Gravity Slingshot question: Does the direction of the rotation of the planet matter?

Factual Questions
1

So, you’re a bigshot at NASA, you’ve blackmailed congress and the executive branch and they’ve decided to fund the Pluto Express (sigh…if only…) but to get the probe out to Pluto, you need to whip the thing around Jupiter to gain a bunch of free (to you) speed. Th’ ol’ gravity slingshot move.

Here’s the question:

Does it matter which direction you whip around the planet (in relation to it’s rotation)?

My pal says “Yes: you have to go in the direction of the planet’s rotation to pick up speed (or to pick up the most speed). Going against the rotation of the planet will either gain you much less speed than going with the rotation, or it’ll cause you to lose speed.”

I say “You’re not zipping into the planet’s atmosphere, just into it’s gravity well. Gravity doesn’t have a “direction” other than down/in. As long as you stay out of the atmosphere, the planet’s rotation doesn’t matter. If you drop a rock into a well, it doesn’t matter what direction the water at the bottom is circulating.”

Who owes who dinner?

Fenris

2

your friend owes you dinner.

3

The planet is, for the purposes of the operation, a point mass; points can’t rotate (or if they did, there would be no way to tell).

4

The direction of rotation of the planet isn’t important, but the direction of revolution of the planet around the sun IS very important, it’s what gives the “slingshot” effect in the first place (if I remember right from college).

Otherwise, you wouldn’t be able to use Uranus as a slingshot planet.

5

Jupiter does have a large electromagnetic field, which is directional. Since a Pluto shot would still be mostly within the plane of the ecliptic, I don’t think it would play much of a role, but what about a “northerly” slingshot as opposed to a “southerly” slingshot? Is Jupiter’s EMF powerful enough to make a difference on a probe?

6

Actually, a rotating massive body does produce a side affect of general relativity called Frame Dragging, which pulls space/time in the direction of rotation.

The effect is significant with black holes and other supermassive objects; a mere planet’s frame dragging will not alter the trajectory in any reasonably measurable way.

7

Enola, don’t you know that it’s impolite to just barely beat me to the GR reference? :wink:

To give an idea as to the strength of the frame-dragging effect for “normal” bodies, when relativists want to measure it around the Earth, they need special-purpose satellites which do nothing but measure frame-dragging, with ultra-precise laser measurements, and thousands of orbits of accumulated effect. Admittedly, Jupiter is both more massive and rotates faster, but it’s still negligible.

One could argue that you’re both wrong (you said it doesn’t matter at all; he said you’d be much slower if you went the wrong way), but you’re much closer to being right.

8

Ok, my friend blew a gasket. He says he didn’t say what I thought he said (he’s probably right). He agrees that the planet’s rotation doesn’t matter, he says (and made me take down his exact words)

“To gain the benefit of a gravitational slingshot, the probe must follow (approximately) the planet in it’s oribit around the sun. If it travels against the direction of it’s orbit around the sun, it gets the opposite effect: a gravitiational brake.”

This is what Ski said. Can I get another confirmation before I conceed? (and an explaination as to why the direction of the planet’s orbit matters would be nice too)

At least I was right about what I thought he said…

Fenris

9

The planet’s rotation could have a very small effect. As stated earlier, for most flybys the planet’s radius is so small relative to the path of the spaceprobe that it’s effectively a point.
But if you have a very tight (cloudtop) flyby, then you might have to take into account any tidal bulges (either solar or lunar) which would distort the planet from an ideal spheroid.

This would probably only effect the Nth decimal place of calculating the spacecraft’s path, but still orders of magnitude greater than any relativistic effects.

10

I mean, why would the direction of the orbit matter? The planet still acts as a point source and it’s not like there’s currents in the ether to worry about…

11

Your friend was considering what major planetary body, when he was talking about objects moving “the other way” in orbits around our sun?

I smell a weasel.

There are ways of using orbits which are at high angles to each other to accelerate the smaller of the two bodies along its own orbit, although the choices are severely limited in the unlikely case where the orbits are coplanar, and opposite in direction. Still, even in the extreme case, an object in an elliptical orbit approaching a larger object orbiting in a wider orbit, in the opposite direction it could be done. The approach could be timed to take advantage of the radial (with respect to the sun) component of acceleration from the objects gravity. Then minimize the duration of the negative tangential acceleration by acheiving a resultant vector that had a sharper angle of escape from the object than the entering portion.

With essentially coplanar orbits, and with all objects moving in the same relative direction, (as in, say, every single damn thing bigger than your friend’s ass, orbiting around the sun, for instance) it is much easier.

