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# Sling Shot Theory

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### #1 medic32v

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Posted 07 December 2013 - 04:55 PM

Hi Group. I've heard this phrase several times, and I hope that someone can explain the Science involved, in very simple terms.
When they say that a Space Craft to " Sling Shot " itself to gain speed. Can anyone explain this to me. Thanks all and Clear Skies Mike

### #2 rdandrea

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Posted 07 December 2013 - 05:29 PM

Here ya go:
http://www2.jpl.nasa...grav/primer.php

### #3 mayidunk

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Posted 07 December 2013 - 06:40 PM

In a nutshell, it is the change in direction, and increase in velocity that happens to a spacecraft when it encounters the gravitational pull of a planet. If the spacecraft is approaching the planet in the same direction as the planet's orbit, the speed of the planet in its orbit adds velocity to the spacecraft. It's quite similar to how the tip of a bullwhip is accelerated to a speed great enough that it momentarily exceeds the speed of sound!

### #4 Kraus

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Posted 07 December 2013 - 11:37 PM

Research Apollo 13. Tell them it's a theory.

### #5 Mikefly

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Posted 08 December 2013 - 02:18 AM

In a nutshell, when a space craft enters a object's SOI (sphere of influence) some of that object's velocity is transferred to that spacecraft. How that works is that the gravity field of the object pulls on the spacecraft trying to pull the craft in towards the object's center of gravity. In turn the craft's minuscule gravitational field tugs ever so slightly on the object which results in a energy exchange of sorts.

How a sling shot works is as following. A spacecraft is sent into the SOI of a celestial object. The object captures the craft with its more massive gravity and tries to pull the craft towards the object's center of mass. The craft begins a free fall towards the object's center of gravity. If the craft had no velocity going into the object's SOI then it just slams into the object while free falling. Normally though the craft will have some lateral velocity going into the SOI which will combine with the velocity that would be gained from the free fall towards the object's center of mass. In that process the sling shot occurs. The object is trying to pull the craft into it but the combined lateral velocity and the velocity of the craft free falling makes it so that the craft swings around the object and gets ejected out of the object's SOI with greater velocity than it entered with.

By the way, Apollo 13 used a free return trajectory which swung it around the moon and directly back into Earth's atmosphere without any course corrections along the way.

### #6 Rick Woods

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Posted 08 December 2013 - 10:33 AM

The sling shot method is the only reason they were able to send the Voyager craft on their tour of the outer solar system. They were able to take advantage of a lucky alignment of the planets to slingshot around one to speed up to the next, then off the next, etc, and pick up speed each time.

I believe Apollo 13 did make one course correction on the way back. They had to eyeball it. Those guys were good.

### #7 Skip

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Posted 08 December 2013 - 01:04 PM

I believe Apollo 13 did make one course correction on the way back. They had to eyeball it. Those guys were good.

Yes they were!! Even if you imagine doing it just sitting comfortably in your living room. Now imagine being cramped in a teeny space, shivering from the cold, sick (in at least one case), and under unbelievable stress. Yep! Very very good!

### #8 ColoHank

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Posted 08 December 2013 - 01:50 PM

So why doesn't the same planet's gravity also tend to slow the outbound space vehicle's velocity after it's been accelerated on its inbound trajectory? Is it due to the change in vector?

### #9 llanitedave

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Posted 08 December 2013 - 03:07 PM

The cool thing about the gravity slingshot is that the spacecraft's velocity is both accelerated and then de-accelerated relative to the planet. But relative to the Sun, it's all energy increase, at the expense of a tiny bit of the planet's orbital energy.

### #10 medic32v

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Posted 08 December 2013 - 04:40 PM

When a Comet approaches Perihelion and survives it's encounter with the Sun intacted, will the sling shot effect apply in this case.
When a space craft uses the sling shot theory. Does the velocity that is reached depend on the mass of the object and also the distance from the object a factor also.
Also, the speed inwhich a Planet orbits the Sun, depend also on the mass and distance from the Sun or is the Velocity remain a constant. Thanks All and Clear Skies. Mike

### #11 Rick Woods

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Posted 08 December 2013 - 05:30 PM

I believe Apollo 13 did make one course correction on the way back. They had to eyeball it. Those guys were good.

Yes they were!! Even if you imagine doing it just sitting comfortably in your living room. Now imagine being cramped in a teeny space, shivering from the cold, sick (in at least one case), and under unbelievable stress. Yep! Very very good!

