Co-Authors: Juliette Becker and Tommy Heavey

This is a write-up of question #1 on worksheet #2.

Before getting started on the actual question, I'm going to quickly go over the basic idea behind sidereal time. As the Earth rotates around the sun, it actually rotates about 361 degrees for every earth-day. A sidereal day uses a very distant star as reference. In this case, the Earth's orbit around the sun is considered negligible. In a sidereal day, the Earth rotates 360 degrees. Setting up a proportional relationship:

we find that the sidereal-day differs from the earth-day by 4 minutes (or 10 seconds/ hour). In other words, 24 hours in earth time will read 24 hours and 4 minutes in LST (Local Sidereal Time).

Given that LST = 0:00 at noon on the Vernal Equinox:

- (a) The LST at midnight on the Vernal Equinox will be 0:00 + :02 = 0:02
- (b) The LST 24 hours later will be 0:02 + 12:00 + 0:04 = 12:06
- (c) The LST right now (October 09, 3:00 pm = 15:00 army time): The Vernal Equinox was on September 3. Right now, it is 16 days and 3 hours later. So the LST is: 15:00 + (16 days)(4 minutes/day) + (3 hours)(10 seconds/hour) = 16:04:30
- (d) Tonight at midnight, the LST will be 0:00 + (16 days)(4 minutes/day) + (12 hours)(10 seconds/hour) = 1:06 (October 10)
- (e) My birthday is December 18, which is 86 days after the Vernal Equinox. The LST at 16:30 (sunset) on my birthday will be: 16:30 + (86 days)(4 minutes/day) + (4.5 hours)(10 seconds/hour) = 20:14:45

The Vernal Equinox is in the spring. September 3? However your time seems right since LST of zero occurs at midnight on the Autumnal Equinox.

ReplyDeleteDid you make the figure? If not, please be sure to attribute where it comes from.