Gravity assist maneuvers in space(jatan.space)
jatan.space
Gravity assist maneuvers in space
https://jatan.space/daring-gravity-assist-maneuvers/
38 comments
> sorry, just learnt this is not an open access article
There is no such thing as "not open access article".
https://sci-hub.se/https://doi.org/10.1119/1.2341882
(With a big thank you to Alexandra Elbakyan.)
There is no such thing as "not open access article".
https://sci-hub.se/https://doi.org/10.1119/1.2341882
(With a big thank you to Alexandra Elbakyan.)
Love the reference to Kerbal space program as orbital mechanics software :)
For fans of the "Rich Purnell Maneuver" from The Martian, check out the NASA paper: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/201500...
relevant scott manley
https://www.youtube.com/watch?v=sF8roW6Cxm0
https://www.youtube.com/watch?v=sF8roW6Cxm0
KSP taught me more about orbital maneuvers than I expected when I bought it.
I find it hard to get my head around gravity assists. Whatever energy you may be gaining from approaching a planet should be lost once you leave the planet. What am i missing?
Imagine you have a big wrecking ball swinging through the air at high speed, you throw a baseball at it and hit it head on. It seems intuitive that when the baseball bounces off it, it will pick up some speed from the wrecking ball. In turn the wrecking ball will slow down the smallest amount from the collision with the baseball.
This is effectively what a gravity assist is. It's a collision with the planet. Because gravity is a weak force, and curving around a planet takes a while, it's a very gentle collision. Regardless, the result is that you pick up some momentum from the planet, and the planet slows down very slightly.
All that gravity really assists you with is increasing the duration of the collision and reducing lost energy from the collision, as the same collision head on would impart the same speed up, but would destroy your spacecraft for a variety of reasons.
They should really call it a gravity bump or something like that.
This is effectively what a gravity assist is. It's a collision with the planet. Because gravity is a weak force, and curving around a planet takes a while, it's a very gentle collision. Regardless, the result is that you pick up some momentum from the planet, and the planet slows down very slightly.
All that gravity really assists you with is increasing the duration of the collision and reducing lost energy from the collision, as the same collision head on would impart the same speed up, but would destroy your spacecraft for a variety of reasons.
They should really call it a gravity bump or something like that.
Isn't it more about changing trajectory without spending fuel? You don't gain or lose momentum in an absolute sense because there is no absolute sense.
Play KSP.
Play KSP.
The size of your orbit is proportional to the energy of your spacecraft. Use manuever nodes to change the trajectory of your encounter with a planet like Eve, and notice how massively you can change the total size of your orbit (up or down, depending on the direction of the encounter). This implies a significant change in your energy during the encounter. This is from your gentle collision with the planet through its gravity field.
Everyone should play KSP. :)
Everyone should play KSP. :)
You absolutely gain or lose momentum from the gravity assist, even in KSP. Changing trajectory is just a side effect.
Think of it maybe as a skateboarder in a skateboard park where each pit is a planet, but because there is no friction, the skater does not lose speed, nor gain speed, relative to the skateboard park (solar system).
As well as the wrecking ball analogy there’s a second effect: if you fall in with one mass but emerge with a lighter mass, and energy is conserved, you’ll come out faster. So how do you lose mass at the bottom of the gravity well? Burn some fuel!
Another good reason to burn fuel at the bottom of the gravity well is that it’s more efficient to eject rocket gas when you are moving faster. Burning and ejecting gas gives it energy (the exhaust velocity from your chemical reaction) but if you do so while moving forward at the same velocity, you effectively leave the exhaust gas behind you standing still with respect to the universe, which is maximally efficient.
Put another way: if you propel yourself through deep space by throwing bricks behind you at 30mph, then this method of propulsion becomes most efficient at 30mph. Each brick you throw backwards ends up standing still, as you sail off at what is now 30.1mph.
(Presumably it’s only inefficient to burn fuel when you are moving slower than exhaust velocity, and not if you are moving at or faster than exhaust velocity?)
