Q&BA: How does a gravity slingshot work?

By Phil Plait | February 17, 2012 11:00 am

In this episode of my live Q&BA chat session, I answered a question about how "gravity slingshots" work. This is the process of using the gravity of a planet to accelerate (or decelerate) space probes so they can more easily get to the inner and outer planets. It turns out gravity is not the only process at work here.

This technique is used all the time for spacecraft, and engineers are pretty good about nailing them perfectly, too. Sometimes the probes pass by Earth and take amazing pictures of us, like when Rosetta did in 2009, and in 2007, or when it passed Mars in 2007.

Be sure to check out all my other Q&BA videos!

CATEGORIZED UNDER: Cool stuff, Q & BA, Science

Comments (43)

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  1. Stuff « Econstudentlog | April 30, 2012
  1. Keith Hearn

    There is also the Oberth effect, which makes a rocket burn more effective if it’s done when the spacecraft is moving quickly during the close pass to the planet.

  2. Boomer

    So how is this used for time travel? :P

  3. PSP

    @Keith: Thanks for the pointer to “Oberth effect” – there’s a nice, simple writeup at Wikipedia.

  4. Darn it, Boomer beat me to it! :D

  5. Dave

    Hi Phil,

    Excellent explanation!

    I think you got something a little backwards near the end (around the 5:46 mark), or at least phrased it a little confusingly. Your first explanation of orbital energy vs. orbital distance was right, but then when you described it again it sounded like you said that you can give energy to a planet and drop it toward the Sun. If you give energy to a planet, the planet moves to a more distant orbit. Maybe you meant that the satellite drops toward the Sun after giving energy to the planet, but it came off a little confusingly.

    Anyway, very nice work.
    Best,
    Dave

  6. @Dave (#5)
    Yes, I was thinking the same.

  7. shunt1

    As explained, a gravity assist can be used to slow down a spacecraft as is often used when sending a probe to Venus or Mercury.

    In classical mechanics, the kinetic energy of a point object (an object so small that its mass can be assumed to exist at one point), or a non-rotating rigid body, is given by the equation

    Ek = 1/2 m * v^2

    where m is the mass and v is the speed (or the velocity) of the body. In SI units (used for most modern scientific work), mass is measured in kilograms, speed in meters per second, and the resulting kinetic energy is in joules.

    For example, one would calculate the kinetic energy of an 80 kg mass (about 180 lbs) traveling at 18 meters per second (about 40 mph, or 65 km/h) as
    Ek = (1/2) · 80 · 182 J = 12.96 kJ

    Since the kinetic energy increases with the square of the speed, an object doubling its speed has four times as much kinetic energy. For example, a car traveling twice as fast as another requires four times as much distance to stop, assuming a constant braking force.

    In an effort to divert an asteroid which has the potential of striking the Earth, increasing the relative velocities between the target and an impacting spacecraft will greatly increase the kinetic energy.

    One method of increasing the relative velocities would be by using a gravitational assist from a planet such as Jupiter.

    In addition to slowing down the spacecraft, the velocity vectors can also me altered so that the impact could be up to a 90 degree relative angle.

    With a train of multiple spacecraft on an impacting trajectory such as this, asteroids could be nudged from their initial orbit and prevented from striking the Earth.

  8. kmw

    Thanks for the explanation!
    I’m assuming this would also happen with Saturn & Jupiter’s moons when they pass each other in orbit? I think the gravity slingshot was mentioned in the Wonders of the Solar System series, but there was never a clear explanation as to what that was.

  9. Dr.Sid

    Interesting analogy came to my mind when listening to this explanation. I almost thought Phil would use it .. but somehow he did not in the end.
    First you show how going around the planet is the same as bouncing of the planet. Easy to imagine.
    Then you show how in planet centered view there is no way to gain energy. Everyday experience.
    Then simply show how the ball gains energy if it bounces off the moving planet. It’s also intuitive to imagine how the planet is slowed by that.

