# Apollo

And while I’m on the subject of the moon, I shouldn’t forget the anniversary of the Apollo 11 moon landing. For the record, the first landing was before my lifetime, but some later ones were not. (Not that I remember them).

Loads has been said in the media already this week, so I’ll just grab one little bit of physics and leave it at that. One thing that has always staggered me about the mission is the sheer size of the Saturn V rocket. 111 m high, 10 m diameter, and a staggering 3000 tonnes, much of which would be fuel – compare that to the tidly amount of fuel a Boeing 747 carries. All to get three men to the moon and back. The surprising issue is this one – how come such a vast rocket was needed for launch from Earth, whereas the small lunar lander was quite capable of getting off the moon’s surface and into moon orbit to meet up again with the command module. The moon has less gravity than the earth, but at a quarter the diameter of the earth it’s gravitational pull on the lander is still significant – about a sixth that of earth. So how come it needs a whole lot less than a sixth of the fuel to escape?

The answer lies with Newton again. A rocket works because mass is ejected backwards at high velocity – because momentum is conserved the rest of the rocket accelerates forward. But most of the stuff that is being accelerated is not the payload, rather it’s the fuel that is needed later on in flight, which means that acceleration depends on the mass of unburned fuel. This means it becomes steadily more difficult to reach higher and higher velocities – you need exponentially more fuel for each extra km/h you want to achieve. So it takes considerably more than six times the amount of fuel to escape the earth than it does the moon.

Next question…if the lunars (the creatures that live on the moon) built a rocket to get them to earth and back, how big would that have to be?….