# Does mean solar time and sidereal time sometimes indicate the same time?

I'm trying to wrap my head around the different definitions of time. Since mean solar time depends on the Sun, and sidereal time depends on the stars, and since the position of the Sun relative to the stars changes over the course of the year, does this mean that the difference between the two times increases and decreases over the course of the year?

Once a year, mean solar time and sidereal time will be the same. Is that right?

• Since one is about 0.3% faster then the other, I assume the answer is "yes, and yes" but I'm not confident enough about that to post as an answer. – uhoh Jan 9 '20 at 11:22
• Not an answer, but I'm pretty sure sidereal time and mean solar time are identical one time per day at any given location. – user21 Jan 9 '20 at 15:36
• @barrycarter But the definition of a second is the same for both times. Only the number of seconds in a day changes. So both times can't line up once a day. – usernumber Jan 10 '20 at 8:05
• @usernumber - Regarding your last comment, "But the definition of a second is the same for both times. Only the number of seconds in a day changes." That's incorrect. A mean solar day comprises 86400 mean solar seconds, while a mean sidereal day comprises 86400 mean sidereal seconds. That means there are about 86636.555 mean sidereal seconds in a mean solar day, and about 86164.09 mean solar seconds in a mean sidereal day. – David Hammen Jan 10 '20 at 12:50
• @usernumber You are correct and my speculation was incorrect. They only catch up once a year – user21 Jan 10 '20 at 15:32

The 3m56s mean difference between solar and sidereal days is due to the Earth's orbital motion around the Sun. This adds up to 1 day per year; for every 365¼ solar days there are 366¼ sidereal days.

Sidereal time equals the right ascension of what's on the celestial meridian at that time. The Sun is on the meridian at 12:00 apparent solar time. These align at the September equinox, when the Sun is at RA 12h. Mean solar time is ~7.5 minutes behind apparent solar time on that date and aligns with sidereal time ~1.9 days earlier.

• Does mean solar time ignore the Equation of Time? I thought that's what mean meant, but I could be wrong – user21 Jan 9 '20 at 17:21
• @barrycarter The equation of time is the difference between mean and apparent solar time. – Mike G Jan 9 '20 at 17:24

the sidereal time is the time measured by the angle between the sight line of an observer and the direct ray of a fixed star to the observer, whereas the solar time is the time measured by looking at the position of the sun in the sky like you can say it's around noon when the sun is overhead... they are just different versions of the same time... like metre and mile are of length 1 mile is not equal to 1 metre... similarly sidereal and solar time are different units of the same time... it's often said that the solar day is 4 mins less than a sidereal day

• Downvote. "sidereal time is the time measured by the angle between the sight line of an observer and the direct ray of the sun to the observer". This isn't true. Sidereal time is measured by the fixed stars, not by the sun. – user21 Jan 9 '20 at 15:35
• @barrycarter but sun is also a star right?? – Harsh Sarkar Jan 9 '20 at 15:36
• I've edited my comment to say "fixed stars"-- in other words, the stars whose right ascension and declination don't change (or at least change very little) – user21 Jan 9 '20 at 15:37
• @barrycarter ok so did i... my mistake – Harsh Sarkar Jan 10 '20 at 14:13