Time & Longitude

Date        | Equation of Time
------------|------------------
Feb 12      | -14.2 minutes (sun 14 min "slow")
May 15      | +3.7 minutes (sun 4 min "fast")
Jul 26      | -6.5 minutes
Nov 3       | +16.4 minutes (sun 16 min "fast")

#!/usr/bin/env python3
"""
Greenwich Mean Sidereal Time Calculator
IAU 2006 Resolution B3 formula
"""

import math
from datetime import datetime, timezone

def julian_date(dt: datetime) -> float:
    """Convert datetime to Julian Date."""
    year = dt.year
    month = dt.month
    day = dt.day + (dt.hour + dt.minute/60 + dt.second/3600) / 24

    if month <= 2:
        year -= 1
        month += 12

    A = int(year / 100)
    B = 2 - A + int(A / 4)

    JD = int(365.25 * (year + 4716)) + int(30.6001 * (month + 1)) + day + B - 1524.5
    return JD

def gmst(dt: datetime) -> float:
    """
    Calculate Greenwich Mean Sidereal Time in hours.
    Uses IAU 2006 algorithm.
    """
    JD = julian_date(dt)
    D = JD - 2451545.0  # Days from J2000.0
    T = D / 36525.0     # Julian centuries from J2000.0

    # GMST in degrees (IAU 2006)
    theta = (280.46061837 +
             360.98564736629 * D +
             0.000387933 * T**2 -
             T**3 / 38710000)

    # Normalize to 0-360
    theta = theta % 360

    # Convert to hours
    return theta / 15.0

def local_sidereal_time(dt: datetime, longitude: float) -> float:
    """
    Calculate Local Sidereal Time.

    Parameters:
        dt: UTC datetime
        longitude: Observer longitude (degrees, positive East)

    Returns:
        LST in hours (0-24)
    """
    gst = gmst(dt)
    lst = gst + longitude / 15.0
    return lst % 24

# Example: Los Angeles (118.24°W) at 2026-03-26 12:00 UTC
dt = datetime(2026, 3, 26, 12, 0, 0, tzinfo=timezone.utc)
lon_la = -118.24
lst_la = local_sidereal_time(dt, lon_la)
print(f"LST at Los Angeles: {lst_la:.4f} hours = {int(lst_la)}h {int((lst_la % 1) * 60)}m")

# Julian Date from Unix timestamp
awk 'BEGIN {
    # Current JD
    ts = systime()
    jd = ts / 86400 + 2440587.5
    printf "Current JD: %.6f\n", jd
    printf "Current MJD: %.6f\n", jd - 2400000.5
}'

# Convert date to JD
date_to_jd() {
    local year=$1 month=$2 day=$3 hour=${4:-12}
    awk -v Y="$year" -v M="$month" -v D="$day" -v H="$hour" 'BEGIN {
        if (M <= 2) { Y--; M += 12 }
        A = int(Y / 100)
        B = 2 - A + int(A / 4)
        JD = int(365.25 * (Y + 4716)) + int(30.6001 * (M + 1)) + D + B - 1524.5 + H/24
        printf "%.6f\n", JD
    }'
}

# Example
date_to_jd 2026 3 26 12
# Output: 2461127.000000

GPS Message Structure:
┌────────────────────────────────────────────────┐
│ Subframe 1: GPS Week, SV Clock Correction      │
├────────────────────────────────────────────────┤
│ Subframe 2-3: Ephemeris Data                   │
├────────────────────────────────────────────────┤
│ Subframe 4-5: Almanac, UTC Parameters          │
│              (includes UTC-GPS offset)         │
└────────────────────────────────────────────────┘

Time of Week (TOW): 0 to 604799 seconds
(Seconds since start of GPS week, midnight Saturday/Sunday)

WWVB, WWV format: DUT1 encoded as double ticks
GPS Navigation Message: WN_LSF, DN, Δt_LSF

Current DUT1 (check IERS Bulletin A):
Example: DUT1 = +0.2 seconds
→ UT1 is 0.2 seconds AHEAD of UTC

Year 1900: excess LOD ≈ +4 ms
Year 2000: excess LOD ≈ +2 ms
Year 2020: excess LOD ≈ -0.5 ms (Earth speeding up!)

This is why no leap seconds added since 2017 -
Earth's rotation has accelerated slightly.

Zone    Central Meridian    Boundaries
UTC+0       0°              7.5°W to 7.5°E
UTC+1       15°E            7.5°E to 22.5°E
UTC-5       75°W            67.5°W to 82.5°W (EST)
UTC-6       90°W            82.5°W to 97.5°W (CST)
UTC-7       105°W           97.5°W to 112.5°W (MST)
UTC-8       120°W           112.5°W to 127.5°W (PST)

Longitude: 98.23°W = -98.23°

Time difference from UTC:
-98.23° ÷ 15 = -6.55 hours

This means solar noon at McAllen is ~6.55 hours after UTC noon.
Standard timezone: UTC-6 (Central Time)

You observe solar noon at 18:30 UTC.
Standard time difference = 18:30 - 12:00 = 6.5 hours

Longitude = 6.5 × 15 = 97.5°W (approximately)

Flying from Los Angeles to Tokyo:
- Depart LA: Monday 10:00 PST (UTC-8) = Monday 18:00 UTC
- Flight time: 11 hours
- Arrive: Monday 18:00 + 11h = Tuesday 05:00 UTC
- Tokyo time (UTC+9): Tuesday 14:00 JST

You "lose" a day crossing westward.

