How Far is the Real Moon's SOI?

[Mr Shifty]

I was playing around in Orbiter, flew a DGIV from Kennedy to space, transferred to the moon, landed at Brighton Beach, refueled, went back to lunar orbit, then transferred back to the Earth.

I noticed that on my return to Earth transfer, my Earth-referenced trajectory ellipse (specifically, the periapsis) kept changing (I assume under the moon's gravitational influence) until I was about 80,000 km from Earth, which means that for about 80% of the journey, the moon's gravity still had a discernible influence. Does this make sense?

[astropapi1]

Water tides.

[metaphor]

In the real world, the sphere of influence of a body is where the gravitational force of that body is larger than the gravitational force of any other body. Outside its SoI you can still feel the gravitational force from that body, it is just less than the gravitational force from the body in whose SoI you are. A body's gravitational field goes out to infinity, it just decreases in intensity with distance. For example, some satellites in Earth orbit have to take into account Jupiter's gravitational influence for long term stability, even though they're nowhere near Jupiter's SoI.

The formula for the size of a body's SoI is r_SOI = a * ( m / M ) ^ (2/5), where a is the semimajor axis of that body, m is the mass of the body, and M is the mass of whatever it's orbiting. The Moon's SoI goes out to 66,000 km, or 38 Moon radii.

[WhiteWeasel]

I think he means Hill Sphere.

[Person012345]

yeah, the SoI model in ksp is massively simplified because n-body physics are hard. It doesn't work quite that way in real life.

[Mr Shifty]

Well yes, I guess I understood that the patched-conic approximation would make for un-realistic effects in KSP, but the extent of the moon's influence is what surprised me. I expected to see some small orbital perturbations out past the edge of the moon's SOI, but I kept seeing it change my perigee all the way out until I was 80% of the way back to Earth. My perigee started at something like -160km at the moon's SOI and ended up at about +200km by the time I got very close to Earth. Some of this, I'm sure was because my return trajectory was in a prograde direction relative to the Earth, so the moon was sort of "following" my vessel as I returned, but it still sort of shocked me that its influence was felt so far out. The Hill sphere of the moon has a radius of about 58,000 km, but I was seeing noticeable effects (e.g. missing instead of hitting the Earth) at 300,000 km away.

EDIT: I guess my point is that "Sphere of Influence" is a term of art that simply means the body's gravity is dominant within. In KSP, the SOI is precise: not only does the primary body's gravity dominate, but it is the only gravity that has any influence at all. Lunar transfer, in particular (because the moon is so large and close relative to its primary), really shows the limits of the approximation.

Edited August 19, 2013 by Mr Shifty

[PakledHostage]

On a related note, I found an interesting essay titled Apollo lunar landing launch window: The controlling factors and constraints on the NASA History Program Office's website. I recall reading in Michael Collin's book that conics were used in planning and executing the Apollo missions. Apparently it lead to some confusion in the media while Apollo 11 was enroute to the moon.

[metaphor]

You can calculate the gravitational force using Newton's formula. In a 100 km low lunar orbit, the Moon's gravity is 1.45 m/s^2 and the Earth's gravity is 0.003 m/s^2, so the Moon is about 500 times more powerful than the Earth. At 60,000 km from the Moon and 320,000 km from the Earth, the Moon's gravity is 1.36 mm/s^2 and the Earth's gravity is 3.89 mm/s^2, so the Earth is about 2.9 times more powerful than the Moon. At 300,000 km from the Moon and 80,000 km from the Earth, the Moon's gravity is 0.054 mm/s^2 and the Earth's gravity is 62.2 mm/s^2, so the Earth is about 1200 times more powerful than the Moon. That's a small but sizable force from the Moon. And the 200 km difference you observe in perigee is still pretty small compared to the actual distances involved.

[Kilmeister]

That essay is an interesting read. It seems there is a little more to it than "burn prograde at munrise" =P

[Mr Shifty]

On a related note, I found an interesting essay titled Apollo lunar landing launch window: The controlling factors and constraints on the NASA History Program Office's website. I recall reading in Michael Collin's book that conics were used in planning and executing the Apollo missions. Apparently it lead to some confusion in the media while Apollo 11 was enroute to the moon.

Fascinating essay. I only have time now to skim through it, but I'll check it out in more detail later. Thanks!

And the 200 km difference you observe in perigee is still pretty small compared to the actual distances involved.

Yeah, I guess this is the salient point. It really shows how precise the calculations had to be to get the Apollo astronauts back home.

[Platofan2]

There is only one moon around orbiting the earth