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SPECULATIVE SCIENCEHow much does the Moon weigh?

  • WELL, of course the answer is 'nothing at all', since the weight of an object is the net gravitational force acting on a body and, as with all other orbiting objects in the solar system, it is just like an astronaut circling around the Earth: weightless. Weight must be distinguished from mass, which is determined by quantity of material; in the case of the Moon it is or about 74 million million million tonnes, according to Tables of Physical and Chemical Constants , by Kaye and Laby. At the Earth's surface a mass of one kilogramme has a weight of one Newton due to gravity but, if, like the Moon, it is orbiting in space, then it has no weight at all. Incidentally, my physics master at the King's School, Grantham, where Isaac Newton was educated, often reminded us that a force of one Newton is about the weight of an apple. A very handy coincidence.

    Michael D. Rowe, Offham, Kent.

  • AS HEAD of physics at Isaac Newton's old school, I am prompted by Mr Rowe's letter to write to explain the misunderstandings he apparently has. Neither an astronaut in orbit round the Earth nor the Moon, which is also in Earth orbit, is weightless, despite the frequent misleading use of the term. As Mr Rowe rightly explains, weight is a force which arises from the gravitational attraction of two bodies and which varies as the inverse square of their distance apart. Zero force, and hence zero weight, will therefore only occur when they are infinitely far apart. The experience of the astronaut is not true weightlessness but he feels weightless because he is in free fall along with his craft. A free-fall parachutist initially experiences the same sensations, as does a high-board diver. In the case of the astronaut and the Moon, the weight force is required to keep them moving in a circle, as required by Newton's first law of motion. It is true that the newton is, conveniently, the approximate weight of an apple but the weight of a mass of 1 kg is actually about 10 N. Both Newton and Mr Rowe were at King's before my time and also before the SI unit system came into general use in schools, which perhaps explains the apparent lapse in his memory, but I would not like anyone to think that we teach the present generation of budding Newtons incorrect physics.

    J. S. Bomphrey, The King's School, Grantham, Lincs.

  • THE head of physics at Isaac Newton's old school he may be, but Mr Bomphrey is surely talking nonsense. Is he not confusing weight and gravity? Gravitational force varies as the inverse square of distance as he rightly says, but what can he mean by saying that the experience of an astronaut 'is not true weightlessness but he feels weightless'? He feels weightless because he is weightless (ignoring the minute attraction to his spacecraft). No experiment he did (short of actually looking out of the window), would enable him to tell that his spacecraft was held, by gravitational force, in orbit around the Earth. Weight is not the force of gravitational attraction, but describes how an object resists gravity. The whole point about orbital free-fall is that the object is not resisting gravity, but is continually accelerating under its influence (the acceleration causing orbital motion, of course, rather than a linear increase in velocity). To use Mr Bomphrey's established analogy, if I pick up an apple I need to apply a force of one newton to hold it up. An astronaut does not need to apply this force, so the apple is weightless. He still needs to apply a force to move it, as it does, of course, continue to have mass. Mr Bomphrey rightly praises the SI system of units which correctly distinguishes between weight and mass. In the Imperial system, with the two different quantities having the same name, there was endless scope for confusion, and for the inventing of alternative obscure units. Whether the Moon is weightless is quite a difficult, and pointless, question to answer. All parts of the Moon are not in free-fall around the Earth, because they are constrained in their orbit by the shape of the Moon. The nearer bits of Moon are moving too slowly for free-fall; the further bits too fast.

    David Gibson, Leeds.

  • THERE is something about physics that makes arguers quite insultingly dismissive of other people's opinions. Mr Bomphrey and Mr Gibson are using different definitions of the word 'weight'; both of them argue correctly from these different definitions. Mr Bomphrey is using the current textbook and physics syllabus definition of 'weight', which says: 'The force of gravity on an object is called its weight' ( GCSE Steps in Physics by Byron). He is therefore correct to suggest that weightlessness will occur only in situations where the object experiences no gravitational attraction towards other objects. Mr Gibson uses the older definition of weight as described in Ordinary Level Physics by Abbott: 'The weight of a body is the force it exerts on anything which freely supports it.' The book goes on to suggest that the body will usually exert this force due to its being attracted towards the centre of the Earth by gravity. This definition makes Mr Gibson's analysis of the situation correct - although suggesting that weight is 'how an object resists gravity' does tend to give the responsibility for weight to the object rather than to that which supports it. The difference in the two views is possibly due to the attempts made over the last 10 years to make physics accessible to a wider proportion of the school population, which has resulted in a simplification of the ideas taught and a significant decrease in the content, which has left Abbott's 'O-level' textbook as a good introduction at A-level to many topics.

    Jonathan Parkinson, Head of Physics, St Thomas More School, Blaydon, Northumberland.

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