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)
There is no such thing as "not open access article".
(With a big thank you to Alexandra Elbakyan.)
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.
Everyone should play KSP. :)
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?)
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).
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..."
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
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 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.
I've heard this referred to as "periapsis below mean radius" which is a euphemism for "the mission just ended."
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.
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.
> 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.
No way everyone can click through every link in every article they read. Glad we were jointly able to bring something interesting from the article to people's attention.
At any rate I suppose computers in the future can calculate these multiples of assist trajectories on the fly...