Where the energy of gravity assist comes from ?

[Red Iron Crown]

EladDv, it is pointless to talk about gravity assists in a single body perspective, they are not possible.

[pellinor]

[quote name='Tatonf']You can't change your orbit without changing the kinetic energy of the ship[/QUOTE]

Actually you can. Radial and normal burns do exactly that. Maneuver nodes have 3 dimensions, energy only has one. So there must be two dimensions of orbital change that keep the orbital energy constant.

[EladDv]

[quote name='pellinor']Within the reference frame/SOI of the body you are right. There is a static gravity field and conservation of energy holds, so the gravity assist can only change the direction but not the magnitude of your speed.

In the reference frame of the parent, things look different. As an example, model the gravity of Mun in the reference Frame of Kerbin. You can do this either with a time-dependent gravity field (the Mun moves), or with a rotating reference frame (coordinates rotate so that the Mnu stays fixed). Both of these models break energy conservation.

Example: Say a vessel stands still at the height of the Mun orbit (zero kinetic energy). (Say it spends a short time there so that falling towards kerbin is not significant) The Mun approaches, when the SOI catches the vessel, it has a speed "v" relative to Mun which is conserved. It passes Mun's SOI on a hyperbolic trajectory, exiting in a different direction with the same relative speed. Now back in Kerbin's SOI the vessel has a speed (up to 2v), and therefore gained considerable kinetic energy.[/QUOTE]

you are right but sadly KSP dosnt model the transfer of energy from the assisted body to the craft due to the on rails system, in a completely accurate simulation conservation of energy stays the same as some of the muns energy is transferred to the vessel via the gravitational field

[quote name='Red Iron Crown']EladDv, it is pointless to talk about gravity assists in a single body perspective, they are not possible.[/QUOTE]
i know, i have got confused about your post's purpose and have interpreted that you meant to say that the object gained energy relative to the assisted object.

[Tatonf]

[quote name='pellinor']Actually you can. Radial and normal burns do exactly that. Maneuver nodes have 3 dimensions, energy only has one. So there must be two dimensions of orbital change that keep the orbital energy constant.[/QUOTE]

True, I should have used "Semi major axis" instead of "orbit".

[More Boosters]

[quote name='pellinor']Actually you can. Radial and normal burns do exactly that. Maneuver nodes have 3 dimensions, energy only has one. So there must be two dimensions of orbital change that keep the orbital energy constant.[/QUOTE]

Your gravitational potential energy is calculated very simply as m*g*h, and radial burns exist to change your altitude.

Energy has no dimensions, it's a scalar quantity.

Assuming you aren't rotating, your kinetic energy in orbit is still your velocity squared times your mass divided by two. I'm not sure why you guys are assuming these are any different just because we are in space.

Your kinetic and potential energy will constantly be converted to each other unless your orbit is perfectly circular.

[EladDv]

orbital energy- sometimes known as mechanical energy is the combined kinetic and potential energy

[GoSlash27]

I wonder what the math of gravity assists is. There's got to be an equation that takes into account all of the major factors and spits out "DV"...
/too tired to think about it today :(

Best,
-Slashy

[Red Iron Crown]

[quote name='GoSlash27']I wonder what the math of gravity assists is. There's got to be an equation that takes into account all of the major factors and spits out "DV"...
/too tired to think about it today :(

Best,
-Slashy[/QUOTE]
Tomorrow, take a look here: [url]http://www.mathpages.com/home/kmath114/kmath114.htm[/url]

[GoSlash27]

[quote name='Red Iron Crown']Tomorrow, take a look here: [URL]http://www.mathpages.com/home/kmath114/kmath114.htm[/URL][/QUOTE]

Ooo, good stuff!
More rep for you!
-Slashy

[Jovus]

[quote name='FancyMouse']Unless you're talking about planet oblateness - otherwise (to be precise, assuming spherical symmetry of planet mass distribution) gravity force passes through both CoM of the ship and planet. How could that change angular momentum of either object?[/QUOTE]

You shouldn't assume that.

But even if you do, the plane of the ship's trajectory around the planet and the planet's CoM is by no means guaranteed to be the same plane as that between the Sun and the planet.

Don't get me wrong. I'm not claiming the effect is big. In fact, it's probably so small it's not measurable with current instruments. But it's there. I'd show you the math, but posting math on a forum is a huge pain in the ass and hard to follow for a reader.