  10. wally

    Wonderful talk. I wish I had been able to show this to my friends who couldn’t understand what was bugging me about the opening episode of Gene Roddenberry’s “Andromeda”, in which in order to escape a pursuing space craft of similar performance, the crew flies close to an object of high mass to use the slingshot effect to overcome their lack of thrust, when of course, the pursuing craft could use the exact same trick, being on the same vector, and emerge on the other side in precisely the same pursuit positioning. :) My Suspension Bridge of Disbelief (or as Scalzi would say, “snowman”) sadly just can’t let that sort of thing go. Pedantic and to my loss, but that sort of sloppy front and centre just couldn’t predict a level of consistency that good storytelling thrives on. I’ll buy slipstream drives and midichlorians, but please get newtonian mechanics right.

  11. Dan

    I guess I’m still missing something: I understand how the spacecraft steals some of the planet’s orbital energy as it approaches the planet, but once it passes the planet and is now in “front” of it, wouldn’t the planet then steal that energy right back from the spacecraft? I.e. once the spacecraft has passed the planet their roles would be reversed?

  12. shunt1

    My only comment would be that the explanation was a little complex.

    If the spacecraft approaches from behind the planet, then a portion of the velocity of the planet is added to that of the spacecraft.

    If the spacecraft approaches from ahead of the planet, then a portion of the velocity of the planet is subtracted from that of the spacecraft.

    If the spacecraft approaches from above or below the planet, then the spacecraft’s orbital inclination around the Sun will also be modified.

  13. shunt1

    You are gravitationally bound to the Earth, so your orbital velocity around the Sun is about 29.783 kilometers per second. That’s the speed the planet is moving through space in its orbit about the sun. Earth’s speed varies a bit because its orbit is slightly eccentric, but that’s why we say mean orbital velocity.

  14. Rob

    Hi Phil,

    Wonderfully explained; I’m just going to be annoyingly pedantic and clarify one small detail: From 3:20 onwards, you state that if a spacecraft is “catching up” (which I interpreted as “going the same direction as”) a planet, then it will steal some of the planets energy. However, if they start off going in the same direction, that’s actually the gravity braking case — where the planet gains energy from the spacecraft (from the sun’s point of view.)

    For the spacecraft to gain momentum, it’s much better off travelling antiparallel (or, more commonly, perpendicular) to the planet.

    Thanks for writing such a fascinating blog!

    — Robert

  15. amphiox

    in which in order to escape a pursuing space craft of similar performance, the crew flies close to an object of high mass to use the slingshot effect to overcome their lack of thrust, when of course, the pursuing craft could use the exact same trick, being on the same vector, and emerge on the other side in precisely the same pursuit positioning.

    IIRC, in that episode of “Andromeda”, the high mass object in question was a black hole, and the slingshot was achieved by flying as close to the event horizon of the black hole as possible, to get the maximum effect. So although the pursuing ship was equally capable of doing the same, the question was did its navigator have the same level of skill to approach so close to the event horizon without falling in, and did its captain have the guts to try it. (And you can also note that the hero’s ship actually failed in this manuever, and approached too close, getting stuck in a relativistic time warp which set up the whole main plot of the show….)

  16. @12. shunt1 :

    You are gravitationally bound to the Earth, so your orbital velocity around the Sun is about 29.783 kilometers per second. That’s the speed the planet is moving through space in its orbit about the sun. Earth’s speed varies a bit because its orbit is slightly eccentric, but that’s why we say mean orbital velocity.

    Indeed. I’ll just add that it is NOT just Earth’s speed that changes based on an eccentric orbit either – Pluto, Mercury and Mars for sure – plus I’d guess some other planets – in our solar system have more eccentric orbits than ours and would therefore vary more in speed too. Wonder if there’s a table of that somewhere online?

    Not to mention the whole class of eccentric orbiter exoplanets. :-)

    The variable orbital speed of Mercury is responsible for its double sunrise phenomena – it orbits faster than it rotates near its perihelion – great youtube clip of that effect is linked to my name for this comment. :-)

    @2. Boomer : “So how is this used for time travel?”

