You really haven't a clue about this sort of thing have you? And you pretend that your famous website has all the answers - what a joke!
Topic is my Challenge about visiting the Moon + return Earth. Let's look at the latter.
I couldn't care less about you stupid unwinnable challenge! NASA used dozens of experts with data that I don't have.
Some, such as ephemeris data could easily be found and the rest could be dug up but the calculations of precisely where the Earth and Moon are and their velocities is outside my capabilities. Plenty of people would know and most competent astronomers could handle it and have the appropriate applications.
Nobody could prove it unless it was flown and YOU know that, so YOU will always wriggle out of paying anyway so toss you silly challenge in the bin!
You are in Moon orbit and want to get back to Earth. So you fire your rocket engine and enter a new orbit around Earth, i.e. your new orbit will arrive almost parallel with Earth ground at top of Earth atmosphere a few days later at great speed. Your last fuel is used for this de-orbiting Moon to get into orbit Earth.
Only an idiot like you would use your last fuel to de-orbit from Lunar Orbit. You will need some for mid-course corrections.
So just explain it in detail! When, where, in what direction and duration and with what thrust in Moon orbit do you fire your rocket engine, so you will arrive almost horizontally safely at the top of atmosphere on Earth a few days later in a new orbit around Earth ... and how much fuel is used?
But if you "arrive almost horizontally safely at the top of the atmosphere on Earth" at, say 200 km or less, you will re-enter in a short time, like it or not - so you plan for a suitable altitude and enter the re-entry phase.
I'm not going to waste time with the burns needed for the actual trajectory flown. Just look up NASA records and find out every last detail.
But a simple case is for a standard transfer orbit at the Lunar orbital radius back to one at the point for atmospheric re-entry.
A satellite in orbit at 200 km has a lifetime, dependent on shape, of only about one day and at 180 km it will re-enter in less than one orbit.
As for "how much fuel is used" - enough for a deltaV of only 826.5 m/s for the bare CM+SM, far less than needed for the insertion into the transfer orbit to get to the moon.
So, just as an example, choose a transfer orbit to change the capsule's (and service module) orbit from 384,400 km (approx) to 180 km.
It seems due to Earth gravity you will go faster all the time and your direction will also change all the time. How do you steer?
And then you arrive at the top of the atmosphere at > 11 000 m/s speed and dip into it
Why do you say "It seems . . . "? Do the sums (or use an online orbital app), even the simpler sums and get a better idea than just saying "It seems . . . "!
In orbit at 384.400 km, for example, the velocity of the CM+SM is about 1010 m/s.
Apply a de-orbit reverse thrust with deltaV = 826.5 m/s to bring the tangential velocity down to 183.50 m/s.
After about 122 hours and 24 minutes, with a bit of luck and a few mid-course corrections, the CM-SM should be down to 180 km at a bit under 10,934 m/s.
The SM would have been discarded no more major mid-course corrections were needed.
As for steering attitude control was via:
the CM had 12 Reaction Control Thrusters each with 410 N thrust and a total impulse of 257 kNs, for attitude control after discarding the SM
and the SM had 16 Reaction Control Thrusters each with 445 N thrust and a total impulse of 3,517 kNs.
Near the end, after detailed instructions from the command centre, use the RCS to orient the CM and jettison the SM just before re-entry.
At this point trust that the CM's Inertial Control System keeps the CM at the correct orientation by altering CofG and using the RCS - don't forget to cross fingers
!
and ... 10-15 minutes later your speed is >100 m/s and you release a parachute. You really have to explain what happens during these 10-15 minutes.
Don't be lazy - go and read it for yourself!
How do you ensure you will arrive at ground zero landing zone in calm water and sunny weather and not hit a mountain on an island before that.
You see - if you start your re-entry dip into the atmosphere 10 seconds late you will miss ground zero landing zone by 110 000 m! Etc, etc.
- You trust that those who designed the system got their sums right but there were numerous similar re-entries but uncrewed for test and with crews from the Mercury, Gemini and earlier Apollo test flights!
- The CM's Inertial Control System, which would have been carefully aligned before loss of signal, can control the pitch of the CM and hence the velocity and rate of descent.
Don't forget that NASA used an aerodynamic re-entry, unlike the Russian near ballistic re-entry. The CM was a lousy glider with a lift to drag ration of only 0.3 but the rate of descent could be controlled in real-time.
Yes, my famous web site does not have the answers. It is one reason for the Challenge. Tell me.
Yes, we know that the reason for your ridiculous
Challenge is to con people into visiting you useless website that "does not have any answers".
It might be OK on maritime safety, I couldn't judge that, but it's a hopeless mishmash on disinformation on anything to do with space!