ÐÓ°ÉÔ­´´

Distant hills

Question: I once read that if you stand on the cliffs at Dover in England and look along a particular compass bearing, there will be nothing higher than the cliffs you’re standing on between yourself and the Urals. Is this true, and what would be the relevant compass bearing?

Answer: This applies to many east-facing hill slopes in Britain that are more than 200 metres above sea level, and to some lower places as well.

The compass bearings that you need are found between due east and 10° north of east.

Draw a line due east from John O’Groats in the far north of Scotland and it just clips the southern edge of the high Norwegian mountains, and continues to the Urals (A). Draw another line a few degrees north of due east from Land’s End in the far south and this will pass just north of the Harz Mountains, near Hanover in Germany, and continue to the Urals (C). Between these two bearings, the ground is no higher than the Russian Uplands, just west of Moscow, which reach barely over 200 metres above sea level.

Britain’s topography tends to become higher the further west and north you go. The Chilterns are higher than Essex, the Cotswolds are higher still, and the Welsh mountains even higher. The Pennines slope gently upwards on their eastern flank, and the lowest parts of northern Scotland are in the east.

If you choose your vantage point and bearing carefully you may get away with a height less than 200 metres, which is about the elevation of the North Downs near Dover. But stand somewhere higher and you could achieve much more. A line of latitude due east from the Brecon Beacons, nearly 900 metres high, passes well above the southern end of the Urals and continues over Kazakhstan before meeting the mountains south of Novosibirsk (B).

Hillary Shaw

Department of Geography

University of Leeds

Answer: The idea that you can see the Urals from the cliffs of Dover is not really true. The curvature of the Earth means that from a height of about 100 metres, you can only see objects at sea level to a distance of about 30 kilometres, which is roughly as far as France if you are on the cliffs at Dover.

However, if the Earth were flat, all sorts of lines of sight would be possible. From Dover you would be able to see Mount Everest and other very high peaks too. Looking approximately east you could see the Urals, and looking roughly north from Cambridge you could see through the Bering Strait and over the Pacific as far as the Ross Ice Shelf in Antarctica, and possibly the South Pole.

C. Hereward

Cambridge

Answer: An observer on the cliffs of Dover at a height of, say, 200 metres can see 50 kilometres to the horizon. This tangent to the Earth is then uninterrupted by any objects except perhaps the Moon, planets and stars.

The Urals are about 60° east of Dover, so this line of sight would pass over them at an altitude of 3200 kilometres.

Jeff Barnes

Harrow, Middlesex

Moonshift

Question: I’ve heard that the Moon is moving away from the Earth by about 4 centimetres every year. What mechanism leads to this shift and how is such a tiny amount calculated?

Answer: The Earth and Moon exert tidal forces on each other. The Moon’s tidal influence raises the ocean tides on Earth, while the Earth causes body tides on the Moon-effectively stretching and squeezing it. This tidal activity dissipates enormous amounts of the Earth’s rotational energy.

Because the Earth rotates faster than the Moon goes round it, the tidal bulges of the oceans don’t point exactly along the Earth-Moon line but are dragged slightly ahead. The gravity from these leading and trailing bulges tugs the Moon forward and transfers angular momentum from the Earth’s rotation to the Moon’s orbit, increasing the total energy of the Moon.

The tidal friction between the oceans and the Earth’s surface causes the Earth’s rotation to slow by approximately 0.002 seconds every century. However, ignoring energy lost to heat generated by the tides, the angular momentum of the Earth-Moon system must remain constant. The Earth’s angular momentum is decreasing, so the Moon’s must increase. The only way it can do this is by moving into a higher orbit around the Earth. Thus, the distance to the farthest point of the lunar orbit is increasing by about 3.8 centimetres per year.

This change is measured by a method called laser ranging. In 1969, the Apollo 11 astronauts placed a reflector array in the Sea of Tranquility on the Moon. Additional reflectors were left on later missions. ÐÓ°ÉÔ­´´s fire a laser beam through an optical telescope pointed at one of these reflectors and the beam bounces directly back towards the telescope, where sensitive filtering and amplification equipment detects the faint return signal. The time taken for the laser pulse’s round trip gives the distance between the Earth and the Moon.

Katrina McDonnell

Macquarie University

Sydney

This week’s questions

Tight squeeze: When you squeeze the end of a hosepipe to make the opening smaller, the water comes shooting out much faster. Why doesn’t this happen when you close a tap? Instead, it just slowly reduces to a dribble.

Raj Mehta

London