angle between... (how do i calculate?)?

Question

I missed a lecture in class as I was out of town, how do I solve this problem. No need to give me the answer, unless your very very kind. In either case i need to know how to do it. Or at least work it in reverse...

You live at a latitude of 39 degrees south. What is the angle between the southern horizon and the south celestial pole?

A. 45 deg. B. 23.5 deg. C. 39 deg. D. 51 deg. E. The answer depends on the day of the year.

Thanks, you help is appreciated.

Answer 1

Both of the previous answers are wrong.

Think of it this way. If you lived exactly on the equator, you would have to look due south, exactly horizontally, to look at the south celestial pole. It would be right on your horizon.

If you go southward by 1 degree (so your latitude is 1 degree south), the pole seems to raise up 1 degree--it's now 1 degree above the horizon.

Go southward 2 degrees, and the pole is now 2 degrees above the horizon. And so on.

So in other words, the angle between the celestial pole and the horizon, is the same as your latitude.

Answer 2

I say C.

Draw a circle on a piece of paper and set of axes through the middle denoting the equator and the line between the N and S poles (make the line through the S pole extend past the circle). Now draw a line to the surface at your angle of latitude (-39 degrees) and now draw a tangent to the circle at this point that intersects the NS line you drew. This represents your horizon looking South. Now the line denoting the south celestial pole can be found by drawing a line straight down (parallel to the NS line) through the point on the surface that you are at (where the circle intersects the latitude line). Since the south celestial pole is so far away you can just draw it as a straight line rather than try to draw a line that will intersect the NS line at infinity ( or some rediculously large distance). Then you can start using some geometry to relate your latitude to the angle between the horizon and the south celestial pole.

If you let the center of the earth be E, the point on the earth where you're at be point L and the point where the horizon interescts the NS line be H, then you have a right triangle ELH (because the horizon line will be perpendicular to the latitude line). Because the equator and NS line will be perpendicular, then angle LEH will be 90-latitude. For two intersecting lines, opposite angles are equal, so angle LHE will equal the angle from the horizon to the south celestial pole (call it phi) which can be found because the sum of all interior angles in a triangle is 180 degrees...l

180 = 90 + phi + (90-latitude) = 180 + phi - latitude

therefore phi = latitude
it will equal your latitude, 39 degrees.

Answer 3

The answer does NOT depend on the day of the year.

If you're at the south pole, you're at 90 degrees latitude, and the angle of the "southern" horizon to the south celestial pole is 90 degrees. If you're at the equator, your latitude is 0 degrees, and the angle of the horizon to that of the pole is the same - so the differece is 0 degrees. So, if you're at 39 degrees latitude South, then the angle to the pole must be 51 degrees.

Answer 4

Hi. The south celestial pole is at 90 degrees.You are at 39. Subtract.