Orbiting the moon
In order to understand this we must consider how the moon differs from the earth. It is, of course, much smaller, its diameter (3490 km) being rather more than 1/4 that of the earth, and its mass, which is more important from the point of view of satellite orbits, about 1/81 that of the earth. The weight of a body on the moon’s surface is about one sixth of its weight on earth – if this puzzles the reader let him work it out, remembering that weight is the force of attraction which is proportional to the two masses multiplied together and inversely proportional to the square of the respective distances, i. e. the radii of the moon and the earth. The acceleration of gravity on the moon is also, of course, about one sixth of that on earth, i. e. just over 1.6 m/s2. But the most interesting difference – and it is the result of the smaller mass of the moon and the lesser weight of bodies near the moon – is that the velocities for moon satellites, circular velocity, escape velocity, etc., are much lower than for earth satellites; the escape velocity at the surface of the moon is only about 2.4 km/s, the circular velocity being 2.4/1.41 or 1.7 km/s. Another important point is that owing to the lack of air resistance it is possible for a satellite to circle the moon very close to its surface.
But if the prospective satellite has been fired to meet the moon, the relative speed between satellite (700 km/h) and moon (3700 km/h) will be much too great, and so, unless the body actually hits the moon, it will merely go past it and escape. Thus, on first thoughts, it would seem that a body fired from the earth cannot become a moon satellite – this is true so long as there is no propulsion in the reverse direction, in other words braking; and the moon has no atmosphere to act as a brake, so the only practical means of persuading a satellite to orbit the moon, under the influence of the moon, is to provide for a rocket to act as a brake on its speed as it gets into the moon’s sphere of influence (Fig. 13.12).
This, in fact, is how the spacecraft is put into orbit round the moon – a burst of power slows it down to the correct speed for the orbit required which, as already explained, can be much nearer the moon’s surface than orbits of the earth (Fig. 13C, overleaf).
Thus far there has been quite a number of flights, manned and otherwise, and there have also been several soft, and some not so soft, landings of craft conveying instruments designed to send messages back to earth; but the actual landing of men on the moon has not been achieved so often that it can be considered as a matter of standard procedure. In the successful attempts so far made a small part of the spacecraft, the lunar module, has been detached at that part of the orbit which, as calculated by computer, will result in a landing at the desired point on the moon’s surface. By a small burst of reverse power the lunar module is again slowed down to bring it closer to the moon, while the command module continues on its circular orbit. As the lunar module ‘falls’ onto the moon, fortunately not so fast as it would onto the earth, but quite fast enough to be uncomfortable, a final reverse rocket thrust is fired to enable the module to land gently on the surface – owing to the lack of air no parachutes, or any kind of air brake, are of avail in controlling the fall (Fig. 13D, overleaf).