Lunar Orbit

[Not Myself]

How low can one go and still be "safe", where you don't have to worry about the perturbations causing you to form a new impact crater?

[ka9q]

I'm not sure that any lunar orbit is indefinitely stable. Everything hits sooner or later. The perturbations change the orbital eccentricity over time until perilune happens to intersect the surface.

At low altitude, the mascons are the major perturbation. If you try to orbit higher to get away from them, the earth and sun become significant.

When you think about it, the only way that a lunar orbit can decay is for the eccentricity to change. Changing the semi-major axis (or mean motion) implies changes in orbital energy and angular momentum, and without an atmosphere to provide drag I can't think of any way to do that. But you can change the eccentricity while keeping the same semi-major axis (and orbital energy).

[ka9q]

To illustrate just how significant the perturbation from the earth can be, consider a non-nominal lunar orbit insertion burn.

If the burn doesn't happen at all, you come back home on your free-return trajectory (assuming you were on one).

If you burn too long, you impact on the near side a half orbit later, just as you'd expect. The astronauts watched the clock, ready to push the manual stop button if the computer didn't stop the burn as it should.

If you burn just a little too short, you'll go into an elliptical lunar orbit with apolune on the near side. Again, just as you'd expect.

But as you decrease the burn time further, something interesting happens. Although the apolune continues to increase, the perilune also decreases. There is a range of burn times, all less than the nominal time, that can result in lunar impact within a single orbit. The cause of this decrease in perilune is the perturbation from earth's gravity at apolune on the near side. You're at a higher altitude, increasing the earth/lunar gravity ratio, and the orbital period also increases, so the earth tugs on you for a longer time.

Apollo had emergency "bailout" procedures in case a dangerously non-nominal burn had ever occurred.

[Kiwi]

How low can one go and still be "safe", where you don't have to worry about the perturbations causing you to form a new impact crater?

I was a bit confused over this post until I read Ka9q's reply, because I thought you were asking our honourable Master of Ceremonies, LunarOrbit, in a rather clever way but in the wrong part of the forum, how low you could stoop as a poster before he went ballistic and dug a hole to bury you in because of "perturbations" from other members.

Got it now.  Case closed!

[LunarOrbit]

I've been stable for 36 years. No one has hit me (so far) despite all of my perturbations.

[Bob B.]

How low can one go and still be "safe", where you don't have to worry about the perturbations causing you to form a new impact crater?

I was a bit confused over this post until I read Ka9q's reply, because I thought you were asking our honourable Master of Ceremonies, LunarOrbit, in a rather clever way but in the wrong part of the forum, how low you could stoop as a poster before he went ballistic and dug a hole to bury you in because of "perturbations" from other members.

That's what I thought he meant too.

[Not Myself]

To illustrate just how significant the perturbation from the earth can be, consider a non-nominal lunar orbit insertion burn.

If the burn doesn't happen at all, you come back home on your free-return trajectory (assuming you were on one).

If you burn too long, you impact on the near side a half orbit later, just as you'd expect. The astronauts watched the clock, ready to push the manual stop button if the computer didn't stop the burn as it should.

If you burn just a little too short, you'll go into an elliptical lunar orbit with apolune on the near side. Again, just as you'd expect.

But as you decrease the burn time further, something interesting happens. Although the apolune continues to increase, the perilune also decreases. There is a range of burn times, all less than the nominal time, that can result in lunar impact within a single orbit. The cause of this decrease in perilune is the perturbation from earth's gravity at apolune on the near side. You're at a higher altitude, increasing the earth/lunar gravity ratio, and the orbital period also increases, so the earth tugs on you for a longer time.

As I would guess they were gunning for a relatively close orbit, if the earth perturbations are still something to worry about, then should I take it that just about any lunar orbit requires relatively frequent course correction?  Can you place yourself in an orbit where you can go a few weeks or months without worrying about it, or is that just not possible?

Apollo had emergency "bailout" procedures in case a dangerously non-nominal burn had ever occurred.

I take it that's "bailout" in a figurative sense, since bailing out of the spacecraft would not seem to improve their situation a whole lot.

In any event, thanks for the information.  What I was really wondering is whether you can park something in lunar orbit, and not worry about it for weeks or months at a time.  My assumption was that the higher orbit would be the more stable, but perhaps that is not the case.

[scooter]

I recollect the initial Apollo lunar orbits had an apolune (is that the right term?) of maybe 2-300km, and would be circularized an orbit or 2 later. Was this maybe a safety measure to preclude an overburn/"crater"?

[Glom]

To illustrate just how significant the perturbation from the earth can be, consider a non-nominal lunar orbit insertion burn.

If the burn doesn't happen at all, you come back home on your free-return trajectory (assuming you were on one).

If you burn too long, you impact on the near side a half orbit later, just as you'd expect. The astronauts watched the clock, ready to push the manual stop button if the computer didn't stop the burn as it should.