That brings to mind the whole "the future isn't what it used to be" thing. When I was a kid (pre-space age), my heroes were spacemen in books, movies, and TV. Now, the days of spacemen going to other planets is nearly a half century in the past. *sigh*
But I'm glad I got to live in both eras.

### #12 Ira

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Posted 08 December 2013 - 07:24 PM

The cool thing about the gravity slingshot is that the spacecraft's velocity is both accelerated and then de-accelerated relative to the planet. But relative to the Sun, it's all energy increase, at the expense of a tiny bit of the planet's orbital energy.

/Ira

### #13 Rick Woods

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Posted 08 December 2013 - 07:39 PM

I think he's referring to the fact that the planet slowed down a little when it imparted the extra velocity to the space probe.

### #14 dan777

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Posted 08 December 2013 - 11:31 PM

So why doesn't the same planet's gravity also tend to slow the outbound space vehicle's velocity after it's been accelerated on its inbound trajectory? Is it due to the change in vector?

For this situation there are two frames of reference - Jupiter and the Sun. (Actually the Milky Way is also a frame of reference because the solar system is moving through it. But since the spacecraft is not leaving our solar system, we don't have to include this third frame of reference in the calculation). If we look at the spacecraft in the Jupiter frame of reference, then yes as the spacecraft approaches and leaves Jupiter, it does indeed accelerate and subsequently decelerate because of Jupiter's gravity. Next we look at the Sun's frame of reference and we note that Jupiter has a velocity relative to the sun. So think of it this way, Jupiter will pull the spacecraft along with it in its orbit around the sun, so the spacecraft gains some or all of the orbital speed of Jupiter (depending on the trajectory of the spacecraft relative to the direction of Jupiter) via an increase in momentum. Jupiter gives up the same amount of momentum but because of the huge mass of Jupiter relative to the spacecraft, Jupiter does not measurably slow down. Keep in mind that all these velocities are "vectors" - they have magnitude and direction. So there is more to the calculation than just "simple adding" of velocities.

And speaking of frames of reference, the universe is also a frame of reference because the Milky Way is moving through it.

### #15 Ira

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Posted 09 December 2013 - 08:20 AM

So why doesn't the same planet's gravity also tend to slow the outbound space vehicle's velocity after it's been accelerated on its inbound trajectory? Is it due to the change in vector?

For this situation there are two frames of reference - Jupiter and the Sun. (Actually the Milky Way is also a frame of reference because the solar system is moving through it. But since the spacecraft is not leaving our solar system, we don't have to include this third frame of reference in the calculation). If we look at the spacecraft in the Jupiter frame of reference, then yes as the spacecraft approaches and leaves Jupiter, it does indeed accelerate and subsequently decelerate because of Jupiter's gravity. Next we look at the Sun's frame of reference and we note that Jupiter has a velocity relative to the sun. So think of it this way, Jupiter will pull the spacecraft along with it in its orbit around the sun, so the spacecraft picks up some or all of the orbital speed of Jupiter (depending on the direction of the spacecraft relative to the direction of Jupiter) via an increase in momentum. Jupiter gives up the same amount of momentum but because of the huge mass of Jupiter relative to the spacecraft, Jupiter does not measurably slow down. Keep in mind that all these velocities are "vectors" - they have magnitude and direction. So there is more to the calculation than just "simple adding" of velocities.

I thought the slingshot effect was due to the gravity of the massive planet, not its speed in orbit around the sun. In that case, why not use a faster moving planet like Mars to create the slingshot, rather than the more massive but slower moving Jupiter?

/Ira

### #16 llanitedave

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Posted 09 December 2013 - 10:58 AM

There's no reason you can't use Mars if the geometry is right.

### #17 Rudra

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Posted 09 December 2013 - 07:49 PM

The sling shot method was used by the Indian Space Research Organization (ISRO) to send its maiden spacecraft called "Mangalyaan" (Mangal: Sanskrit word for planet Mars and Yaan: Sanskrit word for vehicle) through 5-6 orbit raising maneuvers around the Earth to Mars. ISRO could have sent the spacecraft directly to Mars through Trans-Mars Injection, but the lift vehicle for the spacecraft (Polar Satellite Launch Vehicle or PSLV) is a less powerful rocket than its successor Geo-Synchronous Launch Vehicle (GSLV) which is still in testing phase and was the intended vehicle to launch India's Mars mission but owing to some problem minutes before its launch in August 2013, the program was revised and PSLV was used for the mission that included originally 5 but ultimately 6 orbit raising maneuvers.

As of now the spacecraft is on its way to Mars, expected to reach the planet 2 days after NASA's Maven in September 2014.

