posted 12-12-2007 09:33 PM            

What I want to know, though, is did the Apollo missions actually fly a 'figure 8' type trajectory to the moon and back?

My understanding is that practically all launches into Earth orbit launch in a west-to-east direction to take advantage of the Earth's axial rotational motion. If one were to look down at the Earth and moon from a fixed point in space from above the Earth's north pole one would see two spinning spheres, each rotating 'counter-clockwise' with the moon itself orbiting the Earth in a 'counter-clockwise' direction as well (and at such an orbital rate — relative to its own axial rotation — that the same side always faces the earth).

So looking down from a fixed point in space above the north pole the Apollo (and all other manned spacecraft before and since) launched into a 'counter-clockwise' orbit. The moon is orbiting 'counter-clockwise' as well but the mission insignia/figure 8 would have one believe that the Apollo lunar orbit was clockwise (i.e. east-to-west).

It actually goes beyond the mission patch (which I recognize was only cleverly representative of the mission, incorporating the number '8'). This famous John Houbolt diagram seems to also indicate that the lunar trajectory was a 'figure 8' and the Apollo lunar orbit was opposite in direction to that of the Earth orbit (and hence opposite to the moon's own axial rotation).

It would seem to me that Apollo would have wanted to orbit the moon in the same direction the moon was turning (which is the same as the Earth) to take advantage of its motion when the LM ascent stage launched. But that would not give the 'figure 8' profile shown in the diagrams.

posted 12-21-2007 03:19 PM            

4.56 meters/sec or ~15 ft/sec or ~ 10 mph.

posted 12-21-2007 10:40 PM            

quote:

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Originally posted by pterodactyl:
Pretty small compared to the 'delta vee' contribution of the Earth's rotation...

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posted 12-22-2007 09:19 PM            

In the time since I posted my original question I searched online and through the many Apollo/spaceflight historical books that I own. Many of them show the John Houbolt diagram (or a similar NASA diagram) but no where did I read any reason given for the figure 8 trajectory that was, apparently, utilized.

I'm sure the way it was done was the most efficient way from a total mission standpoint taking into effect both earth and lunar gravity. The fact that the moons axial rotation is quite slow and would yield only a small velocity advantage is appreciated —  I only thought that with NASA/Grumman literally trying the slim the LM by ounces it would have seemed reasonable that they would take advantage of even a slight gain from the rotational velocity of the lunar surface.

In thinking about it I also thought, perhaps, that an east-to-west lunar orbit would have some lighting advantage during the critical landing and takeoff phases, but I did not read anything about that.

posted 12-22-2007 10:02 PM            

quote:

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Originally posted by Paul78zephyr:
I wonder if the future Orion missions are being planned with the same type of figure 8 trajectory as used on Apollo?

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posted 12-22-2007 11:03 PM               

I'll say up front that I'm no expert in this subject, but my background in science, engineering, and teaching astronomy and space subjects should serve to give you some confidence in my answer. I find the topic of spaceflight trajectories and rendezvous very interesting.

It is my understanding that the Apollo flights to the Moon did, indeed, follow a "Figure-8" path... relative to the Earth-Moon frame of reference. The image link provided by Paul is more representative, because it shows the effect of the Moon's travel in its orbit. But, you can see that neglecting the Moon's travel (as I say, in the Earth-Moon frame of reference), the path looks like a "Figure-8."

The reasons for this, as I have observed over the years, are as follows:

1. WEIGHT SAVINGS - The primary reason is to save fuel, and therefore reduce weight of the spacecraft. I'm sure you've heard of the "slingshot" maneuver. The Voyager spacecraft are probably the most notable for using this trajectory that uses a planet's gravity to accelerate itself and change direction for its next destination. An easy-to-read scientific explanation is here. On the second page of the explanation, the figures show how this is done.

   In the case of the Apollo spacecraft, the reverse of this was done to reduce the speed of the spacecraft so that less fuel would be needed to slow the spacecraft into lunar orbit. This was done, as I understand it, by approaching the Moon on its advancing (West) side, and thus entering a "clockwise" lunar orbit.

   Again, referring to the diagrams on the JPL web site, the orbital motion of the Moon was essentially subtracted from the velocity of the spacecraft, instead of added to it as in the case of Voyager. So, there was less thrust needed from the Apollo Service Module propulsion system, which translates to less fuel needed, which translates to a lighter spacecraft and a lighter overall rocket and its associated fuel.

