# Homework Help: Celestial Sphere Problem

1. Jan 28, 2012

### ElijahRockers

1. The problem statement, all variables and given/known data

Ok assume we're on earth, we dont know which way is north, and we dont know our latitude.

we can track a single star. We make three measurements (m1, m2, m3) with our sextant and our compass. The first measurement at time=0:00 hours, the third at exactly 1:00 hour, and the second roughly near 30 mins. I converted the spherical coords into euclidean coords:

M1: (.70711, 0, .70711) M2: (.74267,-.1155,.65962) M3: (.75861,-.21125,.61635)

The initial part of the question is to find the length of the sidereal day. I did that by using some dot product angle magic.

The second part, which is arguably much simpler, is giving me some trouble. We are supposed to find the coords of the north star. I know we're supposed to use the cross product, but I completely forgot what im supposed to take the cross product of... I would assume it's the same vectors I used to calculate the length of the sidereal day, but I don't understand how that will give me the coords of polaris.

If someone could explain to me how the cross product of those vectors can yield the north star coords, I would greatly appreciate it, thanks!

3. The attempt at a solution

The answer (in spherical coords) is (240,60), if you assume M1 to lie on the x-axis. 240 is the longitude, and 60 is either the latitude or the colatitude. looking at the next parts of the question (which I know how to do) i am assuming the latitude is 60.