A star has an apparent magnitude of 10 and an absolute magnitude of -5. How far away is it?
The star is
We know that the apparent magnitude
And the absolute magnitude
Difference between apparent and absolute magnitudes of an object,
Magnitude system is based on the response of the human eye which shows a logarithmic response. Also the magnitude system, a logarithmic scale, assumes that a factor of
Therefore, we have this scale of base
For two stars
Taking the log of both sides and using
This is commonly expressed in the form
We know that intensity of a light source follows inverse square law of distances. After comparing intensities and magnitudes of two different stars as in equation (1) let us compare the intensities and magnitudes of the same star at two different distances.
Above can be rewritten as
Inserting given values in (2) above we get