Astronomical system of units

Astronomical unit of mass

The astronomical unit of mass is the solar mass. The symbol M_☉ is often used to refer to this unit. The solar mass (M_☉), 1.98892×10³⁰ kg, is a standard way to express mass in astronomy, used to describe the masses of other stars and galaxies. It is approximately equal to the mass of the Sun, about 333000 times the mass of the Earth or 1 048 times the mass of Jupiter.

In practice, the masses of celestial bodies appear in the dynamics of the Solar System only through the products GM, where G is the gravitational constant. In the past, GM of the Sun could be determined experimentally with only limited accuracy. Its present best known value is GM_☉ = 1.32712442099(10)×10²⁰ m³⋅s⁻².

The nominal value of the solar GM recommended for use in astrophysics as an exactly defined unit by the IAU is 1 (𝒢ℳ)^N
_☉ = 1.3271244×10²⁰ m³⋅s⁻².

Jupiter mass

Jupiter mass (M_J or M_Jup), is the unit of mass approximately equal to the total mass of the planet Jupiter, 1.898×10²⁷ kg. Jupiter mass is used to describe masses of the gas giants, such as the outer planets and extrasolar planets. It is also used in describing brown dwarfs and Neptune-mass planets. The nominal value recommended by the IAU for the GM of Jupiter is 1 (𝒢ℳ)^N
_J = 1.2668653×10¹⁷ m³⋅s⁻².

Earth mass

Earth mass (M_🜨) is the unit of mass approximately equal to that of the Earth, 5.9742×10²⁴ kg. Earth mass is often used to describe masses of rocky terrestrial planets and up to approximately Neptune-mass planets. The nominal value recommended by the IAU for the GM of Earth is 1 (𝒢ℳ)^N
_E = 3.986004×10¹⁴ m³⋅s⁻².

Astronomical unit of length

The astronomical unit of length is now defined as exactly 149 597 870 700 meters. It is approximately equal to the mean Earth–Sun distance. It was formerly defined as that length for which the Gaussian gravitational constant (k) takes the value 0.01720209895 when the units of measurement are the astronomical units of length, mass and time. The dimensions of k² are those of the constant of gravitation (G), i.e., L³M⁻¹T⁻². The term "unit distance" is also used for the length A while, in general usage, it is usually referred to simply as the "astronomical unit", symbol au.

An equivalent formulation of the old definition of the astronomical unit is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.01720209895 radians per day. The speed of light in IAU is the defined value c₀ = 299792458 m/s of the SI units. In terms of this speed, the old definition of the astronomical unit of length had the accepted value: 1 au = c₀τ_A = (149597870700±3) m, where τ_A is the transit time of light across the astronomical unit. The astronomical unit of length was determined by the condition that the measured data in the ephemeris match observations, and that in turn decides the transit time τ_A.

Other units for astronomical distances

The distances to distant galaxies are typically not quoted in distance units at all, but rather in terms of redshift. The reasons for this are that converting redshift to distance requires knowledge of the Hubble constant, which was not accurately measured until the early 21st century, and that at cosmological distances, the curvature of spacetime allows one to come up with multiple definitions for distance. For example, the distance as defined by the amount of time it takes for a light beam to travel to an observer is different from the distance as defined by the apparent size of an object.