Another good reason to burn fuel at the bottom of the gravity well is that it’s more efficient to eject rocket gas when you are moving faster. Burning and ejecting gas gives it energy (the exhaust velocity from your chemical reaction) but if you do so while moving forward at the same velocity, you effectively leave the exhaust gas behind you standing still with respect to the universe, which is maximally efficient.
Put another way: if you propel yourself through deep space by throwing bricks behind you at 30mph, then this method of propulsion becomes most efficient at 30mph. Each brick you throw backwards ends up standing still, as you sail off at what is now 30.1mph.
(Presumably it’s only inefficient to burn fuel when you are moving slower than exhaust velocity, and not if you are moving at or faster than exhaust velocity?)
> if you fall in with one mass but emerge with a lighter mass, and energy is conserved, you’ll come out faster.
It doesn't work that way. If a body loses mass, it loses also kinetic energy that mass was carrying. To make losing mass helpful for acceleration, the mass must be given high enough momentum, i.e. fuel must be burned, not just ejected.
> if you do so while moving forward at the same velocity, you effectively leave the exhaust gas behind you standing still with respect to the universe, which is maximally efficient.
That standing still happens only at one instant of an idealized scenario. It is not the maximum fuel efficiency either. When the rocket accelerates past that point, it gets faster and the fuel efficiency becomes even better. The higher the speed, the better the fuel efficiency (because the same rocket motor force acts on a faster body, generating more kinetic energy per second).
It doesn't work that way. If a body loses mass, it loses also kinetic energy that mass was carrying. To make losing mass helpful for acceleration, the mass must be given high enough momentum, i.e. fuel must be burned, not just ejected.
> if you do so while moving forward at the same velocity, you effectively leave the exhaust gas behind you standing still with respect to the universe, which is maximally efficient.
That standing still happens only at one instant of an idealized scenario. It is not the maximum fuel efficiency either. When the rocket accelerates past that point, it gets faster and the fuel efficiency becomes even better. The higher the speed, the better the fuel efficiency (because the same rocket motor force acts on a faster body, generating more kinetic energy per second).
This is called a powered flyby or Oberth manouver: https://en.wikipedia.org/wiki/Oberth_effect
Playing Kerbal Space Program helped me a lot to get a (more or less) "intuitive grasp" on orbital maneuvers including "sling shots". I can highly recommend giving the game a try if you're interesting in rockets and interplanetary space flight. Even though it looks like a game (and can be hilarious fun at times), it's really a fairly accurate space flight simulator.
Kinetic energy goes as v^2. 2x speed is a 4x car crash. An extra 10 mph is worse at 60 mph than at 30 mph. (40^2-30^2 vs 70^2-60^2). Same 10 mph change, but 2x increased pain.
Momentum goes as v. When you throw something behind you (here propellant), you get the same change in velocity regardless of how fast you already are. But how much energy you take from the thing thrown, depends on how fast the two of you are already moving. A 10 mph change in velocity gains you more energy at 60 mph than at 30 mph. Same throw, but 2x the gain.
Planet gives kinetic energy to you as you approach, and takes it back as you leave. Planet gives kinetic energy to your propellant as it approaches, and then is "WTF propellant, where did all that kinetic energy I loaned you go?! You're messing with my orbit here! You're not running out of here until you pay it back." You: "bye propellant, bye bye planet..."
Momentum goes as v. When you throw something behind you (here propellant), you get the same change in velocity regardless of how fast you already are. But how much energy you take from the thing thrown, depends on how fast the two of you are already moving. A 10 mph change in velocity gains you more energy at 60 mph than at 30 mph. Same throw, but 2x the gain.
Planet gives kinetic energy to you as you approach, and takes it back as you leave. Planet gives kinetic energy to your propellant as it approaches, and then is "WTF propellant, where did all that kinetic energy I loaned you go?! You're messing with my orbit here! You're not running out of here until you pay it back." You: "bye propellant, bye bye planet..."
> Kinetic energy goes as v^2. 2x speed is a 4x car crash. An extra 10 mph is worse at 60 mph than at 30 mph. (40^2-30^2 vs 70^2-60^2). Same 10 mph change, but 2x increased pain.
This should be taught in school.
