**TI-84 Plus: Greenwich Mean Sidereal Time Estimate**

**Introduction**

The program GMST calculates and estimates the Greenwich Mean Sidereal Time for any dates between January 1, 1900 and December 31, 2099.

For any date between 1900 and 2099, the date number is calculated as:

number of days since January 1 + (year – 1900) * 365 + int((1900 – year)/4) + 0.5 + hour/24

Please keep in mind, the formula in this program is from 1978 (see source).

For the hour, a 2400 hour clock format is used. For example, 1 AM = 1, 1 PM = 13.

This program does not take the location of the observer into account.

**TI-84 Plus Program: GMST**

“2019-03-08 EWS”

Disp “1900-2099”

Input “MONTH: “,M

Input “DAY: “,D

Input “YEAR: “,Y

Input “HOUR: “,H

If fPart(Y/4)=0 and Y≠1900

Then

1→L

Else

0→L

End

If M≥3

Then

int(30.6*M+1.6)+D-35+L→T

Else

int(30.6*M+368.8)+D-400→T

End

T+(Y-1900)*365+iPart((Y-1900)/4)+.5+H/4Z

Z/36525→Z

6°38’45.836″+2400.051262*Z+0°0’0.0929″*Z²→E

24*fPart(E/24)→E

Disp “GMST: “,E>DMS

**Example:**

Example 1:

January 1, 1978, Midnight (Hour = 0): 6°41’9.836″

Example 2:

March 13, 2011, 7:00 PM (H = 19): 11°23’54.646″

**Source:**

Jones, Aubrey __Mathematical Astronomy With a Pocket Calculator__ Halsted Press: John Wiley & Sons, New York. 1978. ISBN 0 470 26552 3

Eddie

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