Change in apparent magnitude from distance

The apparent magnitude is a measure of the brightness of a celestial body (more precisely, the illumination created by this body) from the observer’s point of view. The brighter the object, the smaller its magnitude. The relationship of the stellar magnitude scale with real physical quantities is logarithmic, since a change in brightness by the same number of times is perceived by the eye as a change by the same amount. The difference in the stellar magnitudes of two objects is equal to the decimal logarithm of the ratio of their illuminances, up to a multiplier.

Links:

1. Wikipedia, second formula.

first_apparent_magnitude

apparent_magnitude of the first object.

Symbol:

m_1

Latex:

\(m_{1}\)

Dimension:

dimensionless

second_apparent_magnitude

apparent_magnitude of the second object.

Symbol:

m_2

Latex:

\(m_{2}\)

Dimension:

dimensionless

first_irradiance

Observed irradiance of the first object.

Symbol:

E_e1

Latex:

\(E_{\text{e}1}\)

Dimension:

power/area

second_irradiance

Observed irradiance of the second object.

Symbol:

E_e2

Latex:

\(E_{\text{e}2}\)

Dimension:

power/area

law

m_2 - m_1 = -2.5 * log(E_e2 / E_e1, 10)

Latex:

\[m_{2} - m_{1} = - 2.5 \log_{10} \left( \frac{E_{\text{e}2}}{E_{\text{e}1}} \right)\]