    First you need to be in the starship Enterprise … ;-)

    Seriously, I guess if you aquire enough orbital velocity you get some relativistic effects. How much velocity and how massive the object you’d need to do this to any sort of significant extent I’m not quite sure – & it’d only work one way ie taking you further into the future fater than the normal rate NOT allowing you travel to the past.

  17. Messier Tidy Upper

    Continued :

    So by the real physics if I understand correctly if the Enterprise had whipped around the Sun using its gravitational slingshot at relativistic time travelling velocity it would’ve come out far into the distant future, unable to aquire whales and with Earth destroyed by the Alien probe. D’oh! :-o :-(

    Maybe its something to do with the warp engines that does the trick? ;-)

    @10. Dan :

    I guess I’m still missing something: I understand how the spacecraft steals some of the planet’s orbital energy as it approaches the planet, but once it passes the planet and is now in “front” of it, wouldn’t the planet then steal that energy right back from the spacecraft? I.e. once the spacecraft has passed the planet their roles would be reversed?

    I think the simple answer to this is that the spaceprobe is travelling too fast now for the gravity to drag it back and regain that “stolen energy – but I could be mistaken.

  18. shunt1

    I am trying very hard to give my friends some information on orbital dynamics and how to perform a gravitational assist.

    If you have ever used the Orbiter computer simulation, then a full understanding of these basic concepts is almost required.

    http://orbit.medphys.ucl.ac.uk/index.html

    Now for advanced training on using a gravitational assist, try reading these tutorials:

    http://flytandem.com/orbiter/tutorials/

    This is real physics and orbital dynamics. Well worth spending the time to study, if you are interested in the subject.

    Sorry that I could not find something easier, but I wanted to provide something that is both accurate and helpful for those who are truly interested in the subject.

  19. shunt1

    Just for your amusement:

    This is an example of what the Orbiter computer simulation can do. Each and every step is something that you must do, but if done correctly, this is what it may look like:

    http://www.youtube.com/watch?v=xS5HYznzw-k&list=PL0BD0EF0D4C450114&index=1&feature=plpp_video

    When I crashed my airplane in 2006, I was stuck in a hospital bed for over a month. With a laptop, I was able to simulate a trip to the moon in “real time” and had to toggle each and every switch, exactly as it was done in 1969.

    Hey, I was stuck in a bed just like they were and it kept my sanity during such a traumatic time in my life.

    Even the original software used on their on-board computer was being interpreted and used with the simulation. I had to memorize and use the exact same computer codes which the astronauts used in the original mission.

    This is how real and accurate the Orbiter software simulation can be.

    Are YOU up to the educational challenge?

  20. shunt1

    Try this one for a flight to Jupiter!

    http://www.youtube.com/watch?v=MQBiX8STHUk

    If anyone truely wants to understand the physics of space flight, this is the way to learn. But, you will have to study, study and then study even more!

  21. Chris

    How much energy can you actually steal from the planet? In other words, theoretically how many times faster could your exit velocity be?

  22. shunt1

    “How much energy can you actually steal from the planet? In other words, theoretically how many times faster could your exit velocity be?”

    Think about it…

    The maximum possible would be your initial velocity PLUS the velocity of the planet around the Sun. However, for that perfect case you would have to pass through the center of the planet and be destroyed in the process.

    I could make some jokes about “rocket science” but that is exactly what this is.

  23. Rob

    @Chris ,

    @shunt1: incorrect. The maximum velocity gain is TWICE the speed of the planet around sun.

    http://en.wikipedia.org/wiki/Gravity_assist (see picture)

    In order for maximum velocity change, the satellite must be travelling in exactly the opposite direction that it started at. I’m not 100% sure this requires a collision with the planet, a parabolic orbit or a highly eccentric open orbit seem to have this property?

    http://en.wikipedia.org/wiki/Parabolic_orbit

    The wikipedia page on gravity assist implies that the full twice-planet-velocity gain will indeed be achieved (asymptotically.)

