How does the angle of the Sun compare to the arc angle of the Moon? And how does this affect eclipses?

Question

The Sun is 1.5 x 10 to the 8th km away from Earth and has a diameter of 1.4 x 10 to the 6 th km. How large is the angle in the sky? Calculations?

Answer 1

By a stroke of cosmic luck, the Sun and Moon appear to be the same size in the sky, which is 0.5 degrees.
The Sun, while 400 times further away, is also 400 times larger than the moon appears.
This is the reason that we are lucky enough to sometimes experience total eclipses.

Answer 2

That's basic trigonometry. Why can you not do that yourself?

[Edited to add]

All right, I was having a bad day when I put up my first answer. Apologies. Here's the trig for you. Construct it like a right-angled triangle. You are the observer at one corner. The diameter of the sun forms the edge opposite you, and the line connecting your observation point to one edge of the Sun can be considered the hypotenuse of the triangle. The angle subtended by the sun is therefore the inverse sine of the opposite edge over the hypotenuse, according to standard trigonometry.

i.e. sin^-1 (1.4x10^6/1.5x10^8)

= sin^-1 0.00933333333333

=0.535 degrees.

(this would be so much easier if you could put diagrams in!)

The Moon is about 3500km in diameter, and 400,000km away, so doing the same calculation gives an angle of:

sin^-1 (3500/400,000) = 0.501 degrees

These angular diameters vary because neither the Earth's orbit nor the Moon's are precisely circular, but you can see that both objects appear to subtend roughly the same angle in the sky. What this means is that it is possible for the Moon to pass in front of the Sun and cover it entirely, but only just, which means solar eclipses are only visible from a small area. For anyone outside that area the alignment is not exact and so some of the Sun always remains uncovered. The variation in size also means we occasionally get annular eclipses, in which the Moon actually appears slightly smaller than the Sun and leaves a ring of the Sun still visible around it during the eclipse.

And yes, I'd love to see more intellectual questions on here, instead of the tripe about the Moon landings being faked and the REALLY obvious and basic homework questions which seems to crop up every single day.

Answer 3

yeah....NOT.
I consider myself a fairly intelligent individual but I have not as yet entered the informational realm of astronomical angles and arc angles. I would however, love to know the answer to this one.
It would be exciting to have a few more intellectual questions here on yahoo answers, I think.
I will be checking back to find this answer. I hope someone smart enough to answer it happens upon it.
To provide an exact calculation may take more than the info provided because of the of the nature of the rotation of the Earth. The affect on an eclipse may depend on the date and time of the actual eclipse.???? The Earth, in relation to the moon is in an infinite number of angles, let alone directions of sway on its axis, at the time and date of any given eclipse.