# Astrophysics Formulas – Data from Solar System Measurements

### Data from Solar System Measurements: Values of Important Astronomical Quantities

[Note: for solar system objects that are not mentioned on this page, you can consult solarsystem.nasa.gov for quick answers but beware that the NASA website does not give sources or uncertainties for the data. If your application involves serious research (as opposed to, for example, making or answering exam questions), then you will need to investigate the origins and uncertainties of the data by yourself in the scientific literature.)

A 2009 IAU report gives, in painful detail, adopted values of various astronomical quantities. Less painful summaries can be found here.

### Astronomical Unit (AU)

The value recommended in the 2009 IAU report is given as
$1 \ {\rm AU} = 1.49597870700 \pm 0.00000000003 \times 10^{11} \ {\rm m}$
(i.e., the uncertainty is 3 m). The reference cited for this is Pitjeva and Standish (2009: DOI 10.1007/s10569-009-9203-8).

### Solar Luminosity

Noerdlinger (2008) quotes Bahcall’s 1989 book, Neutrino Astrophysics (ISBN: 978-0521379755), with
$L_{\odot} = 3.939 \times 10^{33} \ {\rm erg \ s^{-1}}$
for the solar luminosity, which includes a 2.3% contribution from neutrinos, and
$L_{\odot} = 3.856 \times 10^{33} \ {\rm erg \ s^{-1}}$
without the neutrino contribution. According to Sofia and Li (2000) the solar luminosity had not varied by more than 0.1% in the last 2 to 3 centuries.

The value given for the solar luminosity at solarsystem.nasa.gov is $3.83 \times 10^{33} \ {\rm erg \ s^{-1}}$, which is closest to the value without the neutrino contribution. No sources are given by NASA for the value on its website.

The value obtained from Mercury transits by Emilio et al. (2012) is

$R_{\odot} = 6.96342 \pm 0.00065 \times 10^{8}$ meters.

The value give at solarsystem.nasa.gov is $6.95508 \times 10^{8}$ meters (no error given).

### Solar Mass

The solar mass is obtained from applying Newton and Kepler’s law for orbital motion of the Earth, using the measured orbital period and the semimajor axis of the orbit, along with independently measured value of Newton’s gravitational constant. A reference paper for the solar mass value by Castellini et al. (1996) itself quotes the 1994 Astronomical Almanac, with a value of

$M_{\odot} = 1.98892 \pm 0.00025 \times 10^{30}$ kg.

The value given at solarsystem.nasa.gov is $1.9891 \times 10^{30}$ kg. The NASA website does not give sources for most of the numbers appearing on its website.

### Other Solar Quantities

Other key quantities given at solarsystem.nasa.gov are:

Spectral type: G2V
Density: 1.409 g ${\rm cm}^{-3}$
Surface gravity: 274.0 m ${\rm s}^{-2}$
Effective surface temperature: 5777 Kelvin