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Post by coelacanth on Aug 13, 2011 0:45:20 GMT -4
Wouldn't it, in fact, speed up? Yeah, that's what I briefly thought... but I've been bitten badly by orbital mechanics before.. I once thought it 'wasn't rocket science'.. but I was wrong! Paging Bob B, Bob B... Not Bob B, but I'll do my best ... Assuming a circular orbit (and also assuming I'm doing my calculations right), the velocity is inversely proportional to the square root of the radius of the orbit. Wikipedia reports a mean radius of the not-quite-spherical moon of 1737.1 km. So if we're talking about an orbit 50km above the surface vs. one 20km above, that's only 1787.1 vs. 1757.1, after taking square roots and reciprocals, I'm getting that it should speed up by a factor of about 0.85%. Then it is 20km away instead of 50km, if it is looking straight down and ignoring the curvature of the moon's surface, the distance to the target is 60% less, and should pass out of the field of vision 2.5 times faster. So we're talking a factor of 150% because it is closer, and a factor of 0.85% because it's faster. Again, assuming I haven't made some appalling cock-up here.
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Post by chrlz on Aug 13, 2011 7:29:55 GMT -4
Yes, but what if it is in the process of 'falling? In other words, let's say it uses a brief pulse of thrusters to slow. I assume it will take a measurable length of time as it drops down to the lower orbit - what happens to its speed over the surface during that fall, and then as it levels out in its new orbit? Does it keep recording imagery as it descends? Oh, alright, I admit I'm just being a devil's advocate...
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Aug 13, 2011 15:10:24 GMT -4
You can find all the formula to do these calculations here: www.braeunig.us/space/orbmech.htm#maneuver(The value of GM for the Moon is 4.902794 × 10 12 m 3/s 2) The orbital velocity at 50 km (1,787.1 km semi-major axis) is 1,656.3 m/s, and at 20 km the orbital velocity is 1670.4 m/s. Assuming a minimum-energy Hohmann type transfer is performed, the spacecraft would have to be slowed from 1,656.3 m/s to 1,649.3 m/s to place it into a 50 km × 20 km transfer orbit. When it reaches perigee, the spacecraft would be traveling 1,677.5 m/s. A second burn would have to be done at perigee to slow it from 1,677.5 m/s to 1,670.4 m/s to circularize the orbit at the 20 km altitude. As coelacanth correctly determined, the velocity at 20 km is only 0.85% faster than at 50 km. However, since the spacecraft is closer to the ground, the angular velocity of the spacecraft with respect to a target on the ground is much higher. When passing directly overhead, the angular velocity of the spacecraft in a 50 km orbit is 1.898 o/s. When in a 20 km orbit, the overhead angular velocity jumps to 4.785 o/s.
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Post by trebor on Aug 13, 2011 20:01:55 GMT -4
I imagine such a low lunar orbit could not possibly be that stable, so they probably would not want to risk it for much longer. Why not? Because it would require a lot of energy to constantly refine the orbit and keep it stable..... No idea how much though.
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Post by ka9q on Aug 13, 2011 21:36:53 GMT -4
Lunar orbits are indeed unstable. My understanding is that there are two major perturbations: the gravity of the much more (81x) massive earth, and the moon's irregular gravity field. These typically change the satellite's orbital eccentricity until pericynthion is below the surface.
Apollo had emergency procedures in case of an early shutdown during lunar orbit insertion. For one range of short burn times the spacecraft would be in a highly elliptical orbit with apocynthion high over the near side. During this single loop, if nothing were done, the earth's gravity would tug on Apollo enough to hit the moon before it could return to its pericynthion on the far side.
LRO is probably making these maneuvers now because it has already accomplished its primary objectives. Now they can try fun but riskier things. Eventually LRO will strike the lunar surface as it can't carry an infinite supply of station-keeping fuel. The operators will probably reserve some of that fuel for an eventual de-orbit maneuver to a targeted impact site, perhaps another polar location where there's thought to be water.
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Post by PhantomWolf on Aug 13, 2011 22:28:22 GMT -4
Because it would require a lot of energy to constantly refine the orbit and keep it stable..... No idea how much though. I was actually meaning why would it be so much more unstable that a 50km orbit. It suffers the exact same problems, but unlike about Earth, there is no atmosphere to worry about.
