Time & Julian Dates

Time in astronomy is more nuanced than your watch suggests. This guide explains the time systems astronomers use and how to work with them in starward.

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Why Astronomers Don't Use Regular Dates

Imagine trying to calculate the number of days between February 28, 1900 and March 1, 2000. You'd need to account for:

• Varying month lengths (28, 29, 30, 31 days)
• Leap years (but not century years... except every 400 years!)
• Calendar reforms (Gregorian vs Julian calendar)
• Time zones and daylight saving

Astronomers solved this problem by counting days from a single reference point: the Julian Date.

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The Julian Date System

What Is a Julian Date?

A Julian Date (JD) is simply the number of days (including fractions) since noon Universal Time on January 1, 4713 BCE (Julian calendar).

Why that date? It was chosen by Joseph Scaliger in 1583 as a convenient starting point before any recorded history, so all historical dates have positive JD values.

Key Reference Points

Event	Julian Date
Start of Julian Day system	0.0
January 1, 2000 at noon (J2000.0)	2,451,545.0
Today (approximately)	~2,461,043

Why Noon?

JD starts at noon because astronomers historically made observations at night. Having the day change at midnight would split a single night's observations across two dates—inconvenient! With noon as the start, a night's work all falls on the same Julian Date.

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Working with Julian Dates

Get the Current JD

starward time now

Output:

╭────────────────────────────────────────────╮
│  Current Astronomical Time                 │
├────────────────────────────────────────────┤
│  UTC:                 2026-01-03 00:15:00 │
│  Julian Date:              2461043.510417 │
│  Modified JD:                61043.010417 │
│  T (J2000):                  0.2600550411 │
│  GMST:                     07h 05m 34.60s │
╰────────────────────────────────────────────╯

Convert a Julian Date to Calendar Date

starward time convert 2460000.5

Output:

JD 2460000.500000 = 2023-02-25 00:00:00 UTC

Convert Calendar Date to Julian Date

starward time jd 2024 7 4 12 0 0

This converts July 4, 2024 at 12:00:00 UTC to JD.

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Modified Julian Date (MJD)

The standard JD has a problem: the numbers are getting large. For modern dates, JD is over 2.4 million. This can cause precision issues in some computer systems.

The Modified Julian Date solves this:

$\text{MJD} = \text{JD} - 2400000.5$

This shifts the epoch to midnight on November 17, 1858, giving smaller numbers and starting at midnight instead of noon.

System	J2000.0 Value	Epoch
JD	2,451,545.0	Jan 1, 4713 BCE noon
MJD	51,544.5	Nov 17, 1858 midnight

Converting Between JD and MJD

starward time convert 60000 --from mjd

Output:

MJD 60000.000000 = JD 2460000.500000 = 2023-02-25 00:00:00 UTC

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J2000.0 and Julian Centuries

The J2000.0 Epoch

Modern astronomy uses J2000.0 as the standard reference epoch:

• Date: January 1, 2000 at 12:00:00 TT (Terrestrial Time)
• Julian Date: 2,451,545.0

Celestial coordinates, orbital elements, and many other quantities are referenced to this epoch.

Julian Centuries (T)

Many astronomical formulas express time as Julian centuries since J2000.0:

$T = \frac{\text{JD} - 2451545.0}{36525}$

Where 36,525 is the number of days in a Julian century (365.25 × 100).

In starward, this is shown as "T (J2000)" in the time now output.

Example: T = 0.26 means we're about 0.26 centuries (26 years) past J2000.0.

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Sidereal Time

What Is Sidereal Time?

The sidereal day is the time it takes Earth to rotate once relative to the distant stars—about 23 hours, 56 minutes, and 4 seconds.

Because Earth also orbits the Sun, the solar day (noon to noon) is about 4 minutes longer than the sidereal day. Over a year, this adds up to one extra sidereal day.

Sidereal time tells you which part of the celestial sphere is currently on your meridian (the line from north to south through your zenith).

Greenwich Mean Sidereal Time (GMST)

GMST is the hour angle of the vernal equinox as seen from Greenwich. It's shown in the time now output.

Why does it matter? If an object has Right Ascension = GMST, it's currently crossing the Greenwich meridian.

Local Sidereal Time (LST)

LST adjusts GMST for your longitude:

$\text{LST} = \text{GMST} + \frac{\text{longitude}}{15}$

Where longitude is in degrees (positive east).

Example: Calculate LST for Los Angeles (longitude -118.25°):

starward time lst -- -118.25

(The -- tells the CLI that -118.25 is a value, not a flag.)

Output:

Longitude:    -118.2500° (W)
Julian Date:  2461043.510878
─────────────────────────────────────────────
GMST:         07h 06m 14.11s
LST:          23h 13m 14.11s

Interpretation: At this moment in LA, objects with RA ≈ 23h 13m are on the meridian and highest in the sky.

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The Math Behind GMST

Want to see how GMST is calculated? Use verbose mode:

starward --verbose time now

You'll see the calculation using the IAU 2006 formula:

┌─ Calculate GMST
│  T = (JD - 2451545.0) / 36525 = 0.26005504...
│
│  GMST (degrees) = 280.46061837
│                 + 360.98564736629 × D
│                 + 0.000387933 × T²
│                 − T³/38710000
│  where D = JD - 2451545.0
│
│  GMST = 280.46061837 + 342152.4... + ...
│       = 106.4583...° = 7.097h
└────────────────────────────────────────

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The Julian Date Algorithm

Converting between calendar dates and Julian Dates uses an elegant algorithm. Here's the formula for calendar → JD:

For a date Y-M-D at hour H:

$JD = 367Y - \text{INT}\left(\frac{7(Y + \text{INT}(\frac{M+9}{12}))}{4}\right) + \text{INT}\left(\frac{275M}{9}\right) + D + 1721013.5 + \frac{H}{24}$

This formula handles leap years automatically through integer division tricks.

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Common Tasks

Days Between Two Dates

Julian Dates make this trivial:

# JD of July 4, 1776
starward time jd 1776 7 4
# JD of July 4, 2026
starward time jd 2026 7 4
# Subtract the results: ~91,311 days (250 years)

What Day of the Week?

JD mod 7 gives the day of the week:

• 0 = Monday
• 1 = Tuesday
• ... and so on

The integer part of the JD at noon gives this directly.

Is a Star Visible Tonight?

If an object's Right Ascension equals your LST, it's on your meridian—highest in the sky and best positioned for observation. Objects within a few hours of your LST are well-placed for viewing.

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Python API

For programmatic access:

from starward.core.time import JulianDate, jd_now

# Current time
jd = jd_now()
print(f"JD: {jd.jd}")
print(f"MJD: {jd.mjd}")
print(f"T (J2000): {jd.t_j2000}")
print(f"GMST: {jd.gmst()} hours")

# From calendar
jd = JulianDate.from_calendar(2024, 7, 4, 12, 0, 0)

# To calendar
dt = jd.to_datetime()

# LST for a longitude
lst = jd.lst(longitude=-118.25)

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Key Formulas Reference

Quantity	Formula
MJD → JD	$JD = MJD + 2400000.5$
T (centuries)	$T = (JD - 2451545.0) / 36525$
LST	$LST = GMST + \lambda/15$

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Further Reading

• Explanatory Supplement to the Astronomical Almanac (Seidelmann, ed.)
• Meeus, J. "Astronomical Algorithms" — Chapter 7 (Julian Day)
• USNO Circular 179 — Time systems explained

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Next: Coordinate Systems — Navigate the celestial sphere