### Apparent and Absolute Magnitudes

Brightness-Luminosity-Distance relationship Stellar Magnitudes; Absolute Fluxes (energy per second per area). Both are Practical Issues. The 'distance modulus' is the difference between the apparent magnitude and the relation between the flux ratio of two stars and their apparent magnitudes. The reference magnitude and flux really depends on what filter (i.e. range of wavelengths) the observation was made at (e.g., see the UBV.

How can we mathematically describe the relationship between intensity ratios and magnitude differences?

## Apparent magnitude

While the magnitudes are increasing linearly, the intensity ratios are increasing logarithmically in base 2. Denoting magnitudes by m, intensities by I, and using subscripts A and B to denote stars A and B, we can express the relationship between intensity and magnitudes as follows: Convince yourself that this equation describes the numbers in Table 2.

- How "Bright" is a Star?
- Apparent Magnitude
- Inverse Square Law of Brightness

This form of the relationship is best when you know the relative magnitudes, and want to calculate the intensity ratio. We can manipulate the equation to put it in a more convenient form for the case when we know the intensities, but wish to find the relative magnitudes.

Let's do one more example of the magnitude system, this time using the equations. The intensity of star B is a factor of 10 higher than that of star A. What is the magnitude of star A? First of all, think through the problem intuitively.

Which star is brighter? Estimate by how many magnitudes the stars should differ.

### Magnitude (astronomy) - Wikipedia

Should B have a higher or a lower magnitude? Star B is brighter, so it should have a lower magnitude than A. If the intensities differ by a factor of 10, Table 2 shows that the difference in magnitudes should be somewhere between 2 and 3.

Now let's use the equations. Absolute magnitude Apparent magnitudes describe how bright stars appear to be.

However, they tell us nothing about the intrinsic brightness of the stars. Tycho Brahe attempted to directly measure the "bigness" of the stars in terms of angular size, which in theory meant that a star's magnitude could be determined by more than just the subjective judgment described in the above quote. However, early telescopes produced a spurious disk-like image of a star that was larger for brighter stars and smaller for fainter ones.

## Magnitude (astronomy)

Astronomers from Galileo to Jaques Cassini mistook these spurious disks for the physical bodies of stars, and thus into the eighteenth century continued to think of magnitude in terms of the physical size of a star.

Consequently, a magnitude 1 star is about 2. This is the modern magnitude system, which measures the brightness, not the apparent size, of stars. Scale[ edit ] As mentioned above, the scale appears to work 'in reverse', with objects with a negative magnitude being brighter than those with a positive magnitude. The more negative the value, the brighter the object.

Objects appearing farther to the left on this line are brighter, while objects appearing farther to the right are dimmer. Thus zero appears in the middle, with the brightest objects on the far left, and the dimmest objects on the far right.

Apparent and absolute magnitude[ edit ] Two of the main types of magnitudes distinguished by astronomers are: Apparent magnitude, the brightness of an object as it appears in the night sky.

Absolute magnitude, which measures the luminosity of an object or reflected light for non-luminous objects like asteroids ; it is the object's apparent magnitude as seen from a specific distance, conventionally 10 parsecs The difference between these concepts can be seen by comparing two stars.