There's very little cross-disciplinary teaching in schools, each subject is taught separate. But I'm sure a lot of teenagers would drive more carefully if they got a grasp of the concept that whatever your velocity is, if you hit another car, the energy on your body is velocity^2
This should be taught in school.
There's very little cross-disciplinary teaching in schools, each subject is taught separate. But I'm sure a lot of teenagers would drive more carefully if they got a grasp of the concept that whatever your velocity is, if you hit another car, the energy on your body is velocity^2
Yeah. The sciences and engineering and peoples' lives are this richly and tightly interwoven tapestry... and we make almost no effort to teach it. :/
It's hard to find hope for the near term. XR might contribute some market disruption, perhaps permitting better content to slip in. But the default seems "the usual wretchedness, now in XR!" Further, the bottleneck is as much science side as education side, and there's little recognition or effort to address that. On the other hand, when researchers have an opportunity to directly contribute to creating good XR science content, it can be a challenge to get them to leave. ;) So transformative improvement seems perhaps possible, but the effort would have an odd shape, and I've not seen much work in that direction. One upbeat story might be that the bulk of education in China is so very bad, that if something good is ever created, that large delta might energize rapid mass deployment. Maybe. Sigh.
It's hard to find hope for the near term. XR might contribute some market disruption, perhaps permitting better content to slip in. But the default seems "the usual wretchedness, now in XR!" Further, the bottleneck is as much science side as education side, and there's little recognition or effort to address that. On the other hand, when researchers have an opportunity to directly contribute to creating good XR science content, it can be a challenge to get them to leave. ;) So transformative improvement seems perhaps possible, but the effort would have an odd shape, and I've not seen much work in that direction. One upbeat story might be that the bulk of education in China is so very bad, that if something good is ever created, that large delta might energize rapid mass deployment. Maybe. Sigh.
In the reference frame comoving with the planet the probe leaves with exactly as much energy as it arrived (modulo aerobraking and such). In the reference frame of the solar system's center of mass, the planet will have transferred an imperceptible fraction of its orbital energy to or from the probe.
Momentum exchange between the spacecraft and the planet. Spacecraft weighs next to nothing compared to the planet, so the planet's velocity change is imperceptible.
I think this intuition is correct in a frame of reference attached to the planet; in that frame there is only a change of direction.
In the frame of reference of the solar system, this local change of direction becomes a change of speed, so it can give you a an energy boost.
In the frame of reference of the solar system, this local change of direction becomes a change of speed, so it can give you a an energy boost.
This would be true if the planet were stationary, but since it's orbiting the sun, you can either take some of its momentum, or give it some momentum, by doing a gravity assist in the direction of the planet's orbit, or in the opposite direction.
You're moving much faster when you're leaving. So you spend less time decelerating due to gravity pulling you back. Net increase in speed.
This is the way of thinking about it that works best for me. As you fall into the gravity well of the planet from behind it, the planet is moving in the same direction as you. That means you spend more time in its gravity well catching up to it than if it was stationary. As you pass the planet you have picked up as speed boost from its pull. But as you travel away from it, because you are going faster you spend less time in its influence, so the deceleration is less than the acceleration you picked up on the approach.
As I try to wrap my brain around this could I assume then in order for this to work, on approach to the planet you have to be going in the same direction as its orbit?
Theoretically no, but if you're going the opposite direction the approach velocity is vastly higher and thus you need a (1) very massive planet and (2) much lower periapsis to have meaningful gravitational slingshot effect. In practice, between atmospheres (the big planets being Jupiter, Saturn, and Neptune), and (for non-gaseous planets) planets not being perfectly smooth spheres, that probably decreases the tolerances below any acceptable level in this solar system.
> decreases the tolerances below any acceptable level in this solar system.
I've heard this referred to as "periapsis below mean radius" which is a euphemism for "the mission just ended."
I've heard this referred to as "periapsis below mean radius" which is a euphemism for "the mission just ended."
Yes, generally impact with terrain is unacceptable ;-).
No, the laws of orbital mechanics are time reversible.