DDHHMMZ MMM YY

Where:
DD    = Day of month (01-31)
HH    = Hours (00-23)
MM    = Minutes (00-59)
Z     = Time zone letter (Zulu if UTC)
MMM   = Month abbreviation (JAN, FEB, MAR, etc.)
YY    = Last two digits of year

# Generate current DTG
dtg() {
    TZ=UTC date +"%d%H%MZ %^b %y"
}

# Parse DTG to Unix timestamp
parse_dtg() {
    local dtg="$1"  # e.g., "261430Z MAR 26"
    local day="${dtg:0:2}"
    local hour="${dtg:2:2}"
    local min="${dtg:4:2}"
    local tz="${dtg:6:1}"
    local mon="${dtg:8:3}"
    local year="20${dtg:12:2}"

    date -d "${year}-${mon}-${day} ${hour}:${min}" +%s
}

# Example
echo "Current DTG: $(dtg)"
# Output: 261430Z MAR 26

FM: COMSIXTHFLT
TO: USS ABRAHAM LINCOLN
DTG: 261200Z MAR 26
SUBJ: OPORD 26-04

1. SITUATION...
2. MISSION...
3. EXECUTION...
   a. D-DAY: 281800Z MAR 26
   b. H-HOUR: 281800Z MAR 26
4. SERVICE SUPPORT...
5. COMMAND/SIGNAL...

Mission: Coordinated assault
TOT: 281800Z MAR 26

Artillery:
- TOF = 47 seconds
- Fire time = 281759Z MAR 26 (TOT - 47s)

Infantry platoon:
- Movement time = 45 minutes
- Assembly = 15 minutes
- SP (Start Point) = 281700Z MAR 26

Aviation:
- Flight time = 20 minutes
- Takeoff = 281740Z MAR 26

GPS Master Control Station (Schriever AFB)
         ↓
    GPS Satellites (atomic clocks)
         ↓ L1/L2/L5 signals
    GPS Receiver (timing mode)
         ↓
    1PPS (1 Pulse Per Second) output
         ↓
    Local timekeeping system

Each second is encoded as:
- 0.2s reduced power = binary 0
- 0.5s reduced power = binary 1
- 0.8s reduced power = frame marker

Frame structure (60 seconds):
Second 0: Frame reference marker
Seconds 1-8: Minutes (BCD)
Seconds 9: Unused
Second 10-18: Hours (BCD)
Seconds 19: Unused
Seconds 20-33: Day of year (BCD)
Seconds 34-44: DUT1 correction
Seconds 45-58: Year (last 2 digits, BCD)
Second 59: End marker

# Check NTP synchronization
timedatectl show-timesync --all

# Query NTP servers
chronyc tracking

# Detailed source info
chronyc sources -v

# Force immediate sync
sudo chronyc makestep

# List available timezones
timedatectl list-timezones | grep America

# Current timezone
timedatectl status

# Set timezone
sudo timedatectl set-timezone America/Chicago

# Current time in different zones
TZ=America/Los_Angeles date
TZ=America/New_York date
TZ=UTC date

# Convert specific time
TZ=America/Chicago date -d "TZ=\"UTC\" 2026-03-14 18:00"

# tag::time-calc[]
longitude_to_offset() {
    # Convert longitude to approximate UTC offset
    local lon=$1
    awk -v lon="$lon" 'BEGIN {
        offset = -lon / 15
        # Round to nearest hour
        offset = int(offset + 0.5)
        if (offset > 0) printf "+%d\n", offset
        else printf "%d\n", offset
    }'
}

# Example: McAllen longitude
longitude_to_offset -98.23
# Output: -7 (close to actual -6 CST)
# end::time-calc[]

TAI - UTC = 37 seconds
GPS Time = TAI - 19 seconds
DUT1 = +0.15 seconds

Date: July 4, 2026
Time: 21:00 UTC
Observer longitude: 104°W (Denver, CO)
Right Ascension of Vega: 18h 36m 56s

Current leap seconds since 1980: 18
GPS Week rollover: Every 1024 weeks
Last rollover: April 6, 2019 (Week 2048)

H-Hour: 281800Z MAR 26
Artillery TOF: 47 seconds
Mortar TOF: 22 seconds
Infantry movement: 2.5 km at 4 km/hr
Assembly time: 20 minutes
Aviation flight time: 35 minutes
Smoke mission duration: 4 minutes

You are in survival situation with only:
- UTC watch (accurate)
- Nautical Almanac (current)
- Star chart

Observations:
- Local apparent noon: Watch shows 19:23:15 UTC
- Equation of Time for today: +3 minutes 20 seconds
- Polaris altitude: 38°45'