2. SUN ANGLE - I recall accounts from the astronauts saying that they didn't see the Moon until they were in lunar orbit because they were in the Moon's shadow. I also recall that the landings were done during the Moon's first quarter phase.

   So, how does this support the "Figure-8" theory? Bear with me...

   They also wanted to approach the landing site in the final phase of descent with the Sun behind them at a very low angle. Behind so the sun wasn't in their eyes, and low so the long shadows would provide clear visual cues to the nature of the terrain.

   Putting this all together supports the "Figure-8"/clockwise lunar orbit hypothesis as follows...

   Picture the Earth-Moon system from "above" the North Pole. Put the Earth in the center of the "clock" and the Moon in the "12 o'clock" position. Put the Sun on the extreme right of the picture, illuminating the Earth's and Moon's right sides. The shadows of the Earth and Moon trail off to the left. The Moon's phase in this configuration is the first quarter. Apollo launches from the Earth in a "counter-clockwise" direction to take advantage of the speed of the Earth's rotation (as correctly mentioned by a previous poster). The Apollo spacecraft approaches the Moon on the advancing (or West) side - the left side on our imaginary drawing. The spacecraft is in the shadow of the Moon, and thus the Moon cannot be easily seen except for some amount of reflected Earthshine.

   As Apollo 8 neared its target, the spacecraft was turned so that its rocket engine pointed into the direction of flight. Bill Anders would later describe how he first became aware of the moon, as the spacecraft moved into the shadowed region where neither sunlight nor reflected light from Earth was visible -- what the astronauts called the "double umbra." As Anders recalled, "Suddenly, we saw millions of stars, more than you could see in a planetarium, to the point where it confused the constellations. So that was rather spectacular. And I remember looking at them because I was interested in astronomy, and then I looked kind of over my left shoulder and suddenly, the stars stopped. And there was this big black void, black hole. And that was the moon! That was the moon shielding the stars and yet not illuminated. It was as black as I've ever seen black. That was the only time in the flight the hair kind of came up on the back of my neck a little bit." [Source]

   Apollo enters lunar orbit in a "clockwise" direction, expending a smaller amount of fuel because of the "reverse slingshot" effect. On the far side of the Moon, the Apollo astronauts cross the terminator and get their first close-up look at the sunlit side of the Moon. ("... a vast, lonely, forbidding type of existence or expanse of nothing ..." - Frank Borman, Apollo 8) It is their first lunar "sunrise". Several minutes later, as they come around the East (right) limb of the Moon, they see their first lunar "Earthrise"!

   Another collectSPACE discussion notes that in the famous Apollo 8 image [Source], "North" is to the right. This supports the "clockwise" lunar orbit theory, as well.

   Apollo 11 took it the rest of the way. It's final descent brought it down to the
   landing spot [Source], moving from right to left as viewed from Earth. The Sun was at their backs and the long shadows fell away ahead of them until overtaken completely past the terminator.

   Lunar take-off and rendezvous were in the same "clockwise" direction, as was trans-Earth injection.

posted 12-23-2007 01:01 AM               

I remember, as a kid, having a 4-foot long poster with the Apollo trajectory milestones illustrated. I was curious to see what I could find with a quick image search on Google. Here's what I came up with...

Note on this image [Source, also see this], the dotted line showing the "slingshot" trajectory used to accelerate the S-IVB third stage into a solar orbit.

posted 12-23-2007 11:24 AM            

quote:

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Originally posted by Rocketman!:
They also wanted to approach the landing site in the final phase of descent with the Sun behind them at a very low angle. Behind so the sun wasn't in their eyes, and low so the long shadows would provide clear visual cues to the nature of the terrain...

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posted 12-31-2015 01:29 AM               

quote:

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Originally posted by Paul78zephyr:
The moon is orbiting 'counter-clockwise' as well but the mission insignia/figure 8 would have one believe that the Apollo lunar orbit was clockwise (i.e. east-to-west).

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posted 01-02-2016 02:23 AM               

From a heliocentric viewpoint the Apollo lunar flights became satellites of the Moon as it followed its path round the Sun. Consequently, Apollo 8's path round the Moon is as described in my diagram to show the Moon's orbit round the Earth, simply substitute the Moon for the Earth and Apollo 8 for the Moon.

posted 01-02-2016 10:06 AM            

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Originally posted by moonguyron:
shouldn't that be 23.5 degrees?

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There is a third plane involved: the plane of the Earth's orbit around the Sun. Another diagram shows 23.5 degrees as the angle between the plane of the Earth's equator, and the plane of the Earth's orbit around the Sun.