This program solves the problem of computing any unknown variable given the other three known variables.   Distances can be in any convenient, consistent units, such as AUs, light years, etc.

Apparent Magnitude With Respect to Distance

Using the following equations, we can mathematically move a star around in space and compute its apparent brightness at any given distance from any given known starting values.  This also allows us to mathematically compare the relative brightness of any two stars side-by-side at any common distance.  For example, we might compute how bright a star would our sun appear to be in the sky of a planet orbiting a star 75 light years away.

Let:
m₁  =  Apparent magnitude of a star as viewed from distance d₁
m₂  =  Apparent magnitude of the same star as viewed from distance d₂

Distances can be expressed in any convenient, consistent units, such as AUs, light years, etc.

The relationship between apparent magnitude and distance may be expressed in terms of any of the four variables according to the following equations where each variable is defined in terms of the other three.

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NOTES:

1. log(x) = Common base-10 logarithm of (x)


2. antilog(x) = 10 to the power of (x)


3. These equations were not meant for extreme distances, like beyond our own galaxy.  Distances that extreme require special, sometimes complicated, corrections outside the scope of this simple program.  Here, space is being treated as crystal clear and free of any obscuring gas and dust.

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