Astronomy question - Sidereal time calculation

In summary, a Sidereal day is 4 minutes shorter than a solar day. The December solstice is when the RA of the sun is at its maximum. At that time, the mean sidereal time at Greenwich is 20h 45m.
  • #1
daleklama
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Homework Statement



(a) Calculate sidereal time at 11am on December 8th of any year.
(b) Calculate the Greenwich Sidereal Time when the local sidereal time on longitude 20 degrees (West) is 20h 45m.

Homework Equations



I know from my notes that a Sidereal day is 4 minutes shorter than a solar day, so it's 23h 56 m.
I don't know if it's relevant but I know that Julian Day is the number of days since noon at Greenwich on 1st Jan 4713 BC.
At the December Solstice, the RA of the sun is 18h 00m.


The Attempt at a Solution



(a) At the December solstice, the RA of the sun is 18h 00m.
Rate of change per day at the same time is 4 minutes.

I don't understand my astronomy notes at ALL, so I'm very very shaky on my understanding of these concepts.

Thank you :)
 
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  • #2
Part (a) is rather open-ended and vague since LST (local sidereal time) depends upon the location (longitude) on the planet and hasn't been specified. Also, they don't specify what time scale the 11am is given in; Is it UT, Local Time, or something else?

You can start by deciding on the answers to those loose ends.

Your thought about the Julian Day number (JD) has merit; You should be able to locate an algorithm that uses the JD corresponding to the given date at 0h UT to find the mean sidereal time at Greenwich at 0h UT for that date (GMST). That will serve as a starting point for finding the GMST for the given instant of time, and then the LST.
 
  • #3
Yeah, I thought myself the question was missing something.
This is an Irish exam paper given in Ireland so I guess it assumes an Irish location, which is 53 degrees North and 7 degrees West.

As for the 11am time scale, I can't be sure, but I think it's LCT.

I'm still not sure where to go next though... I don't really understand the Julian Number.

In my notes it gives an example of a Julian Day calculation but it doesn't show the steps and it leaves me completely stumped.
It says '6am 17th February 1985 ≡ JD 2446113.75'

Thanks for reply :)
 
  • #4
You can probably find annotated Julian Day algorithms by web search. But what you REALLY want to get your hands on is a copy of the the book "Astronomical Algorithms" by Jean Meeus. See if your library carries it.
 
  • #5




To calculate the sidereal time at 11am on December 8th of any year, we need to take into account the Earth's rotation and the position of the sun in relation to the stars. The sidereal day is 4 minutes shorter than a solar day because the Earth has completed one full rotation on its axis, but it has also moved slightly in its orbit around the sun. This means that after one sidereal day, the Earth is not yet facing the same stars as it was at the start of the day, but it has completed one full rotation on its axis.

To calculate the sidereal time at 11am on December 8th, we can use the formula: Sidereal Time = Local Mean Time + (Rate of Change per Day * Number of Days Since December Solstice). As mentioned in the homework statement, the December Solstice has a Right Ascension (RA) of 18h 00m. This means that at 11am on December 8th, the sun's RA is 18h 00m + (4 minutes * 8 days) = 18h 32m. This is the local mean time at 11am on December 8th.

To convert this to sidereal time, we also need to take into account the Earth's rotation, which is 4 minutes shorter than a solar day. This means that at 11am on December 8th, the sidereal time is 18h 32m - 4 minutes = 18h 28m. Therefore, the sidereal time at 11am on December 8th of any year is 18h 28m.

(b) To calculate the Greenwich Sidereal Time when the local sidereal time on longitude 20 degrees (West) is 20h 45m, we can use the formula: Greenwich Sidereal Time = Local Sidereal Time + Longitude. In this case, the longitude is 20 degrees West, which is equivalent to -20 degrees. Therefore, the Greenwich Sidereal Time is 20h 45m - 20 degrees = 20h 25m. This means that at the same time when the local sidereal time on longitude 20 degrees West is 20h 45m, the Greenwich Sidereal Time is 20h 25m.

I hope this explanation helps clarify the concepts of sidereal time and how to calculate it. If you have
 

1. What is sidereal time?

Sidereal time is a system of timekeeping based on the rotation of the Earth with respect to the stars. It is the time it takes for a particular star to return to the same position in the sky, and is measured in hours, minutes, and seconds.

2. How is sidereal time calculated?

Sidereal time is calculated by taking into account the Earth's rotation and its position in relation to the stars. It is usually calculated using a formula that takes into consideration the Earth's rotation rate, its axial tilt, and its location in its orbit around the Sun.

3. Why is sidereal time important in astronomy?

Sidereal time is important in astronomy because it is used to determine the positions of stars and other celestial objects in the sky. It is also used to calculate the right ascension and declination of celestial objects, which are important coordinates in the celestial coordinate system.

4. How does sidereal time differ from solar time?

Sidereal time and solar time differ because they use different reference points. Sidereal time is based on the position of the stars, while solar time is based on the position of the Sun. This means that one sidereal day is slightly shorter than one solar day.

5. Is sidereal time the same all over the world?

No, sidereal time can vary depending on the observer's location on Earth. This is because the Earth's rotation and its position in relation to the stars changes as you move across different longitudes. This is why astronomers often use Greenwich Mean Sidereal Time (GMST) as a standard reference point for their calculations.

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