What do you think happened to the Apollo 11 Lunar Ascent Module "Eagle" ?

[AviatorTom]

Lunar Ascent Module orbiting the moon in July 1969

In July 1969, Neil Armstrong and Buzz Aldrin were the first humans to land on the moon. After several hours on the surface, they got into their lunar ascent module named "Eagle", blasted off, rendezvoused and docked with the Command module in orbit, and then the "Eagle" was undocked and left in orbit while the Command Module, with its three astronauts, (Michael Collins was the Command Module pilot) returned to Earth.

In the five decades since the moon landing, several people have tried to figure out what happened to "Eagle", including some sophisticated computer algorithms and simulations, yet no one has found it.

Where do you think "Eagle" is today?

It crashed into the Moon

It's in deep space, orbiting the sun

It's still orbiting the moon

It burned up in Earth atmosphere on reentry of the Command Module

It's in the Smithsonian in Washington DC, with the Command Module

It's still in the warehouse sound stage in Houston, where the moon landing was faked

[abc3643]

A. It likely crashed on the moon.

This is hard to explain...

Orbital mechanics can be finicky stuff and, if your orbits aren't just right, they will ultimately lead to a crash. So, when the separation between the upper (ascent) stage of Eagle (the Lunar Module) and Columbia (the Command Module) happened, if the impulse vector during LM jettison wasn't within a very narrow range, the Eagle would likely have entered into a lunar orbit that would result in a crash albeit it might have been so time before it crashed.

Keep in mind that all 6 of the Lunar Modules are large enough to be detected by telescope. If any were still in lunar orbit, they'd be detected.

Actually, "Snoopy", the Apollo 10 LEM is still in orbit - but heliocentric (about the sun) orbit. But Snoopy never landed on the moon. Apollo 10 was the first manned mission that traveled to the moon but only orbited it. So, when it was time to jettison Snoopy, the impulse vector chosen led to heliocentric, not lunar, orbit.

[AviatorTom]

Good idea, but no one has found its crash site, despite some serious searching.

[abc3643]

Well, that's because, when you fall from 100+ km up, chances are you're not going to remain in one piece at impact.

Let me do a calculation a bit later on what the estimated vertical component of the velocity at impact would be.

[AviatorTom]

Several people have done detailed simulations of where it may have crashed, and Lunar Orbiter has taken thousands of detailed pictures with no sign of any debris.

I'm starting to wonder if maybe some aliens borrowed it for studying human technology, before they make First Contact.

[abc3643]

There's no sign of debris because they are expecting significant clustered debris.
Two things:
1) The force of the impact was likely large enough to create many small pieces that would have had post-impact ejecta over a large area.
2) There likely is a possibility that some of the debris went back into orbit or achieved escape velocity so it never would be in lunar orbit again. I'd have to run the numbers but the escape velocity is going to be higher than the vertical component of the impact velocity

OK, I promised you a calculation...
First, an excerpt from the Smithsonian about Apollo 11...
"Lunar-orbit insertion began at 75:50 ground elapsed time (GET). The spacecraft was placed in an elliptical orbit (61 by 169 nautical miles), inclined 1.25 degrees to the lunar equatorial plane. At 80:12 GET, the service module propulsion system was reignited, and the orbit was made nearly circular (66 by 54 nautical miles) above the surface of the Moon. Each orbit took two hours."

(more)

[abc3643]

So, let's work with that... The least amount of gravitation potential energy (and, thus, the lowest eventual impact speed) would occur at the 54 nautical mile perilune of the orbit. Let's assume that is when the jettison took place. Perilune would also be the point of the highest in-orbit speed and the velocity vector would be perpendicular to the displacement vector from the lunar center to the spacecraft. But I am not interested in that - just what the vertical component of velocity will be upon impact...

OK, well, we need to go metric... 54 nautical miles = 100 km.
To make the calculation easy, we will assume a constant acceleration of gravity which we'll choose at the value at 100 km in altitude. The acceleration of gravity will only get higher the closer to the moon you get, so, by choosing the 100 km value (ALT), the impact speed will be higher than what we compute...

Scientists have measured "GM" of the moon as 4902.8 km^3/s^2 ("GM_moon").
Assuming the moon to be spherical with a radius of 1737.4 km ("R_moon"), that tells us that the acceleration of gravity is...

ACCEL_OF_GRAV_moon = GM_moon / (ALT + R_moon) ^2
= [ 4902.8 km^3/s^2 ] / [ 100 km + 1737.4 km ]^2
= 4902.8 / (1837.4)^2 km/s^2 = 1.45223 x 10^-3 km/s^2 = 1.45223 m/s^2

(more)

[abc3643]

For comparison, the acceleration of gravity at the surface of the Earth is 9.8 m/s^2. So, 100 km about the surface of the moon, the acceleration of gravity is about 1/6.75 that on the surface of the Earth.

OK, now for the payoff...

Under uniform acceleration with no friction, this equation holds:
V_final^2 - V_initial^2 = 2 * acceleration * distance_traveled.

