbital Velocity) <-- J +
+
+
+
+ <-- Path of Probe (+)
+
E
SUNspace@ucbvax.UUCP (11/27/85)
I liked your explanation of the slingshot effect, but I thought I would point out to you that "velocity" with respect to Jupiter is affected. I think you meant to say that the "speed" with respect to Jupiter is unaffected. Remember, velocity has "speed" and "direction." Greg Thorson AT&T Bell Labs Holmdel, NJ 07733 houxa!heli