Kerbonauts, help me figure this out

[RocketBlam]

OK, this is a bit of an odd question, but here goes:

I was reading about Apollo 10, and looked up what happened to the "Snoopy" Ascent Stage, which was jettisoned at some point after they achieved orbit around the moon. Apparently it is now in heliocentric orbit (orbit around the sun). But here's the thing: I don't understand how it can be.

As we know from KSP, it takes a certain amount of energy to escape a planet's orbit. On Earth, that is apparently 11.2 km/s. From the records, though, the Command Module never exceeded 11.08 km/s. It achieved that on the return trip to Earth (and is now on record as being the fastest humans have ever flown).

So... I don't get how the Snoopy Ascent Stage could have left Earth's orbit. At no point in the flight plan did the spacecraft go fast enough to get it out of orbit. Even if they discarded it after achieving their maximum speed, it still wasn't going fast enough to escape Earth's orbit.

I really doubt they lit the thing's engines after it undocked and was empty.

There's only one possible way I can see for it to have escaped: After it was jettisoned on the return trip to Earth, it looped around the earth, then encountered the Moon again, which perturbed its orbit enough to send it out of the system (sort of a gravitational assist maneuver). But I don't get that impression from what I've read. As far as I know, it wasn't tracked after it was discarded, although the math brains on the ground may have figured out that it would be thrown out after re-encountering the moon.

[Superfluous J]

11.2km/s is the escape velocity at Earth's surface. Out at the Moon, it's quite a bit lower. I don't know the exact velocity but according to wikipedia at 9000km (much lower than Lunar orbit) it's a mere 7.1km/s.

[magnemoe]

Also orbit around moon is not stable, not only does earth interfere but more important moon gravity field is uneven so you will end up either crashing or in orbit around earth.

Now you might get gravity assist from moon to put you in sun orbit.

This can not happen in KSP, however an transfeer stage with lowest point at low orbit around Kerbin and highest point intercept Mun SOI will end up in orbit around sun except a low probabliity of it crashing into kerbin or Mun.

[kerbiloid]

Relative to Earth:

V circular = sqrt(6e24 * 6.67e-11 / 3.844e8) = 1020 m/s.

V parabolic - V circular = (sqrt(2) - 1) * 1020 = 422 m/s.

Relative to Mun:

V circular = sqrt(7.35e22 * 6.67e-11 / ~2e6) ~= 1600 m/s.

V parabolic - V circular = (sqrt(2) - 1) * ~1600 ~= 660 m/s.

I.e. 700 m/s more  and you're a planet.

[K^2]

11.2km/s is the escape velocity at Earth's surface. Out at the Moon, it's quite a bit lower. I don't know the exact velocity but according to wikipedia at 9000km (much lower than Lunar orbit) it's a mere 7.1km/s.

Virial Theorem. Learn it. Understand it. Use it.

When applied to circular orbit, it says that you need to double your kinetic energy to escape. Moon's average orbital velocity is just over 1km/s. That means the escape velocity will be just over 1,400m/s. No need to remember a bunch of formulas and constants. If you know one, you know the other. And since sqrt(2) is very close to 1.4, you can do the math in your head.

[Superfluous J]

When applied to circular orbit, it says that you need to double your kinetic energy to escape.

You know I had vague memories of doubling something, but I couldn't remember what you doubled or even if I was remembering correctly at all. If I'd guessed, I'd have guessed velocity which was wrong anyway.

Good to know though that I remember SOMETHING from college (other than where the cheerleaders did their drill practice).

[LordFerret]

I used to meddle with Celestia. I know many of Celestia's users and developers are folks who know what they're talking about. While Celestia has fallen by the wayside and its original Shatters.net forums defunct, most of the original users and devs have moved to the CelestialMatters forum - folks like Dr. Fridger Schremp, Selden Ball, among others... these guys are pros. Curious about your post (OP), I looked around a bit and ran across this - it's from a discussion about an addon for Celestia, an .ssc definitions file for Snoopy.

"From the README file...

The computation of the actual orbit elements of LM 4 was done in a three- step process. From technical references about the Apollo program there is enough information to calculate the delta v of the LM. "Snoopy" didn't land on the moon, so most of the propellant of the ascent engine wasn't yet needed when Mission Control fired it at May 23, 1969 at 6:07 UT. The engine ran until burnout. Delta v can be calculated to 1150 m/s.

1. Under the assumption the LM accelerated parallel to the orbital tangent, the delta v adds to the circular velocity of Apollo around the moon (note the Apollo orbits were retrograd). By this, an escape hyperbola and its asymptotic velocity and angle can be calculated. Snoopy left the moon's gravity well at 1336 m/s and an angle of 58.5 deg against the orbit tangent/moon center.
   
   
2. By a vector addition of the moon's orbital speed one gets the LM's trajectory in a geocentric coordinate system, and doing the same procedure as above for earth again one has the LM's velocity vector with respect to sun center.
   
   
3. Now I had a point in space (vincinity of the moon) and a velocity vector at a certain time (May 23, 1969, 6:00). It was now possible to calculate the elements of a sun orbit by means of common formulas of celestial mechanics [10].
   
   

Nevertheless some fine adjustments in the .ssc file had to be done - I also desire the LM to be in the vincinity of the moon on May 23, 1969 but obviously some of the assumptions I made were only rough approximations of what really happened.

So please note the calculated orbit is only a rough approximation of where "Snoopy" would be located really today - despite of any bugs in the calculation I might have done.

"

Source: http://www.collectspace.com/ubb/Forum29/HTML/001171.html

I haven't been to the CelestialMatters forum in a long time, but I'm there as I am here - "LordFerret". I'm sure you'd find welcome serious discussion if you asked some questions there.

Site: http://www.celestialmatters.org/

Good luck with your quest!