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Astronomical Constants

Astronomy relies on precisely measured physical constants and defined reference values. This guide explains the constants available in starward and their significance.

Why Constants Matter​

Every astronomical calculation depends on physical constants and conventional reference values. Using outdated or inconsistent constants leads to systematic errors. starward uses the most recent authoritative values from:

  • IAU — International Astronomical Union (astronomical definitions)
  • CODATA — Committee on Data for Science and Technology (physical constants)
  • IERS — International Earth Rotation Service (Earth parameters)
  • SI — International System of Units (fundamental definitions)

Viewing Constants​

List All Constants​

starward constants list

Search for Constants​

starward constants search solar

Show a Specific Constant​

starward constants show c

Fundamental Physical Constants​

Speed of Light (c)​

PropertyValue
Value299,792,458 m/s
UncertaintyExact (defined)
ReferenceSI 2019

Since 2019, the meter is defined such that light travels exactly 299,792,458 meters per second. This makes c an exact constant by definition.

In astronomy: Light travel time is often more practical than distance. "The Sun is 8.3 light-minutes away."

Gravitational Constant (G)​

PropertyValue
Value6.67430 × 10⁻¹¹ m³/(kg·s²)
Uncertainty±0.00015 × 10⁻¹¹
ReferenceCODATA 2018

G is notoriously difficult to measure precisely. It's the least precisely known fundamental constant!

In astronomy: Appears in Kepler's third law, orbital mechanics, and gravitational physics.

M=4π2a3GP2M = \frac{4\pi^2 a^3}{G P^2}

Astronomical Distance Units​

The Astronomical Unit (AU)​

PropertyValue
Value149,597,870,700 m
UncertaintyExact (defined)
ReferenceIAU 2012

The AU was historically the Earth-Sun distance, but since 2012 it's a defined constant. It's approximately the mean distance from Earth to Sun.

Use: Solar system distances. Jupiter is ~5.2 AU from the Sun.

Light-time: 1 AU ≈ 499 seconds ≈ 8.3 minutes

Time Constants​

Julian Date of J2000.0​

PropertyValue
Value2,451,545.0 days
ReferenceIAU (exact)

The standard astronomical epoch: January 1, 2000 at 12:00:00 TT.

Julian Year​

PropertyValue
Value365.25 days
ReferenceIAU (exact)

A defined unit of time, not the actual tropical or sidereal year (which vary).

Julian Century​

PropertyValue
Value36,525 days
ReferenceIAU (exact)

100 Julian years. Used in precession and nutation calculations.

Modified Julian Date Offset​

PropertyValue
Value2,400,000.5 days
ReferenceIAU (exact)

MJD = JD - 2,400,000.5

Angular Constants​

Arcseconds per Radian​

PropertyValue
Value206,264.806247...
ReferenceDerived (exact)

180°×3600"π=648000π≈206264.806\frac{180° \times 3600"}{\pi} = \frac{648000}{\pi} \approx 206264.806

Essential for small-angle conversions.

Mean Obliquity at J2000.0​

PropertyValue
Value23.439291111°
ReferenceIAU 2006

The angle between Earth's equator and the ecliptic plane at J2000.0. This value slowly changes due to precession and nutation.

Also known as: ε₀ (epsilon-naught)

Earth Parameters​

Earth Equatorial Radius​

PropertyValue
Value6,378,137 m
ReferenceWGS84

The semi-major axis of the WGS84 reference ellipsoid.

Earth Flattening​

PropertyValue
Value1/298.257223563
ReferenceWGS84

Earth is an oblate spheroid—the equatorial radius exceeds the polar radius by about 21 km.

f=a−baf = \frac{a - b}{a}

Where a is equatorial radius and b is polar radius.

Earth Rotation Rate​

PropertyValue
Value7.292115 × 10⁻⁵ rad/s
ReferenceIERS

Angular velocity of Earth's rotation.