So, what we want is V_final where:
V_final is the vertical component of the LM's velocity when it impacts the lunar surface.
V_initial = 0 (when the LM was jettisoned, we assume no vertical component of velocity).
acceleration = ACCEL_OF_GRAV_moon = 1.45 x 10^-3 km/s^2
distance_traveled = ALT = 100 km.

Let's run the numbers...
V_final^2 - 0 = 2 * [ 1.45 x 10^-3 km/s^2 ] * [ 100 km ]
= 0.29 km^2 / s^2
So...
V_final = [0.29 km^2 / s^2]^(1/2) = 0.53893 km/s = 538.93 m/s

(more)

[abc3643]

Let that number sink in... and remember - it's a low-ball estimate and is only the vertical component of the velocity at impact.
538 m/s is rather fast... It is faster than the speed of sound which is about 330 m/s. So, the vertical component of the LM's impact velocity is at least 1.6 times the speed of sound.

So, upon impact at that speed, this relatively fragile piece of equipment is going to be obliterated making just another crater on the moon... (and, for all we know, that crater is on the dark side).

But I owe you one more calc... the escape velocity at the surface of the moon.
That's:
V_escape = [ 2 * GM_moon / R_moon ]^(1/2) = 2.3756 km/s
Because V_final is considerably less than V_escape (which is over 4 times V_final), most of the debris of the obliterated LM would still rain down on the surface of the moon. HOWEVER, because that impact does have such a high velocity (which includes a tangential component) and a non-trivial fraction of V_escape, the debris would be scattered over a large fraction of the lunar surface.

In other words, there's not going to be an "Aha! There it is!" moment. You can say that only when talking about and pointing at the whole moon!

[AviatorTom]

Wow, you really took this to the extreme. Interesting calculations.

[abc3643]

Oh, this video is good. It illustrates what happened to the LMs and - I had forgotten this - that they were also deliberately crashed. Crater creation was important geophysics...

https://www.youtube.com/watch?v=U4BxDyYLzzc

[AviatorTom]

Good video. Note that all of the LEMs except for two were intentionally crashed into the moon to gather moonology data from the seismometers left there. Apollo 10's LEM had its engine intentionally fired until it ran out of fuel, which took it out of lunar orbit and into space, where it is now orbiting the sun. Apollo 11's LEM ascent stage was just undocked from the command module and left in lunar orbit. What happened to it from there depends on orbital mechanics, and there doesn't seem to be any agreement on where it ended up.

[abc3643]

Thanks, but my calculations weren't hard or complex because I understood the physics for many years and knew these equations off the top of my head (although I did double-check the escape velocity equation).

They are all in this book from 1971, "Fundamentals of Astrodynamics" by Bate, Mueller, and White (*). The first edition you can read free, but paying Dover Books for a copy is cheap, so consider getting a copy - and notice the cover picture on the book...



There is a second edition and I am thinking of buying it.

The first edition in PDF:
cmp.felk.cvut.cz/.../...s%20of%20Astrodynamics.pdf

(*) In the space industry, this book is affectionately called "BMW".

[horsenrhinounicorn]

It may be still orbiting around the moon, however they do not have the proper equipment to track it. Its like contacting NASA to find out where you parked your car, they have the technology to do it if you can see the sky from the car, however it takes a lot of time to search for it if they don't have an approximate location to search. They have to search the entire moon or they have to place a tracker on the moon that records all objects that pass the moon in orbit and have it record for the proper amount of time that it takes for the object to be viewable from the moon to the expected distance in orbit.

[horsenrhinounicorn]

If it crashed on the moon, they would eventually be able to find pieces as long as it is not buried underground. In the next 10 years there should be several other countries that will be next in landing on the moon and doing research.

[NamerOfStars]

If it was left in orbit of the moon, then either it's still there, or it's since crashed into the moon. Stable orbits are tricky, and doubly so when it's orbiting another body (well, technically the barycenter of its own orbit, but let's not make this more confusing than we have to). Since there's no one monitoring it and telling it when to apply thrust, my guess would be it's crashed by now.

[AviatorTom]

Excellent thought

[DeeDeeDeVour]

Most likely, the moon's gravitational pull (no matter how weak) pulled back to the lunar surface where it crashed in the dark side where it cannot be traced or tracked.

[DeeDeeDeVour]

pulled *it back to the lunar surface

[AviatorTom]

Interesting theory. Dark side can't be seen from earth, but all of the lunar satellites (Lunar Orbiter, for example) have taken detailed pictures of the entire moon, so wouldn't it have shown up in one of them?

[DeeDeeDeVour]

Lunar orbiters must have technologically advanced, powerful imaging & tracking systems. However, one such lunar satellite orbiting the moon isn't gonna be enough to accomplish the task of finding the Eagle. NASA wasn't/isn't gonna spend billions of dollars to find something no longer useful to them.

[exitseven]

It is in Bernie Sander's basement.

[Iron_Man]

I’m not really sure didn’t it hit the ocean

[AviatorTom]

Definitely not. The Command Module splashed down in the ocean, but the Lunar Module was left back at the moon.

[Iron_Man]

Hmmm not sure