If you burn just a little too short, you'll go into an elliptical lunar orbit with apolune on the near side. Again, just as you'd expect.

But as you decrease the burn time further, something interesting happens. Although the apolune continues to increase, the perilune also decreases. There is a range of burn times, all less than the nominal time, that can result in lunar impact within a single orbit. The cause of this decrease in perilune is the perturbation from earth's gravity at apolune on the near side. You're at a higher altitude, increasing the earth/lunar gravity ratio, and the orbital period also increases, so the earth tugs on you for a longer time.

Apollo had emergency "bailout" procedures in case a dangerously non-nominal burn had ever occurred.

Damn n-body mechanics. Gives my PC a headache.

[Bob B.]

I recollect the initial Apollo lunar orbits had an apolune (is that the right term?) of maybe 2-300km, and would be circularized an orbit or 2 later. Was this maybe a safety measure to preclude an overburn/"crater"?

The first four lunar flights – Apollo 8, 10, 11 and 12 – performed lunar orbit insertion (LOI) in two separate maneuvers using the SPS of the CSM. The first maneuver, LOI-1, was initiated after the spacecraft passed behind the Moon and crossed the imaginary line through the centers of the Earth and Moon at approximately 160 km above the lunar surface. The SPS burn was a retrograde maneuver that placed the spacecraft into an elliptical orbit that was approximately 111 × 315 km. After two revolutions and a navigation update, a second SPS retrograde burn, LOI-2, was made as the spacecraft crossed the antipode behind the Moon. On Apollo 8 and 10, LOI-2 was an orbit circularization burn that placed the spacecraft in a 111 km orbit. On Apollo 11 and 12, LOI-2 placed the spacecraft in an elliptical orbit approximately 101 × 122 km. This orbit became circularized at 111 km by the time of the LM rendezvous due to the effect of variations in the lunar gravitational potential on the spacecraft as it orbited the Moon.

Starting with Apollo 14, LOI placed the spacecraft in an approximate 107 × 315 km elliptical lunar orbit, similar to previous missions. However, rather than performing the LOI-2 maneuver, the SPS performed the descent orbit insertion (DOI) maneuver, which placed the CSM/LM into an elliptical orbit approximately 20 × 109 km from which the LM would begin the later powered descent to landing. In Apollo 11 and 12, DOI was a separate maneuver using the LM descent engine. The Apollo 14-17 DOI maneuver in effect was a combination LOI-2 and DOI that produced two benefits: conserved LM descent propellant that would have been used for DOI and made this propellant available for additional hover time near the surface, and allowed additional lunar revolutions of spacecraft tracking in the descent orbit to enhance position and velocity data for updating the LM guidance computer during the descent and landing phase. (Apollo 13 was planned as the first flight to employ this technique, but the mission was aborted prior to LOI.)
 

[ka9q]

The reason for the two LOI burns on 8, 10, 11 & 12 was simple engineering conservatism. Shortening the first LOI burn increases its margin against a dangerous overburn. The resulting elliptical orbit can be carefully tracked and compared with the expected orbit to analyze SPS performance and to reveal any unexpected platform drift, accelerometer bias, or errors in the gravity model. Then the more critical circularization burn can be done more safely.

With the experience of these four flights, NASA decided that they didn't need to be quite so conservative and it was safe enough to perform LOI in a single burn.

I knew about the CSM performing the descent orbit maneuver starting with A14. I've always seen that as an indication that the original spacecraft mass budget probably wasn't optimum. It allocated too much to the CSM and not enough to the LM. It's more efficient overall to put only the LM in the descent orbit than both the CSM and LM, but doing that with sufficient margin would entail a major redesign to enlarge the LM's descent propellant tanks. The CSM could be kept as-is, with some of its SPS propellants offloaded if necessary to conserve total mass.

The SPS did have a slightly greater Isp (314.7 sec measured during Apollo 15) than the LM's DPS (305.8 sec measured on Apollo 15 during the full throttle braking phase). This might have tilted the balance in favor of having the CSM perform the descent orbit maneuver, but I'd have to work out the detailed numbers.





 

[ginnie]

How low can one go and still be "safe", where you don't have to worry about the perturbations causing you to form a new impact crater?

I was a bit confused over this post until I read Ka9q's reply, because I thought you were asking our honourable Master of Ceremonies, LunarOrbit, in a rather clever way but in the wrong part of the forum, how low you could stoop as a poster before he went ballistic and dug a hole to bury you in because of "perturbations" from other members.

That's what I thought he meant too.

I thought the thread was about the moon getting closer and closer to the earth.
In fact, the moon is increasing its distance from the earth.

[gwiz]

Just to add this mission to the debate.  They've been orbiting at a mean altitude of 55 km up to now, but plan to go down to 23 km.

http://www.nasa.gov/mission_pages/grail/news/grail20120529.html