### #18 dan777

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Posted 09 December 2013 - 11:13 PM

When a Comet approaches Perihelion and survives it's encounter with the Sun intacted, will the sling shot effect apply in this case.

No, the reference frame we using when referring to the comet's velocity is the solar system and relative to the solar system, the sun is not moving. If we were interested in the velocity of the comet in the reference frame of the Milky Way galaxy then yes the sun would provide gravitational assist.

When a space craft uses the sling shot theory. Does the velocity that is reached depend on the mass of the object and also the distance from the object a factor also.

No, only on the velocity of the planet and the trajectory of the space craft relative to the planet's direction.

Also, the speed inwhich a Planet orbits the Sun, depend also on the mass and distance from the Sun or is the Velocity remain a constant.

The velocity of a planet as it orbits the sun is a function of the mass of the sun, the mass of the planet and the distance from the center of the sun to the center of the planet. Since the orbits are elliptical (they are not perfectly circular), when the planet is closer to the sun its velocity is increased due to the conservation of angular momentum.

### #19 groz

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Posted 11 December 2013 - 01:05 PM

So why doesn't the same planet's gravity also tend to slow the outbound space vehicle's velocity after it's been accelerated on its inbound trajectory? Is it due to the change in vector?

It does, but, the math gets complex when all bodies are in motion.

But there is an easy way to explain the whole thing, that doesn't require understanding the complex math of a 3+ body problem, in 3 dimensions.

Preposition 1. Everybody understands the concept of a circular orbit, ie, there is a magic velocity, if achieved at a specific altitude, an object will be in a circular orbit. The object is literally falling inward, and travelling along at a velocity where centripedal force exactly counters gravitational pull. We will call that velocity X.

Preposition 2. Everybody has heard of 'escape velocity', which is a magic number. Any object travelling faster than escape velocity, will be moving away from the larger object, in this case planet, faster than can be overcome by the planet's gravity, so once enroute, it'll never come back. Call this velocity Y.

An object travelling at a velocity lower than X, will impact the planet. An object travelling at a velocity between X and Y, will end up in an eliptical orbit, and something going faster than Y, will escape out of the gravitational influence of the planet.

So, to make it clear and simple, also consider there is another magical place, where the gravitational influence of the planet, and the sun, are exactly equal, so anything sitting at that point, has a 50/50 chance of 'falling' toward the sun, or the planet, if it's disturbed from resting at that point.

For this example, to keep things clear, we will use earth as the planet, and Sun as the Sun. In reality, earth is actually a two body system, as the moon is significant, but, for this exercise, pretend we dont have a moon in the equation.

Object is sitting exactly at the legrange point, where earth and sun gravity are equal and opposite, and stationary at this point. Now it's bumped ever so slightly, and starts falling toward earth. If earth and sun were stationary, then it would just continue to fall, till it hits earth, all done. But, if we are using sun as our point of reference for zero point, then earth is not stationary. So our object starts to fall toward earth, but while it's falling, earth moves just a little farther away. Object continues to fall toward earth, accelerating due to gravitational pull from the earth. At the same time, Earth moves a little farther along it's orbit. It's the carrot on a stick leading the donkey type of situation, no matter how fast the donkey runs, it never quite gets the carrot.

So, now advance in time, and object continues to accelerate toward earth, which continues to move away. BUT, in our first case, object does catch up to earth, and when it finally does, it has accelerated to some velocity, just below X mentioned above. We already know, from the above prepositions, if velocity is below X, object will eventually impact.

Re-consider the scenario, but now object takes a slightly different trajectory, such that it spends a little more time falling toward earth, and arrives in the vicinity of earth, with a velocity greater than Y. It will pass by the earth, with a velocity greater than escape on this trajectory. Again, from the above premises, we can see then, it will continue on it's way, and leave the gravitational influence of the earth, it's going faster than escape velocity, so it'll continue on to a point where primary gravitational influence is the Sun.

Now, if you are looking at this as a simple one dimensional 'falling' problem, the issue is, no matter what velocity is achieved during the 'fall' toward earth, impact is inevitable. But, expand it now to two dimensions, so the earth is actually in it's stable orbit 'falling' around the sun. As our object 'catches' up to earth from falling toward it over time, the earth actually 'steps aside' as it continues around the circle, so, our object misses the impact, and passes by at some velocity. That's where the above mentioned X and Y thresholds come into play, and in essence, a vast oversimplification can state this. Object spent some amount of time accelerating toward earth, and arrived with such a velocity, that after passing, it'll spend considerably LESS time moving away, before it leaves the gravitational influence of earth, so, if it spent a year accelerating toward, then 5 months decelerating away, it's left with a velocity accumulated over the difference of 7 months.