  24. Plutofan

    Phil, I suspect the ‘slingshot’ term comes from the kind of slingshot always shown in pictures of little David fighting Goliath — a sling holding a rock, whirled around and released at high speed.

    Also, I think a somewhat clearer idea of the velocity gain comes from thinking about what happens when a tennis ball approaches a racquet. If the racket is not moving, the ball cannot rebound with greater velocity than it came in with. But if the racket is moving, the ball will rebound faster than its approach. Likewise for the retarding situation — if the racket is receding from the ball, the ball will lose velocity.

    Some may think a collision (ball hitting racquet) is different from a gravitational interaction, but from a momentum analysis, they are analogous.

    One other way of thinking about this — if you drop a ball onto a planet, it can’t bounce any higher than the height it was released from (your example). But if the planet happens to be speeding (with respect to the sun) toward the ball, the ball will gain speed with respect to the sun.

  25. Paul

    The simple way to think about this is to consider frames of reference. In some frames of reference, the spacecraft gains kinetic energy from the planet. In others, it loses kinetic energy to the planet. The total energy is conserved, it’s just partitioned differently in different reference frames.

  26. John

    @Dan I believe you intuition is correct. As @Rob mentioned, I believe Phil got the directions reversed. At 2:58 he mentioned that the probe is traveling in the same direction as the planet, but I believe this would be the case for if the probe needed to slow down. The wikipedia article shows that for a gravitional assist, the probe and planet are headed towards each other: http://en.wikipedia.org/wiki/Gravity_assist

    I think it’s best just to treat it as a perfectly elastic collision. They “bounce” off each other. If i throw a basketball at you and you throw a tennis ball at the basketball, that tennis ball is going to come back at you a whole lot faster than you threw it and the basketball will be coming at you slightly slower. Likewise, if the basketball is moving away from you and you throw a tennis ball at it, the tennis ball will slow down a lot and the basketball will speed up slightly.

    Phil’s description of the probe stealing or giving energy to the planet is…right on the ball. Couldn’t resist :)

  27. Whomever1

    So my plan is to apply thrust to the moon ( by smashing asteroids into it, or otherwise) in order to tug the Earth into a wider orbit over the next few million years, to compensate for the sun’s expansion. Is this the same problem in reverse?

  28. kmw (#8):

    I’m assuming this would also happen with Saturn & Jupiter’s moons when they pass each other in orbit?

    That’s my understanding. The pairs of co-orbital moons swap orbits as they approach each other. This page is supposed to show Janus and Epimetheus doing just this, but my browser only shows a still image.

    http://www.nasaimages.org/luna/servlet/detail/NVA2~1~1~1750~101889:Janus-Epimetheus-Swing

    Or, use your favorite search engine and look for “co-orbital moon animation”.

  29. JB of Brisbane

    Further to what Plutofan commented, just to clarify – a forked device with two strips of elastic and a pouch for launching projectiles is only called a slingshot in North America. Everywhere else, such a device is called a shanghai.
    A slingshot is exactly as Plutofan describes as written about in the account of David’s defeat of Goliath.

  30. Jared

    http://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html

    Under the preselected scenarios, choose Slingshot or Double Slingshot. It instantly made sense of the whole mechanism to me. You sneak up from behind a planet to gain speed, or get in its way to lose it. It also explains why it’s so hard for one body to permanently catch another, because it has to come in from just the right direction and at just the right speed so that it loses enough of its velocity that it can no longer escape, but not so much that it enters a lithobraking orbit.

    I guess you could also do the same trick with the sun, but you’d have to be moving independently of its own orbital mechanics, otherwise all you’d get would be, as Newton and Phil pointed out, a temporary boost in speed?

    East takes you out, out takes you west, west takes you in, in takes you east.

  31. Messier Tidy Upper

    @26. Whomever1 :

    So my plan is to apply thrust to the moon ( by smashing asteroids into it, or otherwise) in order to tug the Earth into a wider orbit over the next few million years, to compensate for the sun’s expansion. Is this the same problem in reverse?

