27.5 Worked Example: Gravitational Slingshot

MIT 8.01 Classical Mechanics, Fall 2016
Instructor: Prof. Anna Frebel

License: Creative Commons BY-NC-SA

[mitocw]

The technology used in the MIT Lightboard interactively flips the image and adds auxiliary images and video inputs into the captured video. One can also incorporate PowerPoint into a portion of the screen and annotate these during the video capture, thereby reducing the need for post processing.

[ucheucheuche]

I'm always more fascinated about the writing backwards part

[csx]

i was more fascinated by the simple way this was recorded, the original you read in reverse, so she flipped the video so we can read it. We'll need that in 2020 for our college professors.

[winstongludovatz]

The velocity is a 3d vector, it does not "go in the minus i-hat direction". Quite obviously from this drawing and intuition the initial and final relative velocities do not sum to zero.

[amirrahiminia]

It is nice to know the theory about it but the actual calculation is far more complex.

[sayanjitb]

Shouldn't we consider y direction as well because clearly from drawing probe also has a vertical component along side horizontal.

[michaelhansen]

I see. It depends on how you look at it. I was thinking that the integration of the path in and out would be such that the acceleration in would be cancelled by a deceleration out. But looking at it as relative velocities, this simple calculation shows that the difference in masses results in an additive effect. This bothered me for a long time. Many science communication videos state conclusions without explaining the steps that are interesting to me. Then I have to dig around and sometimes I find an answer. Thanks so much.

[chrisrinker]

The math confuses me, I feel like direction and time has an effect. How close do you approach? Velocity relative to the Sun or each other somehow? Big planets... more gravity, where is that in the equation? I feel like I am missing the forest for the trees.

This is how I figured gravity assist works(different scenario): The satellite approaches Saturn from behind as it orbits the Sun. As they are both orbiting the sun essentially, the approach takes longer and Saturn's gravity has more time to pull on the spacecraft, accelerating it. This craft then orbits (slingshots) around Saturn about 90 degrees to shoot out towards Pluto. Now that their directions are different, Saturn has less time to pull on the spacecraft, so the gravity deceleration is less. All of this is possible because everything orbits the Sun, so all speeds are relative to the Sun. You cannot slingshot around the Sun, unless you are trying interstellar travel. Without the Sun, the planet cannot have a velocity relative to anything, and the satellite cannot depart any faster than it approached. In the video example above it would appear that the satellite would actually decelerate.

[DainawlTheMagne]

This is massively counter intuitive!
It is one of the points where I would say: Math does not describe the world I live in....
:D

[videozz]

If she was my teacher at school i would never miss any claassss

[cyh]

But why doesn't the spacecraft slow down departing the planet when the gravitational pull of the planet (the planet now chasing the spacecraft) should impose the opposite effect?

[kreynolds]

I was wondering if an example of a rotating Martian Tethered Orbital Momentum Transfer Space Station could be presented. One that could be used to slow a spaceship down for landing on Mars minimizing the fuel to slow down on Mars aproach. Then later reuse the rotating Tethered Momentum Transfer Space Station to sling the same spaceship back to Earth. Maybe a rotating Tethered Momentum Transfer Space Station near earth could also help lower the cost of getting to Mars and back with less time spent in transport.

Tethered Momentum Transfer Space Stations conserve momentum beteeen incoming and outgoing craft. That reduces the fuel requirements that not only may save money but may increase the size of the payload, reduce both the size of space ship and amount of rocket fuel for a given payload, and to do so with less time spent in transit between Earth and Mars

I'm just hoping to get more people thinking about this. One day soon, we may use another kind of tethered system to launch system like SpinLaunch to cheaply get much of the mass behind a "Tethered Momentum Transfer Space Station" up in space and assembled. They would be solar PV powered and could use relativly cheap but efficent high specific impulse plasma thrusters to get to their destination and to do station orbital keeping while in their proper orbits.

Tethers will play a big part in maned exploration of the solar system.

[ThePeterDislikeShow]

What I can't understand is how we can use earth itself to give gravity assists (we apparently did so for Cassini and more recently Juno). If the spacecraft originated from earth, wouldn't everything be relative to earth?

[barberianking]

Surely Saturn will cry after seeing it's image 📢 Where are my rings...😣

[boriskaragiannis]

a huge problem in your theory is that the planet moves vertically to the direction you guys need to slingshot...so no extra speed can be gained towards the center (sun) or opposite to this

[Hwaism]

why initial velocity of spacecraft was 3x velocity of saturn?

[namho]

How many times could we use gravitational slingshots before Jupiter is noticeably late for its course?

[agam]

So we figured out GrAvItAtIoNaL Slingshot without even writing the formula for GrAvItY

[carlosantuckwell]

Is it really that simple, that one can just linearly add the velocities like that?? Shouldn't we need vectors more subtle than just + or -- ?? I mean, of varying degrees.

[FCKWnee]

Herzlichen Dank! Jeztt klappt das mit den Slingshots!!