I know, this is a DRASTIC oversimplification, but, is a way of illustrating this effect, without doing hard math, in front of a classroom full of children with only a basic grasp of arithmetic, in such a way, it 'makes sense'.

Ofc, when you reach this same problem, in a post grad situation, with a full grasp of differential calculus, then you get to remove some of the simplifications. Earth / Moon is a two body system unto it's own, and space has 3 dimensions. The math gets way more complicated, and starts to approximate exact solutions, but, general gist is the same.

And then when you finally do end up with relatively exact equations, some professor is going to point out another problem, called conservation of energy, and force you to figure out how your object that started at rest, ended up with a significant amount of energy once back out of the earths gravitational influence. And the final solution will be, the earth / moon system slowed down by an infinitesmally small and unmeasurable amount during this process, because it was affected by the gravitational pull of our small object passing thru the system. Then you extrapolate forward umpteen billion years, and realize, due to this encounter, earth orbit will eventually decay, causing earth to impact sun, but, it's sooo far in the future, sun will be long gone by the time it happens. ie, it's insignificant because there are other / bigger issues coming about on a much shorter time scales, ie sun running out of fuel for it's nuclear reaction.

### #20 Mister T

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Posted 11 December 2013 - 03:50 PM

I always thought "Sling Shot Theory" was:

If you shoot a sling shot at a 700lb. Bengal Tiger often enough you will get him mad enough that he will scale a 20ft wall and eat your *BLEEP*.

### #21 Ira

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Posted 11 December 2013 - 11:13 PM

Well wait...in your example it is the gravitational force of the planet that creates the slingshot effect, not the orbital motion of the planet. So, a more massive planet like Jupiter is more efficacious in creating the slingshot effect than a faster orbiting planet like Mars.

/Ira

### #22 Rick Woods

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Posted 12 December 2013 - 12:35 AM

I always thought "Sling Shot Theory" was:

If you shoot a sling shot at a 700lb. Bengal Tiger often enough you will get him mad enough that he will scale a 20ft wall and eat your *BLEEP*.

That's no theory!

### #23 dan777

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Posted 12 December 2013 - 12:44 PM

I thought the slingshot effect was due to the gravity of the massive planet, not its speed in orbit around the sun. In that case, why not use a faster moving planet like Mars to create the slingshot, rather than the more massive but slower moving Jupiter?

The term "gravity assist" comes from the fact that the spacecraft must move through the gravitational field of the planet.

The spacecraft picks up velocity because of a transfer of angular momentum from the planet to the spacecraft. If the planet had an enormous gravitational field but was stationary (no velocity relative to the sun) the spacecraft could not increase its speed because the angular momentum of the planet is zero. The final velocity of the spacecraft is based on the vector addition of the planet's velocity and the spacecraft's velocity relative to its trajectory around the planet.

Indeed Mars can be used for gravity assist, but there are several variables to consider. Here's one to ponder, if you want to send a spacecraft (Voyager for example) out of the solar system, then you need to exceed the escape velocity of the sun. At Mars the sun's escape velocity is 34.1 km/s and at Saturn it's 13.6. Voyager used both Jupiter and Saturn for assists.

### #24 llanitedave

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Posted 12 December 2013 - 11:28 PM

I always thought "Sling Shot Theory" was:

If you shoot a sling shot at a 700lb. Bengal Tiger often enough you will get him mad enough that he will scale a 20ft wall and eat your *BLEEP*.

That's no theory!

I was going to post exactly that, but I deleted it!

### #25 llanitedave

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Posted 12 December 2013 - 11:38 PM

Well wait...in your example it is the gravitational force of the planet that creates the slingshot effect, not the orbital motion of the planet. So, a more massive planet like Jupiter is more efficacious in creating the slingshot effect than a faster orbiting planet like Mars.

/Ira

With a more massive planet you can get more of a full slingshot effect at a greater distance. It's still the orbital velocity of the planet that's accelerating you relative to the Sun, but you can get more of that effect from a larger planet without passing quite so close to it. You have more leeway in the precision of your encounter that way -- the aiming requirements aren't quite as unforgiving. Also, being farther from the Sun, there's more bang for your buck from the extra acceleration that you do get.

In principle, there's no reason why you can't use Mars to get you where you need to go, if your timing and precision is right.

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