Why can鈥檛 one of our space telescopes, capable of seeing galaxies many light years away, be pointed at the site of the moon landings where one can assume there are some remnants from the visits. Would this definitively prove to any sceptics that humans landed on the moon?
鈥� The resolving power of a telescope 鈥� the size of the smallest object it can see at a given distance 鈥� is inversely proportional to the diameter of its lens. In other words, to see something small a long way off you need a very big telescope.
Apollo 11鈥檚 Eagle lunar module measures about 4.3 metres across, and to see it from Earth, when we are at our closest to the moon, would require a telescope with an angular resolution of 670 billionths of a degree. If we take the wavelength of the reflected light from the moon as being 550 nanometres, the middle of the visible range, then to see the lunar module would require a telescope with a diameter of nearly 60 metres. The largest telescope now in existence, the on the Spanish island of La Palma, has a diameter of 10.4 metres.
Advertisement
鈥淭o see the lunar module on the moon would require a telescope with a diameter of nearly 60 metres鈥�
Larger telescopes would be very expensive. The cost of building the European Southern Observatory鈥檚 proposed Overwhelmingly Large Telescope, with a diameter of 60 to 100 metres, is estimated at 鈧�1.2 billion.
Alby Reid, Redhill, Surrey, UK
鈥� We can see distant galaxies but cannot see the much closer footprints left on the moon because galaxies and galaxy clusters represent a bigger target: they take up, or 鈥渟ubtend鈥�, a much larger angle in the sky. Galaxies are also bright, making them stand out against the blackness of space. Footprints are simply impressions left on the lunar surface, offering no contrast at all. We would be reduced to looking for shadows cast by the tread.
Imagine two walkers about half a metre apart. In your mind鈥檚 eye, draw lines from the focal point of your eye to the two figures. The angle between the two lines gets smaller as the figures walk away. The smallest angle at which the two figures can still be resolved is a measure of the resolving power of an optical instrument, in this case your eye. We use telescopes because they have a greater resolving power, so they can distinguish between objects that subtend a smaller angle.
With the naked eye 鈥� whose pupil has an aperture of about 2 millimetres 鈥� the two ramblers would blur into one object at a distance of about 2 kilometres, assuming perfect eyesight in which the ability to resolve two objects is limited only by diffraction. The best terrestrial optical telescope, the Gran Telescopio Canarias on La Palma, has an aperture of about 10 metres, giving it about 5000 times the resolving power of the naked eye. A telescope of this power would be able to resolve our two ramblers even if they were 10,000 kilometres away. However, the moon is 380,000 kilometres away, and at this distance the telescope has no chance of separating the walkers, let alone their footprints.
To determine the resolving power of a telescope we use the Raleigh criterion. This tells us that the angle subtended by the smallest object an optical telescope can detect is roughly the wavelength of visible light divided by the aperture of the telescope. Multiply that by the distance to the object and we get the minimum size that can be resolved.
Taking visible light to have a wavelength of 555 nanometres, the aperture of our terrestrial telescope to be 10 metres and the moon to be 380,000 kilometres away, the smallest object that can be resolved on the moon would be about 20 metres across, assuming no atmospheric aberration. The ability to resolve footprints would require a telescope with an aperture of about 20 kilometres.
If the Hubble Space Telescope were brought to within 40 kilometres of the lunar surface it could achieve a resolution of 1 centimetre and make out footprints. Lunar-orbiting telescopes have come this close but their optics are not as good. Another option is to use an array of terrestrial telescopes to simulate a large effective aperture.
In any case I suspect that there are more interesting things to study, given that the sceptics would not be convinced anyway.
Mike Follows, Willenhall, West Midlands, UK
鈥� On () you can see the trail of footprints left on the moon by the Apollo 14 astronauts, photographed from the Lunar Reconnaissance Orbiter between 11 and 15 July 2009.
Bill Watson, Department of Mathematics and Computer Science, St John鈥檚 University, Jamaica, New York, US
鈥� If the sceptics who doubt the moon landing don鈥檛 believe the photos taken on the moon by the people who were standing there, why on earth (no pun intended) would they believe pictures beamed down from a telescope operated by the very organisation they suspect of lying to them?
Stephen Gisselbrecht, Boston, Massachusetts, US