    That’s been seriously suggested actually although using a “gravity tractor” rather than impacts as this link observes :

    http://www.space.com/7084-life-earth-escape-swelling-sun.html

    A long shot exists for life to survive Earth’s fate, but it would involve some novel solutions or a serious space colonization effort. One team at Santa Cruz University in California has proposed capturing a passing asteroid and using its gravitational effects to “nudge” Earth’s orbit outward. A continuous asteroid passage every 6,000 years or so could keep Earth at a comfortable distance and give life another 5 billion years on the planet.

    With more details about that idea – & some of its possible drawbacks – here :

    http://www.usatoday.com/news/science/astro/2001-02-15-orbit.htm

    or see ‘Sun too close? We’ll just change Earth’s orbit’ by Dan Vergan of USA TODAY published 15th Feb. 2001.

    BTW. Off topic but thinking of the Sun and its increasing activity this :

    http://www.space.com/14620-sun-tornadoes-nasa-video-sdo.html

    was pretty spectacular footage released recently showing solar “tornadoes” in action. :-)

  32. amphiox

    If in 500 million years we still haven’t figured out a solution to the warming sun problem then…. well, we don’t deserve to survive…..

  33. CJ Nerd

    In everyday British usage, this is called a catapult:
    http://wartimehousewife.files.wordpress.com/2010/05/dennis-the-menace-27-05-10.jpg

    and this is called a slingshot:
    http://childrenschapel.org/biblestories/graphics/dav-goliath.gif

    The name “slingshot effect” IMHO isn’t terribly helpful in understanding the spacecraft navigation manoevre.

  34. CJ Nerd

    Hi Phil,
    About 3:30 in the video, you refer to Jupiter being best for this sort of manouevre.

    I recently attended a talk on this, where the lecturer started by asking the audience to guess if Venus, Jupiter or Saturn was best. Most plumped for Jupiter, a few for Venus.

    The correct answer, the lecturer said, was Venus- because it moves faster than the other two, so more change in velocity is available.

    In the Wikipedia article
    http://en.wikipedia.org/wiki/Gravitational_slingshot
    a graph shows that Cassini gained ~9km/sec from two passes of Venus, and just ~1.5km/sec from its one pass of Jupiter.

    The total gain AFTER two passes of Venus and one of Earth is about 13km/sec- but that’s AFTER those passes, not FROM them, because obviously falling towards the Sun accounts for quite a bit.

    I’d love to understand more about what’s going on in that graph- especially on the first Venus pass. Could you possibly comment?

  35. shunt1

    Does this actually need a reply?

    The higher the orbit, the greater the velocity.

    Please list the orbital velocity of each of the planets (or even satellites) and see if I am correct.

    But to follow this logic, the lowest velocity has the highest orbit? Then all we have to do to place a satellite in geosynchronous orbit would be to throw it into the air a couple of feet!

    Wikipedia is saying that a gravity assist adds the velocity of a space probe plus DOUBLE the velocity of the Planet?

    Giggle, I would love to see a demonstration of those physics!

    Passing a heavy truck in the other lane where each has a speed of 60 mph and throwing out a grappling hook with a very strong cable.

    After you spin around and are going in the same direction as the truck, your car would now be going 180 mph?

    I DO NOT THINK SO!

  36. Dave

    @shunt1,

    Yes, you would be going 180 mph! Your relative velocity between you and the truck is 120mph. Perhaps it’s a bit easier to imagine if the truck has a giant trampoline attached to the grill, and you drive right into the trampoline. You come in at 120mph relative to the trampoline, so you’ll go back out (the opposite direction) at 120mph relative to the trampoline. Since the trampoline is affixed to the truck and is traveling at 60mph relative to the ground, you’ll be traveling at (60+120)mph or 180mph relative to the ground after the bounce.

