Just How Close Can Cassini Come to Enceladus? Options

[pioneer]

According to this press release, Cassini will fly 25 Km from the surface of Enceladus in October I know the escape velocity of Enceladus is low, but just how close can Cassini come to the surface without the gravity pulling it in? What is the escape velocity of Enceladus?

[ugordan]

No matter how strong the gravity of a body you're flying by is, unless you do a braking burn at some point in the flyby you cannot get captured. From that body's point of view, you're coming in via a hyperbolic trajectory coming from "infinity" and the body's gravity accelerates you enough that by the time you pass closest point you have picked up just enough additional speed to leave the body and its gravity well with the same speed you came in. No gain, no loss, only your direction is changed, e.g. the trajectory is "bent" by a certain angle as seen from that body, in this case of Enceladus. The stronger the gravity, the more the trajectory is bent.

From the point of view of Saturn, the situation is a bit more complicated. The spacecraft actually ends up giving or stealing a bit of it's orbital energy (relative to Saturn!) to the moon, but in no practically conceivable circumstance can Cassini get captured by any moon (including much more massive Titan) just by passing by. It would need to do a propulsive maneuver to do that, and to get captured by Enceladus during these flybys it would actually have to get rid of some 18 kilometers/second velocity, which is a huge amount and well beyond Cassini's capabilities even if the propellant tanks were full again. For comparison, that's a much higher velocity than Cassini was even launched from Earth with and it took a really big rocket to do that!

[Holder of the Tw...]

Unless there is something to slow it down, such as retrorockets, or atmosphere, or a solid surface, any spacecraft falling into the gravity of a moon or planet is going to maintain an escape velocity. There are some boundry conditions involving two and three body interactions where, if you a careful enough, you can go into an orbit, but these have to be set up pretty carefully. (Edit: and you can't start out with very much speed relative to the object you are trying to orbit. Example of a three body interaction is Earth, Moon, and Sun, using the gravity of Earth and Sun to guide a spacecraft into lunar orbit).

If your question is "how close can you come to Enceladus before the gravitational deflection causes it to crash?", then the theoretical answer is zero, just skimming the surface. You just take the moon's gravity into account as you plot your course. As a practical matter, there is always some error in your aim, so if you try to come too close, the chances will be good that you will impact. Some one from the Cassini team will have to answer just how close they can come without too much risk, I don't know about that. I know that as you model the moon's gravity and position more precisely, your error box gets smaller.

Escape velocity for Enceladus from the surface, according to wikipedia, is 860.4 km/hour. Its surface gravity is 0.0113 g.

[ugordan]

Unless there is something to slow it down, such as retrorockets, or atmosphere, or a solid surface

Ahhhh... the infamous lithobraking method!

[djellison]

18 kilometers/second velocity,

That would take all of Cassini's fuel tanks...and probably the Titan rocket that launched it

[volcanopele]

I'm busy at the moment, but can someone do a quick calculation on how close Cassini has to come to Enceladus to get the equivalent of a Titan flyby (1000 km) in terms of a gravity assist. Basically, what is the distance from Enceladus where the gravitational force is equal to that of Titan's at a distance of 1000 km?

[djellison]

Well - my maths is probably off, but I get 1.86 km above the centre of mass of Enceladus - so basically an altitude of minus 248km

ish

[remcook]

I get negative numbers for altitude

edit: not as much as doug though..(hope my maths is right)

GM1/R1^2 = GM2/R2^2
R2= sqrt(M2*R1^2/M1)
= -166 + 249
=h+r
(we need a latex plug-in like they have at physics forums )

[volcanopele]

lol, good to know I was thinking it was below the surface, but I just hadn't bothered to do the math.

[ugordan]

I don't think the "same gravity force" and "same gravity assist" are equivalent. My ballpark calculation says you need to get 35.3 times closer to the center of Enceladus to feel the same gravitational force (rather than same trajectory bending) as during a Titan approach of 1000 km (which translates to 3576 km from Titan's center). That gives 101 km flyby distance to Enceladus' center.

So... yeah, lithobraking.

[MahFL]

16 miles is a bit close isn't it ? You'd feel pretty stupid if a navigation error resulted in a collision.........

[volcanopele]

I'd be concerned if that were our first flyby. But the navigation team has been pretty spot on and have gotten quite used to driving Cassini. I'm confident that they can get us there on the button.

[remcook]

I think ugordon is right though. You'd need to do calculations in terms of delta-V, which depends on the hyperbolic velocity etc.

[ugordan]

Remcook, I think your calculation missed the fact it's 1000 km altitude above Titan!

[tasp]

Just a quick break here to give a tip of the hat to the amazing trajectory the skillful techs behind the amazing Messenger mission to Mercury computed.

Their fuel stingy gravity pong technique for burning off velocity to get Messenger in orbit about Mercury, might someday be applied (??) in conjunction with the compelling Ariel orbiting option for the Uranus orbiter plan that Alex Blackwell referenced for us some time back.



{Some joker a while back has suggested a variation on the litho-braking technique wherein a Callisto approaching probe might brake in the debris plume generated by the precisely timed impact of it's launching rocket upper stage upon Callisto.}






Either (?) technique may someday find utility in the Saturn realm . . .