What would it have taken to launch an unmanned sample return mission?

Comment on Apollo Moon Landing Hoax – Scientific Evidence by jfb.

27 of 61 space rocket launches in 1968 were secret, and 20 of 47 were secret in 1969. That’s 47 secret launches. What were they doing? Sending probes to pick up lunar samples? Sending probes to place mirrors on the Moon? Doing their camera tricks in Earth’s orbit to make it appear as if they were much farther from Earth than they really were?

Given that this was during the height of the cold war, it’s virtually certain that those were all spy satellites, not unmanned lunar missions.

However, let’s be generous and assume 10 of those launches (over 20%) were supar-sekrit unmanned lunar sample return missions (we only managed to send 8 manned missions, 6 of which landed on the Moon). Each of those had to be capable of returning roughly 84 lbs of material (38 kg) to account for the 840 lbs retrieved. From there, we can work backwards to spec out the kind of rocket needed to launch it.

We need a sample return vehicle large enough to hold ~40 kg of lunar regolith. We’ll use a WAG of 1 m^3 for the volume required (which is probably generous). That’s about 1/6 the interior volume for the Apollo CM. We don’t need air, food, or water, so we’ll ballpark the mass at 1/10 the CM, or around 600 kg (the return vehicle needs to be able to survive re-entry and splashdown, meaning it needs a heat shield, parachutes, thrusters, guidance equipment, etc.).

We need enough propellant to launch the sample return vehicle from the lunar surface and get it back to Earth. Delta-V from lunar surface to lunar orbit is roughly 1600 m/s, then from lunar orbit to low Earth orbit requires roughly 3900 m/s (we’ll assume re-entry at that point, although I’m not sure if we’d need another burn or not to commence re-entry – IANARS).

The Tsiolkovsky rocket equation can give us a rough idea of the amount of propellant necessary to get our vehicle back from the Moon:

delta-V = Ve * ln (m0 / m1)

where

Ve is the effective exhaust velocity of the rocket
m1 is the final mass (payload + dry mass (engines, tanks)), and
m0 is the total mass (payload + dry mass + propellant)

In this case, we know our delta-V (4500 m/s) and m1 (640 kg, not counting dry rocket mass), and we want to find m0 (payload + propellant mass). Doing a little algebra, we get

m0 = m1 * e(delta-V / Ve)

Figure 3500 m/s for Ve (a reasonable estimate for most chemical rockets), and we get m0 ~ 2315 kg. Since we didn’t count dry mass in m1, it’s actually going to be a bit higher than that, but we’ll ignore that for now.

So the sample return component of our mission masses around 2315 kg. We need to get this system from lunar orbit to the lunar surface. Again, the delta-V required is 1600 m/s, so going by Tsiolkovsky, we’d need around 3656 kg of propellant to deorbit and touch down. Again, we didn’t count dry mass (engines, tanks) in that equation, so the real value would be a bit higher than that. This also doesn’t account for the equipment to scrape material off the surface and into the sample container.

So the sample return component and the descent stage component of our mission combine to be around 5971 kg. We need to get these components from low Earth orbit (LEO) to lunar orbit, and the required delta-V for that is 3900 m/s. Crunching numbers again, that requires roughly 11143 kg of propellant, again not counting dry mass.

So the total mass we need to launch from the Earth’s surface to LEO is, very conservatively, around 17115 kg; accounting for dry mass, it’s easily over 20000 kg and probably closer to 25000 kg.

That requires a heavy lifter – Saturn 1B or equivalent. These aren’t small rockets and can’t be launched from just anywhere.

Then there’s also the issue with launching at the right inclination for a trans-lunar injection, which further limits available launch sites (unless you do an orbital plane change, which takes a boatload more propellant, meaning an even bigger booster up front).

If we assume that 20 launches were supar-sekrit sample return missions, then we can cut the payload requirements in half, which brings us down to the 8500 kg range, which is still heavy but would have been within the capability of the Titan IIIC or similar launchers.

If 40 of those launches were devoted to sample returns, then we could potentially get the launch mass down into the range of the old Titan II variants.

I’ll bet real money those were all spy sat launches, though.