Differences

This shows you the differences between two versions of the page.

--- train:lectures:siderealtime [2024/03/18 13:46] – Roy Prouty
+++ train:lectures:siderealtime [2024/03/18 16:10] (current) – Roy Prouty
@@ Line 8: / Line 8: @@
 \\
 \\
-That $~1^\circ$ extra (did you catch why $~1^\circ$?) amounts to 4 minutes of extra rotation. It is on this 4 extra minutes of rotation that we base our 24h clock. So the Sidereal Day is 4 minutes shorted than the Solar Day (23h 56m).
+That $~1^\circ$ extra (did you catch why $~1^\circ$?) amounts to 4 minutes of extra rotation. It is on this 4 extra minutes of rotation that we base our 24h clock. So the Sidereal Day is 4 minutes shorted than the Solar Day (23h 56m). We still use the 24 hour clock, so we must account for this discrepancy.
 \\
 \\
-Isn't that fun!?
 ==== Sidereal Rate ====
-The rate at which objects embedded in the Celestial Sphere move through our sky
+Since RA($\alpha$) is divided into $24^h$, one might assume that stars travel through our LHCS sphere in $360/24 = 15^\circ/hr$ or (equivalently) $15''/s$ along the CEq. However, the $24^h$ of RA is not quite right. It should be $23^h56^m$ for the Sidereal Day. This comes out to $23*3600 + 56*60 = 86160s$. So our earlier estimate of $15''/s$ is off by a factor of $(24*3600)/86160$.
+\\
+\\
+Accounting for this discrepancy, we find that the rate at which objects move through our LHCS along the CEq is $15*(86400/86160) = 15.0417 ''/s$.
+===COS(d)===
+Since DEC($\delta$) is measured from the CEq, we find that lines of constant DEC trace out concentric circles on the CNP and CSP. The radius of these circles of constant DEC decrease with $\cos{\delta}$. So at $\delta=\pm 90^\circ$ (at either CNP or CSP) the circle of constant DEC is a point and at $\delta=0^\circ$ (along the CEq), the circumference of the circle of constant DEC is maximized. In the same way, the rate of motion along these circles of constant DEC also decreases off of the Celestial Equator with the $\cos{\delta}$.
+===Challenge===
+The next time you are participating in an Observing Session, calculate how long it will take for a star (not near the CNP) to move from one side of the frame to the other side.
+----
+Written by Roy Prouty 20240318\\
+Reviewed by