A Real Slingshot
00:00 The 2U formula is an oversimplification. It doesn’t account for the entry angle of the rocket or the exit angle, and in fact, it assumes a perfect U-shaped travel to get a full boost.
00:13 Gravity assist maneuvers often get used to change direction as well as to provide a velocity boost, and if that’s not enough, there was a big gaping hole in the example I gave you.
00:23 Turns out the sun also has gravity and that pulls back on your rocket ship. The constant velocity value I used in traveling between planets is incorrect. The rocket would actually slow down.
00:35 My rocket was special though, it had enough fuel to counteract this problem. My rocket was imaginary, so I can imagine that someone has figured out how to produce enough propulsion to maintain a stable velocity over the path of a year.
00:48 The other complication, of course, is that planets don’t stay still. To use an actual gravity assist, the stars may not have to align, but the planets sure do.
00:58 The Voyager 1 deep space probe launched in 1977, did a fly by of Jupiter and Saturn using them as a gravity assist. To give you an idea how that worked, it left Earth traveling at 40 kilometers per second.
01:13 The drag from the sun had slowed it to 25 kilometers per second by the time it got to Jupiter. Jupiter’s slingshot didn’t actually speed it up. It was used to help maintain velocity while changing directions.
01:27 And as it got further and further out, the drag from the sun lessens. So it arrived at Saturn doing about 20 kilometers per second. Saturn was used for a small boost leading to 22 kilometers per second.
01:40 And again, the 2U formula here doesn’t work because it didn’t go all the way around. From there, it kept going at about that pace off into deep space.
01:51 And thanks to user Phoenix 7777, you can visualize all that. The values at the bottom of this show the velocity and the absolute distance to the target, which is Saturn.
02:23 Because the distance is absolute, the number shrinks as it approaches Saturn, but then increases once it passes the planet.
Christopher Trudeau RP Team on Aug. 21, 2024
Hi Ross,
I have no idea how it was made. You can find it on Wikimedia here:
commons.wikimedia.org/wiki/File:Animation_of_Voyager_1_trajectory.gif
The post credits the source of data but doesn’t say anything about the tools used to create the animation.
There is an astronomy library for visualization of orbits called Orbitronomy. I haven’t played with it, so I have no idea what it can and can’t do, but it may be worth checking out if you’re interested in this stuff:
orbitronomy.gitbook.io/orbitronomy-official-documentation
The other place that might be interesting is Stephen Gruppetta’s book, it has a chapter on simulating gravity in Matplotlib:
thepythoncodingbook.com/2021/12/11/simulating-3d-solar-system-python-matplotlib/
Ross on Aug. 28, 2024
Many thanks,Christopher!
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Ross on Aug. 21, 2024
quick question, did user Phoenix 7777 used Python when created that visualization? If he did so is there any chance I can read about it? :)