ω=2π86164.1 rad/s\omega = \frac{2\pi}{86164.1} \text{ rad/s}

(86,164.1 seconds is a sidereal day)

Galactic Reference Frame​

North Galactic Pole (ICRS)​

CoordinateValue
RA192.859508333° = 12h 51m 26.28s
Dec+27.128336111° = +27° 07' 42"
ReferenceIAU 1958, precessed to J2000

The direction perpendicular to the Galactic plane, in the northern hemisphere.

Galactic Longitude of Ascending Node​

PropertyValue
Value32.932°
ReferenceIAU 1958

The galactic longitude where the Galactic plane crosses the celestial equator heading north. Used in coordinate transformations.

Solar Constants​

Solar Mass (M☉)​

PropertyValue
Value1.98841 × 10³⁰ kg
Uncertainty±4 × 10²⁵ kg
ReferenceIAU 2015

The Sun contains 99.86% of the Solar System's mass. Stellar masses are typically expressed in solar masses (M☉).

Note: The product GM☉ is known much more precisely than M☉ or G individually!

Solar Radius (R☉)​

PropertyValue
Value695,700,000 m
UncertaintyNominal (defined)
ReferenceIAU 2015

The IAU nominal solar radius, used as a reference for other stars.

Solar Luminosity (L☉)​

PropertyValue
Value3.828 × 10²⁶ W
UncertaintyNominal (defined)
ReferenceIAU 2015

Total electromagnetic power output of the Sun. Stellar luminosities are expressed in L☉.

Using Constants in Calculations​

Example: How long for light to reach us from the Sun?​

t=AUc=149597870700 m299792458 m/s=499.0 s≈8.3 mint = \frac{AU}{c} = \frac{149597870700 \text{ m}}{299792458 \text{ m/s}} = 499.0 \text{ s} \approx 8.3 \text{ min}

Example: Earth's orbital velocity​

v=2π×AUP≈2π×1.496×1011365.25×86400≈29.8 km/sv = \frac{2\pi \times AU}{P} \approx \frac{2\pi \times 1.496 \times 10^{11}}{365.25 \times 86400} \approx 29.8 \text{ km/s}

Example: Solar angular diameter​

θ=2×arctan⁡(R☉AU)≈2×695700000149597870700×206264.8≈1919"≈32′\theta = 2 \times \arctan\left(\frac{R_☉}{AU}\right) \approx \frac{2 \times 695700000}{149597870700} \times 206264.8 \approx 1919" \approx 32'

Python API​

from starward.core.constants import AstronomicalConstants

# Get the singleton
const = AstronomicalConstants()

# Access individual constants
print(f"Speed of light: {const.c.value} {const.c.unit}")
print(f"Reference: {const.c.reference}")

# Access as attributes
print(f"AU = {const.AU.value} m")
print(f"Solar mass = {const.M_sun.value} kg")
print(f"J2000.0 = JD {const.JD_J2000.value}")

# List all constants
for c in const.all():
    print(f"{c.name}: {c.value} {c.unit or ''}")

# Search constants
for c in const.search("solar"):
    print(f"{c.name}: {c.value}")

Complete Constants Reference​

NameSymbolValueUnitSource
Speed of lightc299,792,458m/sSI 2019
Gravitational constantG6.67430×10⁻¹¹m³/(kg·s²)CODATA 2018
Astronomical UnitAU1.495978707×10¹¹mIAU 2012
Julian Date J2000.0JD₀2,451,545.0daysIAU
Modified JD offsetMJD₀2,400,000.5daysIAU
Julian year—365.25daysIAU
Julian century—36,525daysIAU
Arcsec per radianρ206,264.806″/radDerived
Mean obliquity (J2000)ε₀23.4393°—IAU 2006
Earth equatorial radiusa6,378,137mWGS84
Earth flatteningf1/298.257—WGS84
Earth rotation rateω7.292115×10⁻⁵rad/sIERS
North Galactic Pole RAα_NGP192.8595°—IAU 1958
North Galactic Pole Decδ_NGP27.1283°—IAU 1958
Galactic lon. asc. nodel_Ω32.932°—IAU 1958
Solar massM☉1.98841×10³⁰kgIAU 2015
Solar radiusR☉6.957×10⁸mIAU 2015
Solar luminosityL☉3.828×10²⁶WIAU 2015

References​

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