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Q: I am confused by the appearance of a gibbous Moon. On Monday 31 January, I was driving eastwards at dawn towards the rising Sun. Through the side window of my car – about 120 degree to the right – I could see the Moon with its fuller surface directed towards the Sun.

Well, not quite. The Moon was tilted a few degrees upwards and did not present its illuminated face slightly downwards or horizontally as you might expect.

I confirmed the tilt of the Moon against a nearby vertical pole, as did my wife who was sitting in the passenger seat. She dismissed my protestations with a throwaway: ‘I expect it’s an optical illusion’.

Maybe it is, but how . . . and why?

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A: The simple answer is that, in imagining the direct line from the Moon to the Sun, the questioner, Mr Grandage, needed to do his geometry on the surface of the celestial sphere, not on a flat plane. The shortest air route from London to New York is a great circle curving north over Greenland, not a straight line on a Mercator projection map. In the same way, the ‘line’ joining the Moon to the Sun is an arc of a great circle through the sky (see top diagrams).

The axis of the Moon’s phase (that is, the line joining the tips of the incomplete moon) is at right angles to the plane in space which is defined by the Sun, the Moon and the observer. The tilt of this plane for any observer on Earth depends on his or her latitude.

If Mr Grandage was near his home in Cambridge (51 degree N) when he made his observation on 31 January 1994, the Sun rose at 7.41 am at an azimuth of 117 degree.

At that time, the gibbous Moon (18 days old) was at an altitude of 10 degree and azimuth 248 degree. (Sun and Moon were separated by about 130 degree so Mr Grandage’s estimate of 120 degree was close.) The Moon would have appeared to be tilted ‘upwards’ by about 22 degree. Had Mr Grandage been at a more southerly latitude and able to see the Moon’s phase in an already daylight sky, the effect would have been even more striking.

Jacqueline Mitton Royal Astronomical Society, London

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A: John Grandage’s upturned Moon was no illusion. Since the Sun is so far away, it can be regarded as being at infinity (that is, it will appear at pretty well the same point in the sky whether viewed from the Earth or the Moon).

Thus the rays of the rising Sun did not travel ‘uphill’ from the horizon to the Moon in the sky above, but along an (almost) horizontal path parallel to the east-running road along which Mr Grandage was travelling. The sunlit part of the Moon therefore was at right angles to this horizontal.

The Sun is at infinity, not just beyond the horizon as it appears to the observer from millions of miles distant. The light from the Sun therefore strikes the Moon not from the Sun’s perceived position of just below the Moon and just beyond the horizon but from a point in the far distance. From the Earth, however, the sunlit part of the moon appears to be tilted upwards.

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C. J. Collins Llandrindod Wells, Powys

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A: Because of their similarity in apparent size, observers on Earth suffer from the illusion that the Sun is not much different in distance from us than the Moon, when in fact it is nearly 400 times further away. However, light travels in a straight line (as shown in the bottom diagrams) which creates the illusion.

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B. Fisher Hitchin, Hertfordshire

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Interested readers might like to write in and explain if (and why) these explanations – one employing spherical geometry and one plane geometry – are essentially the same. And you must explain one more thing too – if the rays of light from the Sun are parallel, why is it that sunbeams penetrating a hole in the clouds spread out in the fan-shaped pattern that has so often been depicted by Turner and other painters of seascapes. Another consequence of geometry, an illusion, or something else? – Ed

Strange spuds

Q: Why do boiled potatoes taste horrible the next day? Surely, having been prepared by a method of sterilisation, they should not have ‘gone off’ so soon?

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A: Boiling potatoes results in gelatinisation of potato starch. Depending on the potato variety, cell wall rupture and some breakdown of the middle lamella occurs. Additionally, chlorogenic acid and iron in the tuber interact during cooking and then oxidise on cooling to give a dark pigment, the intensity of which increases with time. This is known as ‘after cooking blackening’.

All of these factors contribute to the texture, flavour, aroma and acceptability of the boiled potato. They can continue to develop after cooking has been completed and the potatoes left to stand.

Your correspondent has used varieties of potato where this has occurred to an unacceptable extent, whereas certain other ‘salad potato’ varieties have an excellent texture and flavour when eaten cold the following day.

Michael Storey Potato Marketing Board, Cowley, Oxford

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A: Dice horrible, day-old potatoes. Get some mayonnaise. Harvest and chop fresh chives from the garden. Mix and chill. Simply delicious!

Ian Sheldon Cambridge

This week’s questions – Baa-rmy

Why do sheep always run in a straight line in front of a car and not to the side?

Aled Wynne Jones Cambridge

This week’s questions – Heated argument:

Why is it that when I get into a bath at 39 degree C I feel totally relaxed and yet, when I enter a room at the same temperature, I feel totally stressed?

Alan Parr Corwen, Clwyd

This week’s questions – Comes in handy

Why do we have fingerprints? What beneficial purpose could they have evolved to serve?

Mary Newsham London