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Post by ka9q on Aug 13, 2011 23:17:28 GMT -4
I was actually meaning why would it be so much more unstable that a 50km orbit. It suffers the exact same problems, but unlike about Earth, there is no atmosphere to worry about. Well, the lower you go the greater the effects of the higher order terms of the gravity field. I.e., smaller mascons start to have an effect. They may not be as well known, so it would be harder to predict the exact path of the satellite very far ahead and to ensure its safety. And it's obvious that you have less margin for error at lower altitudes -- the moon has some pretty tall mountains.
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Post by ka9q on Aug 13, 2011 23:28:00 GMT -4
Yes, but what if it is in the process of 'falling? In other words, let's say it uses a brief pulse of thrusters to slow. I assume it will take a measurable length of time as it drops down to the lower orbit - what happens to its speed over the surface during that fall, and then as it levels out in its new orbit? Bob's answer is the technically complete one, but I can give you a qualitative answer. Let's say you start in a circular orbit. You make an "impulse" burn, i.e., a very short one, against your direction of motion. You immediately slow down. But you continue to hurtle forward, your inertia taking you around the moon so fast that the surface curves away as you fall toward it. But you will begin to fall a little faster than the surface curves away; i.e., you'll descend. As you descend, you'll pick up forward speed. When you reach the point on your orbit that's exactly on the other side of the moon or planet from where you did your burn, you'll reach your minimum altitude. This is your new periapsis (general term for the lowest altitude point of an orbit around any body). But because you picked up speed as you fell, you'll be going too fast to remain at that lower altitude. You'll climb right back up to your starting altitude, slowing a little as you go. You'll return right to the point where you fired your engine, going at the same speed you were going just after your burn. This is your apoapsis (again the general term). However, you'll reach that point sooner than you would have had you not fired your engine. That's because your orbital period is shorter (remember, you sped up as you fell, and you didn't return to your original speed until you climbed all the way back up to apoapsis.) If you had left an orbiting spacecraft in your original circular orbit, you would now be ahead of it even though you're moving more slowly. This is an example of the counter-intuitive nature of orbital mechanics. But it's true, and the formulas, simulations and most of all real life flights demonstrate it all the time.
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Post by gonetoplaid on Aug 26, 2011 23:58:31 GMT -4
Assuming that the lens is not the limiting factor (i.e., it's operating within its diffraction limit), the transverse resolution is set by the pixel spacing. The resolution along the direction of motion is limited by the finite pixel height and/or the exposure time, i.e., how much the spacecraft moves during the exposure, whichever is worse. I don't know the limits of the sensors on LRO, but in this lower orbit it might achieve better transverse than longitudinal resolution for this reason. Quite correct. The LRO NAC camera resolution is limited by the 7 micron pixel size of its CCD sensors. The lower 20 km minimum orbit will allow for approximately 4 times the spatial resolution or twice the resolution along the horizontal and vertical axes. The increased spatial resolution is what will really make the images "snap" with detail.
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Post by gonetoplaid on Aug 27, 2011 0:06:26 GMT -4
LRO is probably making these maneuvers now because it has already accomplished its primary objectives. Now they can try fun but riskier things. Eventually LRO will strike the lunar surface as it can't carry an infinite supply of station-keeping fuel. The operators will probably reserve some of that fuel for an eventual de-orbit maneuver to a targeted impact site, perhaps another polar location where there's thought to be water. The LRO has dropped down to 20 km to use the Apollo landing sites for calibration purposes. Eventually the plan is to put the LRO into an orbit which is stable for the long term, allowing for an extended mission of another 2 to 3 years.
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Post by ka9q on Aug 27, 2011 0:45:08 GMT -4
Interesting. I take it they'll use the well-known locations of the LRRRs at the Apollo 11, 14 and 15 sites.
By now they must have a pretty detailed model of the lunar gravity field from these low altitude orbits and especially from the Japanese Kaguya mission. It carried a separate relay satellite to permit ranging the main spacecraft on the far side. The far side models had always been coarse because of this inability to track in real time.
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Post by tikkitakki on Sept 2, 2011 6:03:36 GMT -4
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Post by trebor on Sept 2, 2011 9:22:00 GMT -4
Nice, It will be interesting to see what extra detail can be seen.
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Post by abaddon on Sept 2, 2011 12:57:55 GMT -4
dammit, I have to wait 4 more days?
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Post by trebor on Sept 6, 2011 12:09:45 GMT -4
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