The equations below are concerned with how bright a star might appear from the surface of a planet orbiting it. Absolute and apparent magnitudes of stars as seen from Earth are covered in great detail elsewhere [1], but are less useful to us in building stars for fictional planets/worlds.

## Absolute Apparent Brightness

Using the equation below, the apparent brightness of a star relative to the brightness of the Sun as seen from Earth can be calculated using the actual values for the star's luminosity in watts/cm² and distance from the observer in meters.

## Relative Apparent Brightness

This perhaps more useful equation allows calculation of the apparent brightness of a star in solar units, using relative values for the luminosity of the star and its distance from the observer.

## Example 1

How bright does the Sun appear from Mars?

The value for the luminosity (L) will be 1.0, since the Sun is the standard candle for this equation. The value for the distance (D) is the distance from the Sun to Mars [2] in Astronomical Units, or ~1.524 AU.

The equation works out as:

The value for the luminosity (L) will be 1.0, since the Sun is the standard candle for this equation. The value for the distance (D) is the distance from the Sun to Mars [2] in Astronomical Units, or ~1.524 AU.

The equation works out as:

... so the Sun is about 43% as bright as seen from Mars as it is from the Earth (see how this is related to the inverse-square law as discussed in this previous blog?)

## Example 2

Let's specify a star called Kalvéru which has a luminosity of 1.618 times that of the Sun. At a distance of 1 AU—the distance between the Sun and the Earth, it would have an apparent brightness of:

... 1.618 times that of the Sun as seen from Earth. Obvious, no?

Kalvéru is 1.618

The safer route is just to calculate the apparent brightness directly.

So, if Kalvéru has a planet (Dynón) orbiting at Mars' distance from the Sun (1.524 AU), how bright does Kalvéru appear to inhabitants of Dynón?

Setting

Kalvéru is 1.618

*times*as bright as the Sun at any particular distance, but this little bit of knowledge can be a dangerous thing. Finding Kalvéru's apparent brightness this way means that one must always remember to calculate the apparent brightness of the Sun at a given distance and then multiply that result by the luminosity of the star in solar units (in this case, 1.618) to get the*relative apparent brightness*of Kalvéru compared to the Sun.The safer route is just to calculate the apparent brightness directly.

So, if Kalvéru has a planet (Dynón) orbiting at Mars' distance from the Sun (1.524 AU), how bright does Kalvéru appear to inhabitants of Dynón?

Setting

*L = 1.618*and*D = 1.524*, the equation tells us:So, we see that while Dynón is the same distance from Kalvéru as Mars is from the Sun, Kalvéru's higher inherent brightness than that of the Sun means that it

If we divide the result for Dynón by the result for Mars:

*does*appear brighter as seen from Dynón than the Sun is as seen from Mars.If we divide the result for Dynón by the result for Mars:

... we see that Kalvéru is, indeed, 1.618 times brighter from Dynón as the Sun is from Mars.

But, since Kalvéru's planets aren't likely to be at exactly the same orbital distances as are the Solar System planets from the Sun, the apparent brightness for any and each of Kalvéru's planets needs to be calculated independently.

But, since Kalvéru's planets aren't likely to be at exactly the same orbital distances as are the Solar System planets from the Sun, the apparent brightness for any and each of Kalvéru's planets needs to be calculated independently.