4.4 Sidereal Time
51
For example, we wish to know at what time the star Vega crossed the meridian from the viewpoint of an observer in Boston on 7 July 2015. Boston is at
43
◦ 21
29
N 71
◦ 3
49
W and Vega is located at 18
h 36
m 56
s
+38
◦ 47
01
. Hence,
the transit occurred at approximately 18:37 LST. We need to find the GST for that
LST, which we do as follows:
1. Convert the LST to decimal hours. So 18
h 36
m 56
s becomes 18.61555556.
2. Convert the longitude into decimal degrees. So 71
◦ 3
49
W becomes 71.06361111
◦ W.
3. Covert the longitude to hours by dividing by 15, to give 4.737574074.
4. If the location is west of Greenwich, add the longitude to the LST; if east, subtract
it. If the result exceeds 24, subtract 24; if it is negative, add 24. Hence our decimal
GST is 23.35312963, or 23
h 21
m 11
s .
Now that we know the GST of the transit, we need to find UT for 23
h 21
m 11
s ,
GST on 7 of July 2015. For this, we need the Julian date at 0
h , which is found as
follows:
1. Denote the year, month, and day by y, m, and d respectively. Hence, 7 July 2015
becomes y = 2015, m = 7, d = 7.
2. If m ≤ 2, then subtract 1 from y and add 12 to m.
3. If the date is greater than 14 October 1582, find A = INT (y/100) and B = 2 +
A + INT (A/4). Hence A = 20 and B = −13. If the date is earlier than 15 October
1582, then B = 0.
4. If y < 0, then C = INT (365.25 × y) − 0.75). Otherwise, C = INT (365.25 × y).
Hence C = 735978.
5. D = INT (30.6001 × (m + 1)). So D = 244.
6. The Julian date is then JD = B + C + D + d + 1,720,994.5, or for 7 July 2015,
2,457,210.5.
We can now find the UT for the GST we found above.
1. Calculate S = JD− 2,451,545.0. S = 5665.5.
2. Calculate T = S/36,525.0. T = 0.155112936.
3. Calculate T 0 = 6.697374558 + (2400.051336 × T ) + (0.000025862 × T
2
). T 0 =
378.9763853.
4. Reduce T 0 to the range 0–24 using T 0 = T 0 − INT (T 0 /24) × 24, T 0 = 18.97638528.
5. Convert GST to decimal, which we already have: 23.35312963.
6. Subtract T 0 from the decimal GST, adding or subtracting 24 as appropriate, which
gives 4.376744348.
7. Multiplying by 0.9972695663 gives the decimal UT, i.e., 4.364793938, or 4
h 21
m
53
s UT.
Boston’s local time is UTC-5, so the local UT is 23
h 21
m 53
s . As it turns out, this
is the transit for the previous evening. However, we can safely assume that the transit
will be around the same time. Otherwise, we will have to perform the calculation.
51
For example, we wish to know at what time the star Vega crossed the meridian from the viewpoint of an observer in Boston on 7 July 2015. Boston is at
43
◦ 21
29
N 71
◦ 3
49
W and Vega is located at 18
h 36
m 56
s
+38
◦ 47
01
. Hence,
the transit occurred at approximately 18:37 LST. We need to find the GST for that
LST, which we do as follows:
1. Convert the LST to decimal hours. So 18
h 36
m 56
s becomes 18.61555556.
2. Convert the longitude into decimal degrees. So 71
◦ 3
49
W becomes 71.06361111
◦ W.
3. Covert the longitude to hours by dividing by 15, to give 4.737574074.
4. If the location is west of Greenwich, add the longitude to the LST; if east, subtract
it. If the result exceeds 24, subtract 24; if it is negative, add 24. Hence our decimal
GST is 23.35312963, or 23
h 21
m 11
s .
Now that we know the GST of the transit, we need to find UT for 23
h 21
m 11
s ,
GST on 7 of July 2015. For this, we need the Julian date at 0
h , which is found as
follows:
1. Denote the year, month, and day by y, m, and d respectively. Hence, 7 July 2015
becomes y = 2015, m = 7, d = 7.
2. If m ≤ 2, then subtract 1 from y and add 12 to m.
3. If the date is greater than 14 October 1582, find A = INT (y/100) and B = 2 +
A + INT (A/4). Hence A = 20 and B = −13. If the date is earlier than 15 October
1582, then B = 0.
4. If y < 0, then C = INT (365.25 × y) − 0.75). Otherwise, C = INT (365.25 × y).
Hence C = 735978.
5. D = INT (30.6001 × (m + 1)). So D = 244.
6. The Julian date is then JD = B + C + D + d + 1,720,994.5, or for 7 July 2015,
2,457,210.5.
We can now find the UT for the GST we found above.
1. Calculate S = JD− 2,451,545.0. S = 5665.5.
2. Calculate T = S/36,525.0. T = 0.155112936.
3. Calculate T 0 = 6.697374558 + (2400.051336 × T ) + (0.000025862 × T
2
). T 0 =
378.9763853.
4. Reduce T 0 to the range 0–24 using T 0 = T 0 − INT (T 0 /24) × 24, T 0 = 18.97638528.
5. Convert GST to decimal, which we already have: 23.35312963.
6. Subtract T 0 from the decimal GST, adding or subtracting 24 as appropriate, which
gives 4.376744348.
7. Multiplying by 0.9972695663 gives the decimal UT, i.e., 4.364793938, or 4
h 21
m
53
s UT.
Boston’s local time is UTC-5, so the local UT is 23
h 21
m 53
s . As it turns out, this
is the transit for the previous evening. However, we can safely assume that the transit
will be around the same time. Otherwise, we will have to perform the calculation.