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mikusingularity
So how did they know when to launch the Apollo missions to the moon?
Flight Question The orbital plane of the moon never intersects Cape Canaveral (afaik)
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garyw
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You launch at a point when it's close-ish to KSC then do an off-plane intercept.
Urwumpe
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The same way how the Russians managed to send the first probes to the moon, despite being much further north: Off-plane.
A coplanar transfer (you being in the plane of the target orbit) is easier, but not the only way. You can also travel to the moon at any angle to the moons orbital plane.
In fact, all Apollo missions arrived at the moon with some inclination to the lunar orbit, so they had been able to enter a rather polar orbit on the moon.
AFAIR, the Luna 3 probe (or THE Probe for most of us here) was launched over Earths North pole so it was possible to control the insertion burn by ground stations.
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mikusingularity
I don't want close-ish. I want to know when the plane is the closest to KSC. How did the scientists at NASA determine that?
garyw
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Map MFD - Target - Moon.
and close-ish will be obvious from the line of the moons orbit near KSC. Time accel and watch it move.
and close-ish will be obvious from the line of the moons orbit near KSC. Time accel and watch it move.
Urwumpe
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Simple math and a slide rule.
You just need to know one date when the orbital plane is closest, and you can quickly calculate by adding the length of one half sidereal year and a few hours because of the perturbations of the lunar orbit, to know when the next such launch windows is.
The final launch date is then chosen so that the landing site has the proper sun angle, when the spacecraft lands - NASA never launched when the moon ground track was closest, but when the conditions had been optimal for the mission.
kwan3217
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If I understand correctly, the original poster plans to boost to LEO from Canaveral, then do a plane change to the Moon's orbit, so that the resulting transfer problem is purely 2D. They want to know when the plane is closest so that the plane change is minimized.
When the launch site latitude is greater than the Moon's inclination, you can never do an in-plane launch like you can to ISS. The best you can do is launch at 90deg azimuth at the right time. For any site in the Northern hemisphere, the right time is when the longitude of ascending node of the target is 90deg west of the launch site, or as I think of it, the descending node is 90deg east. If you launch at that time, your descending node with the equator is at the same longitude as the target's. If you use the map mfd (in orbit mode, not ground track mode) you can see the Moon's orbit as the yellow curve, and while sitting on the ground, your "orbit" is the green curve and matches what you would get if you launched due east. When the intersection between the yellow and green curves is at the equator, the desired condition is satisfied and the inclination between the orbits is minimized. Launch due east at that instance, and do a plane change as you cross the equator.
As Urwumpe mentioned above, NASA didn't do it that way. You can do a transfer from LEO at any inclination to the moon, completely in the original LEO plane (no out-of-plane TLI component). The constraint is that the intersection between the LEO and moon plane has to be at the same place as the moon is when you intercept.
For convenience, let's say that the Moon's orbit is over the equator and has an inclination of zero. Your satellite is like Luna 3 mentioned above and has an LEO inclination of 90deg. So, some convenient orbit when you are travelling north across the equator, you do a pure in-plane prograde maneuver and set up a Hohman transfer with your apogee right at the Moon's distance from the Earth. Since the maneuver is in-plane, you continue north and streak over the pole. Some time later, you reach apogee going south across the Moon's orbit, which we said was over the Earth's equator. Because you timed things right, the Moon is there at the same time you are and you can enter lunar orbit if you want.
Since the Moon is not over the equator, and since NASA didn't do a Hohman transfer, things get complicated. That's when TransX or IMFD is needed. I am more familiar with TransX. In it, when you are already in orbit, there is a gray line through the center of the plot, along the line of nodes of the start and target orbit (the line where the planes of those orbits intersect. Then there is a solid brown line showing where you are when you are closest to the Moon, and a dotted brown line showing where the Moon is. If all three of those are along the same line, you can do a transfer with no plane change. If you set up that transfer as stage 2 when you are on the ground, stage 1 will help you launch. (I think. Consult the manual.) I am sure IMFD does all this as well, I just don't know it.
Having said all that, I think I read in another post that NASA used a small out-of-plane component when they did TLI with Apollo -- just not big enough to match planes between the transfer orbit and the Moon's orbit.
When the launch site latitude is greater than the Moon's inclination, you can never do an in-plane launch like you can to ISS. The best you can do is launch at 90deg azimuth at the right time. For any site in the Northern hemisphere, the right time is when the longitude of ascending node of the target is 90deg west of the launch site, or as I think of it, the descending node is 90deg east. If you launch at that time, your descending node with the equator is at the same longitude as the target's. If you use the map mfd (in orbit mode, not ground track mode) you can see the Moon's orbit as the yellow curve, and while sitting on the ground, your "orbit" is the green curve and matches what you would get if you launched due east. When the intersection between the yellow and green curves is at the equator, the desired condition is satisfied and the inclination between the orbits is minimized. Launch due east at that instance, and do a plane change as you cross the equator.
As Urwumpe mentioned above, NASA didn't do it that way. You can do a transfer from LEO at any inclination to the moon, completely in the original LEO plane (no out-of-plane TLI component). The constraint is that the intersection between the LEO and moon plane has to be at the same place as the moon is when you intercept.
For convenience, let's say that the Moon's orbit is over the equator and has an inclination of zero. Your satellite is like Luna 3 mentioned above and has an LEO inclination of 90deg. So, some convenient orbit when you are travelling north across the equator, you do a pure in-plane prograde maneuver and set up a Hohman transfer with your apogee right at the Moon's distance from the Earth. Since the maneuver is in-plane, you continue north and streak over the pole. Some time later, you reach apogee going south across the Moon's orbit, which we said was over the Earth's equator. Because you timed things right, the Moon is there at the same time you are and you can enter lunar orbit if you want.
Since the Moon is not over the equator, and since NASA didn't do a Hohman transfer, things get complicated. That's when TransX or IMFD is needed. I am more familiar with TransX. In it, when you are already in orbit, there is a gray line through the center of the plot, along the line of nodes of the start and target orbit (the line where the planes of those orbits intersect. Then there is a solid brown line showing where you are when you are closest to the Moon, and a dotted brown line showing where the Moon is. If all three of those are along the same line, you can do a transfer with no plane change. If you set up that transfer as stage 2 when you are on the ground, stage 1 will help you launch. (I think. Consult the manual.) I am sure IMFD does all this as well, I just don't know it.
Having said all that, I think I read in another post that NASA used a small out-of-plane component when they did TLI with Apollo -- just not big enough to match planes between the transfer orbit and the Moon's orbit.
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