Earth's tilt.

[kags]

The earth is tilted at an angle of 23.5 degrees. At the summer solstice, in the UK, we will be nearer the sun than at the winter solstice. Does anyone know by how many miles exactly? My geometry is not up to this. (And before someone tells me, I know that the increase in temperature in the summer is to do with the angle of the sun's rays not the relatively tiny reduction in distance - just curious as to what that reduction is).  

[kempie]

I don't see the need to calculate this too accurately so I shall use approximate figures as I see fit;

Radius of Earth ~ 3960 miles
Point in UK to measure (Birmingham) ~ 53.5�N
Difference in distance from Sun = 3960 x (cos 30� - cos 77�) = 2538 miles

The greatest difference would be seen in North Scotland so if we pick 58.5�N
Distance = 3960 x (cos 35� - cos 82�) = 2693 miles

And for Cornwall ~ 50�N we have 3960 x (cos 26.5� - cos 73.5�) = 2419 miles

[brachiopod]

The Earth is at aphelion during July, which means it is at the point in it's orbit furthest away from the sun, a distance of around 95.5 million miles. Perihelion, the point in the Earth's orbit when it is closest to the sun, occurs during January (distance = 91.4 million miles).

As you can see, the Earth is around 3 million miles closer during the Winter solstice than the Summer solstice.

Thus, the extra few hundred miles the UK is closer to the sun at noon on the solstice due to the tilt of the Earth, is pretty insignificant.

Assuming the latitude of the UK to be 54� thus the 'apparent' latitude at the Summer solstice (with respect to the ecliptic) is 54 - 23� = 20��, and the radius of the Earth is 3959 miles, then the actual distance the UK is closer to the sun due to the tilt of the Earth is given by;

{Cos 20�� x 3959} - {Cos 54� x 3959} miles

I now realise I haven't got my calculator in the room with me, and risk waking my son if I go and get it. Anyone care to do the calculations? (I think that should be the correct formula)

[brachiopod]

Sorry, kempi cross-posting!

*mutter still looking for bloody calculator*

Are my calculations wrong then?

[kempie]

brachi - Did you factor in the greatest distance being during the Winter Solstice (i.e. 54� + 23.5�)?

[brachiopod]

No, I was basing my answer on the difference between a non-tilted Earth and a tilted Earth at summer solstice.

I figured that, even if we assumed that the Earth's orbit is totally symmetrical...... arrr.

See what you mean now;

Apparent latitude (with respect to ecliptic) at S.S. = 54-23�� = 30��
and App Lat (w.r.t. ecliptic) at W.S. = 54 + 23�� = 77��

Right, I've got you now. (I mean, I see where you get your figures from) Cheers !!

*It would also help if I could subtract 23.5 from 54 !!! *

[kags]

Fantastic, you clever people! Thank you.

[Loosehead]

The distance to idividual points is irelevant as the whole planet rotates daily so UK may be closer in the day but it's further awya at night!!? The perihelion and aphelion point made by Brachiopod is more relevant to the distance but as you say the heat is about ray concentration not distance.

[brachiopod]

Re; Planet's rotation.

That's why I qualified it as 'at noon'

[Gef]

The Earth's orbit around the Sun is elliptical but also symmertrical. The Earth is the same distance form the Sun on any two dates which are six months apart. Therefore the Earth is the same distance from the Sun on both solstices.

[bernardo]

Gef is correct in saying that "The Earth's orbit around the Sun is elliptical but also symmetrical" but not that "The Earth is the same distance form the Sun on any two dates which are six months apart" and therefore is also not correct in saying "Therefore the Earth is the same distance from the Sun on both solstices".

The Earth is actually closest to the Sun (91.5 million miles) on 5th January and furthest (94.5 million miles) in early July.  Therefore the correct answer to the question as asked is that at the Summer solstice (late June) the Earth is actually about 3 million miles further away from the Sun than at the winter solstice.

However, the questionner seems to be referring to the difference caused by the angle of the Earth.  Therefore the answer given above by kempie is correct, but only if we pretend that the Earth's orbit around the Sun is exactly circular (i.e. a constant 93 million miles).

Incidentally, Gef would have been correct in saying "The Earth is the same distance form the Sun on any two dates which are six months apart" only if the Sun were at the centre of the eclipse (which it isn't) rather than at its focus (which it is).

[bernardo]

P.S. This means that Gef would have been correct in saying "The Earth is the same distance form the Sun on any two dates which are equally distant from the perihelion (5th January)".  e.g. the Earth is the same distance from the Sun on 5th March as on 5th November, or the same distance on 1st January and 9th January, etc. [all dates are approximate]

[Gef]

Thanks bernardo for clearing that up. Yes, I had forgotten that the Sun is not at the centre of the ellipse.