Tris

12

Well as I remember it from college physics slingshots are about the only true example of a perfectly elastic collision. You get the extra velocity from the planet’s kinetic energy.(And velocity does have a directional component to it.) If you go with the planet’s direction you gain kinetic energy, if you go against the planet’s direction you lose it. I’m sure someone else will come around and explain it better however.

13

Actually, if your probe starts off retrograde, you can get an even bigger slingshot.

We start off with Voyager and Jupiter far away from each other. At this point, we can consider them to be in independent orbits around the sun. Jupiter is in an approximately spherical orbit, and the probe is probably in an eliptical orbit, tangent to both the Earth’s orbit (because that’s where it was launched from) and to Jupiter’s. The probe’s launch was timed such that it’ll reach the apihelion of its orbit (far point from the Sun) just as Jupiter is reaching that same point. When the probe reaches the collision point, it’ll be going slower than Jupiter.

In the usual case, the probe will be orbiting the Sun in the same direction as both Jupiter and the Earth, so Jupiter is catching up to the probe. The probe has speed V[sub]p[/sub], and Jupiter has speed V[sub]J[/sub]. That means that the relative speed of the probe and Jupiter is V[sub]J[/sub] - V[sub]p[/sub] .

Now, Jupiter and the probe get really close together. Now, Jupiter has much more gravitational influence on the probe than the Sun does, so let’s switch to Jupiter’s frame of reference. In Jupiter’s frame of reference, Jupiter is at rest, and the probe comes in at speed V[sub]J[/sub] - V[sub]p[/sub] . It swings around the planet on a very tight orbit, and comes back out in almost opposite the direction that it came in. In other words, after the encounter, the probe has a speed relative to the Sun of 2*V[sub]J[/sub] - V[sub]p[/sub] , which is a good bit greater than the original speed.

OK, that’s the standard case. Now let’s look at the retrograde case your friend is talking about. In this case, instead of Jupiter catching up to the probe, we’ve got a head-on collision. The objects approach each other at a speed of V[sub]J[/sub] + V[sub]p[/sub], so after the interaction, they’ll be receding from each other at that same speed, and the final speed of the probe will be 2*V[sub]J[/sub] + V[sub]p[/sub], which is actually faster than if they’re going the same direction.

So, to sum up: The direction of the orbits does matter, but not in the way that your friend claims. A retrograde slingshot gives you more than a prograde slingshot, not less.

14

Ok, since I started this argument with Fenris (I’m the friend in question), I’m jumping in. Quoting from a Scientific American website:

This seems to contradict what Chronos said regarding the direction from which the probe approaches the planet.

15

Chronos, I think you’re wrong. At least what you say doesn’t agree with JPL.

Basics of Space Flight, chapter on Interplanetary Trajectories, including Gravity Assist.
http://www.jpl.nasa.gov/basics/bsf4-1.html

Their description agrees with gorillaboy.

16

I believe Chronos is right, as usual. The text quoted by gorillaboy and Irishman assume that the planet and spacecraft are orbiting the sun in the same direction. If the directions are opposite, then the spacecraft must approach the planet from the front (front of the planet’s orbit, that is) to gain speed.

17

Something is bugging me about Irishman’s link. It says that if Jupiter had not been there for Voyager 2’s slingshot, “Perihelion would have been at 1 AU, and aphelion at Jupiter’s distance of about 5 AU.” That means that its orbit looked something like the picture 25% of the way down the page. It should have come upon Jupiter directly from the back. However, look at the last diagram on the page, and compare the vectors “Resultant V[sub]IN[/sub]” and “Planet’s Sun-Relative Velocity”. These vectors are not parallel. If they were, the speed boost would not work. This is what Chronos was referring to about it not helping.

18

gorillaboy’s quote from Scientific American and Chronos are both right, because they are talking about two different things. I’m not certain which case gorillaboy has in mind. In Chronos’ retrograde case, the probe is initially retrograde, and is still passing behind Jupiter (i.e. where Jupiter had been in its orbit) at closest approach. In SciAm’s gravitiational braking case, the probe is initially moving in the same direction as Jupiter (but more slowly), and passes in front of Jupiter at closest approach, and its delta V is in the retrograde direction.

When the Scientific American link says “approach the planet from the front” it is, I think, just poorly worded. It would be more clear if it said something like “pass in front of the planet” instead.

Achernar wrote:

Voyager 2 would be initially moving slower than Jupiter, so it would have approached from the front. This is the first case Chronos described.

19

Actually, upon further reflection, I think the Scientific American quote is more likely muddled thinking rather than just poor wording.