Yes but in the time-reversed version, the planet would be moving the opposite direction so you'd be doing a "reverse gravity assist" which slows you down.
I don't think that is the right way to think about it, it has more to do with trajectory bending. For example, let's say an object is going radially outwards away from the sun at 10 km/s when it encounters a planet that is orbiting at 30 km/s.
Let's say the trajectories are at right angles, so their relative speed difference before the encounter is 31.6 km/s.
I now claim that this relative speed difference is the same before and after the encounter, so there's no "less time spent decelerating on the way out". (This is an approximation, I'm pretending that the planet provides an inertial reference frame with conservation of energy. The centripetal/sunward acceleration is small enough for that.) Let me show how you can still get a gravity assist under this assumption.
If the object passes "in front" of the planet in such a way that its trajectory gets bent towards the retrogade direction of the planet, then its speed becomes 30 - 31.6 = -1.6 km/s. So 1.6 km/s relative to the sun, and direction retrograde of the planet.
If the object passes "behind" the planet in such a way that its trajectory gets bent towards the prograde direction of the planet, then its speed becomes 30 + 31.6 = 30 + 31.6 = 61.6 km/s relative to the sun, this time in the prograde direction of the planet.
I hope I've convinced you that gravity assists work by taking the relative speed difference, and reorienting it.
Let's say the trajectories are at right angles, so their relative speed difference before the encounter is 31.6 km/s.
I now claim that this relative speed difference is the same before and after the encounter, so there's no "less time spent decelerating on the way out". (This is an approximation, I'm pretending that the planet provides an inertial reference frame with conservation of energy. The centripetal/sunward acceleration is small enough for that.) Let me show how you can still get a gravity assist under this assumption.
If the object passes "in front" of the planet in such a way that its trajectory gets bent towards the retrogade direction of the planet, then its speed becomes 30 - 31.6 = -1.6 km/s. So 1.6 km/s relative to the sun, and direction retrograde of the planet.
If the object passes "behind" the planet in such a way that its trajectory gets bent towards the prograde direction of the planet, then its speed becomes 30 + 31.6 = 30 + 31.6 = 61.6 km/s relative to the sun, this time in the prograde direction of the planet.
I hope I've convinced you that gravity assists work by taking the relative speed difference, and reorienting it.
Rosetta would be in Mars’ shadow, having to rely on the limited battery supply instead of solar panels. The risk was that the batteries weren’t designed for the task.
Huh? This implies a change in mission parameters or doubt whether the engineering was adequate. The link in that sentence doesn't mention either. Just that the craft entered a "sleep" mode to conserve power. I expect the power subsystem was designed specifically for the task.
Huh? This implies a change in mission parameters or doubt whether the engineering was adequate. The link in that sentence doesn't mention either. Just that the craft entered a "sleep" mode to conserve power. I expect the power subsystem was designed specifically for the task.
Interestingly, that's apparently not quite correct. From the ESA link in the article:
> Rosetta's original trajectory and engineering design did not include an eclipse, but unavoidable launch delays forced the trajectory to be replanned. Mission controllers working on Rosetta have spent months carefully planning and testing a low-power configuration which will allow the spacecraft to safely operate on batteries.
> Rosetta's original trajectory and engineering design did not include an eclipse, but unavoidable launch delays forced the trajectory to be replanned. Mission controllers working on Rosetta have spent months carefully planning and testing a low-power configuration which will allow the spacecraft to safely operate on batteries.
I am just amused at all the gravity assist loop de loops portrayed in The Expanse. That seems to take just 10 minutes at a time...
At any rate I suppose computers in the future can calculate these multiples of assist trajectories on the fly...
At any rate I suppose computers in the future can calculate these multiples of assist trajectories on the fly...
The executive producer actually wrote a post after the episode in Season 2 as a bit of an explanation/apology for how it ended up that way, which I thought was a nice touch: http://www.danielabraham.com/2017/04/04/guest-post-losing-sc...
https://aapt.scitation.org/doi/full/10.1119/1.2341882 - sorry, just learnt this is not an open access article
https://aapt.scitation.org/doi/full/10.1119/1.5126818 (Oberth Effect)