Astronomy Calculations

Relationship between:

• The parallax angle of a star, expressed in arcseconds.
• The star's distance from the Sun, expressed in parsecs.

The equations are: \[\small \text{parallax} = {1 \over \text{distance}}\] \[\small \text{distance} = {1 \over \text{parallax}}\]

Relationship between:

• The apparent magnitude of an object, m, has no unit of measure.
• The absolute magnitude of the object, M, has no unit of measure.
• The distance of the object, d, expressed in parsecs.

The equations are: \[ \small \text{m} = \text{M} + 5 \times log_{10}(d) - 5 \] \[ \small \text{M} = \text{m} - 5 \times log_{10}(d) + 5 \] \[ \small x = {m - M + 5 \over 5} \text{then } d = 10^x \]

Relationship between:

• The temperature of an object emitting a thermal spectrum, expressed in kelvins.
• The wavelength of the peak of the spectrum, expressed in meters by default.

The dropdown menu provides alternative wavelength units.

The equations are: \[\small \text{wavelength} = {2.898 \times 10^{-3} \over \text{temperature}}\] \[\small \text{temperature} = {2.898 \times 10^{-3} \over \text{wavelength}}\]

Relationship between:

• A star's luminosity, \( \small L_{star} \) expressed in solar units. For example:
  • a star with half the luminosity of the Sun would have \(\small L_{star} / L_{Sun} = 0.5\)
  • a star with 100 times the luminosity of the Sun would have \(\small L_{star} / L_{Sun} = 100\)
• The star's surface temperature, \( \small T_{star} \), expressed in kelvins
  • Sun's surface temperature, \( \small T_{Sun} \), is 5,800 K
  • Stars typically have surface temperatures between 3,000 and 50,000 K
• The star's radius, \( \small R_{star} \), expressed in solar units by default. For example:
  • a star with a radius 4 times smaller than the Sun would have \(\small R_{star} / R_{Sun} = 0.25\)
  • a star with a radius 10 times larger than the Sun would have \(\small R_{star} / R_{Sun} = 10\)

The dropdown menu provides alternative units of stellar radius.

The equations are:

Note: In the equation for luminosity, the first quantity on the right side is multiplied by the second.
In the equations for temperature and radius, the first quantity on the right side is divided by the second.