[Snark]

[quote name='Tatonf']So, question : If a planet were staying still in space (meaning it doesn't rotate around itself), would it be able to provide gravity assist ?[/QUOTE]

[quote name='Red Iron Crown']EladDv, it is pointless to talk about gravity assists in a single body perspective, they are not possible.[/QUOTE]


It depends what you mean by "gravity assist." In the strict sense of "use the orbital energy of a body around its primary to give a velocity boost to a completely passive ship going past," then yes, you are correct.

However, it is certainly possible to use the Oberth effect combined with ship thrust to get a big boost from the gravity of a planet, even in a single-body system. This is, in fact, using the planet's gravity to assist you. Whether one calls it a "gravity assist" is a question of nomenclature. ;)

Suppose I have a planet floating all alone in the universe (i.e. this is a single-body system), and I have a ship orbiting that planet in a circular orbit, and it's a very high orbit so the ship's orbital velocity is very low. Suppose I want to leave the planet going as fast as possible.

If I simply burn prograde until I'm out of fuel, I'll leave with basically just the inherent dV of my ship.

However, if I do an initial burn [I]retrograde[/I] to drop my Pe down so that it's grazing the planet's surface (this will be a tiny burn, since my orbital velocity is low), then wait until I'm at Pe, and then do my main burn down there next to the planet's surface: then I will leave the planet with a considerably higher velocity, much higher than my ship's inherent dV.

This leads to the interesting question of "where did the energy come from." In the classic case of a two-body gravity assist (i.e. what this thread has been discussing for the most part), the energy comes from the assisting planet's orbital motion; the planet is slowed down.

In the Oberth case I'm describing here, the energy comes from a different place: when you do your burn down near the planet, you're leaving all your fuel down there deep in the gravity well. That's giving up a lot of potential energy, and where it shows up is in your ship's kinetic energy.

[Red Iron Crown]

Snark, the "Oberth maneuver" you describe is not a [URL="https://en.wikipedia.org/wiki/Gravity_assist"]gravity assist[/URL] (though it is often combined with one). Misusing the term that way only adds confusion to what are already two fairly unintuitive concepts.

[Snark]

[quote name='Red Iron Crown']Snark, the "Oberth maneuver" you describe is not a [URL="https://en.wikipedia.org/wiki/Gravity_assist"]gravity assist[/URL] (though it is often combined with one). Misusing the term that way only adds confusion to what are already two fairly unintuitive concepts.[/QUOTE]

Absolutely... I only bring it up simply because there [I][U]are[/U][/I] two different things floating around out there that both involve assistance from gravity, and which people could potentially confuse. It's important to be aware that they're two different things and both have benefits.

[CaribouGone]

Here's a nice article about gravity assists: [URL]http://www.planetary.org/blogs/guest-blogs/2013/20130926-gravity-assist.html[/URL]
He explains the event from the both the sun's and the planet's frame of reference, which i found very helpful. He explains the transfer of energy between planet and spaceship quite well, too.
As it turns out, each Voyager flyby slowed Jupiter down by 10^-24 km/s.

[Yasmy]

[quote name='More Boosters']Your gravitational potential energy is calculated very simply as m*g*h, and radial burns exist to change your altitude.[/QUOTE]
This is only approximately true, useful only for very small height changes relative to the distance to the center of the body you are orbiting.
Otherwise you should use the full form: PE = - GMm/r.
For very small changes in height, h = dr << r: PE = -GMm/(r+dr) ~= -GMm(1-dr/r)/r = -GMm/r + GM/r^2 m * dr = -GMm/r + m g h, where g is the local acceleration of gravity, g = GM/r^2. Then the change in PE as a function of height is mgh, using the local g. But for orbital mechanics, you usually can't use this approximation.

[Person012345]

[quote name='Red Iron Crown']It's like throwing a tennis ball at the front of a moving semi truck, some momentum is transferred from the truck to the ball but only the ball's speed changes significantly. In KSP the planet's infinitesimal loss of momentum is rounded down to zero.[/QUOTE]

I very much doubt it's calculated at all. I don't think planets are physics bodies, I don't think they're subject to tidal deceleration or anything of that sort either, I believe that their orbits are simply fixed and there's no way to change that. I could be wrong but that's the impression I am under. Edited November 22, 2015 by Person012345

[Red Iron Crown]

That's what I meant by "rounded to zero", the effect is not considered. :)