RE:Apparently I have no math skillsFarquar, I agree with you on many things but I have to stop you here, being a life long Apollo program buff and knowing a little bit about it, you are mistaken on so many levels regarding the Moon missions.
First of all, the speed at which the Earth and Moon orbit the Sun has no relevance at all, the only thing that matters is the distance and movement of the orbiting Moon relative to the Earth.
After the Apollo ‘Stack’ got into orbit, they were moving about 17,500 mph, this is the speed needed to reach and maintain orbit, something that Musk and Branson did not achieve, they flew straight up and back down, only becoming weightless for a few seconds as they reached the apex and started to fall back to earth. After making sure all systems were go, they fired the 3rd stage engine, leaving Earth's orbit toward the Moon and accelerated to just under 25,000 mph, the calculated speed needed to arrive at the point where the Lunar gravity and Earth gravity are equal and they can start falling toward the Moon at another calculated speed. The burn lasted a bit over 5 minutes. But - here’s the thing - as soon as the burn was finished, Earth’s gravity began to slow them. Just like throwing a rock up - it’s moving fastest as it leaves your hand, but immediately begins to slow once released, due to Earth’s gravity.
Their speed lessened almost all the way to the moon, (this is why it took 3 days) out to the point where lunar gravity and Earth’s gravity were about equal. At that point, they were moving in the neighborhood of about 2,300 mph. Another point you were mistaken about was "no brakes and no steering", when the spacecraft and rocket engine are inverted via the reaction control thrusters (steering, the Command, Service and Lunar Modules all had them) then fired, that is the braking system.
For the next several hours, they began to ‘fall’ toward the moon, ( engine first) accelerating once again. The trajectory was designed such that, if the engine failed to ignite on the back side of the Moon to achieve calcualted orbit velocity, they’d be swung around the moon, and headed back to Earth (It was called a ‘free-return’ trajectory…) and they would be moving about 4,400 mph at their closest approach to the moon. But, if the engine worked, they’d slow down, and go into lunar orbit around the Moon, which by the way has no atmosphere.
Coming home was similar: They fired the engine, leaving Lunar orbit toward the Earth, accelerating to about 4,400 mph, and they’d cross the same point where Earth’s and the Moon’s gravity were about equal, then, they’d fall all the way back to Earth - accelerating all the way… by the time they began their re-entry, they were once again moving about 25,000 mph. Steering with the reaction thrusters they set the angle of reentry and over a 6 minute time frame (not 1.98 seconds) the Earths atmoshere slowed the Command module down from 25,000 mph (never exceeding 7 G's) to a speed where the chutes coud be deployed.