  37. CJ Nerd

    @shunt1

    Assuming your “Does this actually need a reply?” refers to my post 34… well, no-one *has* to reply, but surely sharing understanding with others is what this sort of thread is about? If I’m wrong, I would hope that someone would be able to explain why.

    “The higher the orbit, the greater the velocity.
    Please list the orbital velocity of each of the planets (or even satellites) and see if I am correct.”

    I’m not sure if you’re agreeing or disagreeing. But let’s try it:
    http://www.windows2universe.org/our_solar_system/planets_table.html
    Merc Ven Earth Mars Jup Sat Ura Nep
    mean orbital velocity (km/sec) 47.89 35.03 29.79 24.13 13.06 9.64 6.81 5.43

    Higher orbit seems to imply slower velocity, much as I thought.

    I’m not sure where you’re getting “the lowest velocity has the highest orbit”- who’s suggesting that?

    “Wikipedia is saying that a gravity assist adds the velocity of a space probe plus DOUBLE the velocity of the Planet?”

    Wikipedia is indeed saying that- see the first two paragraphs and the diagram under the heading “Explanation”. If Wikipedia is wrong, then it would be good if someone were to correct it.

    The point of my lecturer’s question is that the mass of the planet doesn’t really matter- any planet is WAY big enough- but the speed does.

    The Cassini graph in Wikipedia, near the bottom of the article, and here
    http://en.wikipedia.org/wiki/File:Cassini%27s_speed_related_to_Sun.png
    is attributed to JPL, and it shows Venus and Earth affecting the spacecraft’s speed far more than Jupiter. Are you saying the graph is wrong?

    I’m not sure your analogy with trucks holds, as it doesn’t appear to represent the kinetic energy that the spacecraft can gain by slowing the planet down.

    Best
    CJ Nerd.

  38. Dave

    @CJ,

    Did you see my reply about the truck? The analogy works just fine, if you assume a (nearly) infinitely massive truck.

    Also, you write, “I’m not sure where you’re getting “the lowest velocity has the highest orbit”- who’s suggesting that?”

    Why do you say “who’s suggesting that?”? The numbers you just wrote show that the orbital speed goes inversely with orbital radius (actually goes as r^(-1/2), where r is the orbital separation), just as the claim “the lowest velocity has the highest orbit” suggests.

  39. CJ Nerd

    @Dave
    Sorry, I made a nonsense of my point by copying and pasting the wrong bit of shunt1’s post at 35.

    Where I put:
    > I’m not sure where you’re getting
    > “the lowest velocity has the highest orbit”-
    > who’s suggesting that?

    I should have had:
    > I’m not sure where you’re getting
    > “The higher the orbit, the greater the velocity.”-
    > who’s suggesting that?

    Turning to the truck analogy… ok, if it’s a nearly-infinitely-massive truck and a neglibly-massive car, and a 100% efficient trampoline, I can see that it would work that way. I had to force myself to make those assumptions before I could see it.

  40. Dave

    @CJ

    Yeah, basically you throw a SuperBall at 60mph North, toward a truck that’s heading 60mph South, and the SuperBall ends up going 180mph South (if you ignore air resistance — SuperBalls are quite efficient in their bounce).

  41. Alex

    @kmw (#8),
    You’re right about moons experiencing this effect. When you get more than two bodies involved, the math gets pretty tricky. What usually happens is something called Orbital Resonance. If, say, the moons of Jupiter were all on arbitrary orbits, they would eventually tug eachother out of place, and the system would fly apart. If their orbits align, however – with their periods being a ratio of some small integers – they actually serve to stabilize eachother.
    http://upload.wikimedia.org/wikipedia/commons/8/83/Galilean_moon_Laplace_resonance_animation.gif

  42. Matt B.

    It’s much easier to understand with vectors. Taking a hyperbolic orbit around a planet changes your direction, though not your speed, relative to the planet. However, the planet has a non-zero velocity relative to the sun, and you get to add twice the planet’s velocity vector to your own, when looking at things from the reference frame of the sun. You just choose how close to pass the planet in order to choose your exit direction.

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