# Right ascension and sidereal time difference

I've read quite a few articles about this and watched visualisations but I still struggle to get a mental map of how this works

I understand that on March 21/22 RA 0 is on my meridian at local noon. Ignoring the sunlight, say there is a star also on that meridian at noon, in a month (April 21st) I understand that solar and sidereal time will have a difference of about two hours - does this mean the star will now be about 30 degrees west of the noon meridian?

Also I read that sidereal time means celestial objects are always appearing in the same place in the sky but the sidereal times can be different? I think my main confusion is how sidereal and RA relate.

To summarise I'm looking for more explanation regarding the two hour rule per month. Everything makes sense on the date of the vernal equinox but on say April 21st why is Sirius appearing two hours earlier? I know it's going to be obvious when it hits me :D

Thanks

Question 1: How do sidereal time and RA correlate together?

1. Think of the sky as a globe. The constellations and lines of right ascension (RA) are painted on the globe. Because of the Earth's rotation, it appears that the sky globe rotates east to west once every 23 hours 56 minutes 4 seconds.
1. The meridian is the line of RA that goes from due south to the zenith (the point overhead) to due north. The meridian splits the sky into an eastern half and a western half.
2. The sidereal time is just the RA that is on the meridian. Because of the rotation of the sky, the sidereal time increases by approximately 15 degrees (or 1 hour of RA) every hour of time.

Question 2: Why do the stars rise earlier each month (and each day!)?

1. The Sun (and Moon and planets) are not painted on the globe of the sky. They move on the globe at different speeds (depending on the distance from the Earth and Sun). The Sun moves west to east and goes through 360 degrees along the ecliptic in 1 year, or approximately 30 degrees per month.
2. Because we use the Sun to tell time, the Sun is on the meridian at local noon.
3. But one month after March 21, the Sun is at 2 hours RA (= 30 degrees east of 0 RA). Therefore, the star that is at 0 RA and was on the meridian at noon on March 21 is now 30 degrees west of the meridian at noon on April 21.

In other words, because the Sun moves west to east, at the "same time of day" the stars appear to move westward by 4 minutes per day, 32 minutes per week, approximately 120 minutes per month (2 hours per month). That's why Sirius appears 2 hours earlier each month.

Technically, the stars appear earlier because it only takes 23 hours 56 minutes for the Earth to rotate 360 degrees measured relative to the stars, but it takes 24 hours (on average) for the earth to rotate 360 degrees relative to the Sun. The 4 minute difference is due to the motion of the Earth around the Sun, or the apparent motion of the Sun on the globe of the sky.

• Thanks for this John - I think it's starting to sink in! So because the celestial sphere appears to move east-west and the sun appears to move west-east (over the year) this "gap" between local noon and the celestial sphere / RA on the meridian each day keeps increasing four mins or so as Earth makes the extra degree turn to point at the same place in the sky? So in a month my meridian at local noon is approx 2 RA meaning Sirius (in solar time) rises two hours earlier? Appreciate your time :) May 7, 2020 at 13:50
• @MichaelHarper Yes, that is correct. May 7, 2020 at 13:56