# Absolute magnitude and apparent relationship problems

### Mathematical Applications

The ordinary convention is to write apparent magnitudes with a lower-case letter m, and absolute magnitudes with an upper-case M. One can derive a formula. Apr 10, Apparent magnitude m of a star is a number that tells how bright that star Then, like the formula above, we say that its absolute magnitude is The above relation can also be used to determine the distance to a star if you. Nov 2, If you measure a star's apparent magnitude and know its absolute magnitude, Because the surface area is also in the luminosity relation, the.

If we were to pick up Sirius and move it so that it was at the same distance as HDhow many times fainter would it become? Which star would look brighter if they were sitting side-by-side at the same distance? The answers Since we often want to compare the intrinsic properties of stars, we'd like to have some measure of brightness which is connected directly with luminosity; a type of magnitude which does not depend on distance. Astronomer convert apparent to absolute magnitudes to compare stars fairly, as if they were all side-by-side at a standard distance.

The ordinary convention is to write apparent magnitudes with a lower-case letter m, and absolute magnitudes with an upper-case M. One can derive a formula which connects the apparent and absolute magnitudes of a star, using the inverse square law. If we express the distance d in parsecs, then Q: The distance to Sirius is 2. What is the absolute magnitude of Sirius? What is the absolute magnitude of HD ?

Stars with small absolute magnitudes are truly luminous beasts, radiating huge amounts of energy into space each second. Stars with large absolute magnitudes are relatively feeble creatures, dimly illuminating their immediate surroundings but little else.

## Brightest Stars: Luminosity & Magnitude

Rough zeropoints for the apparent and absolute magnitude scales As some of you have already noticed, the magnitude scales -- both apparent and absolute -- are defined in relative terms: Is it possible to attach real physical units to the intensity of light coming from a star if we know its magnitude? In other words, can we measure the zeropoint of the magnitude scale? To a first approximation, yes, we can. The precise flux of energy from a star depends on a number of factors the filter through which you are looking the color of the star how high the star above the horizon atmospheric properties altitude, humidity, dust content, etc.

In other words, each second, one million photons from the star would enter a box of area one square centimeter. How many photons enter the telescope each second?

• The Magnitude System
• Absolute and apparent magnitudes

Again, there are a lot of complications in defining the precise value, but to an order of magnitude 28 A star of absolute magnitude 0 has power 3 x 10 Watts Q: What is the power of the Sun?

The distance modulus The difference between the apparent and absolute magnitude of a star, m - Mis called its distance modulus. As the equation above shows, it is a simple function of the distance to the star. In practice, astronomers sometimes prefer to specify the distance to a star by its distance modulus, rather than by the distance itself. For example, Look at an extract from the abstract to this paper on the distance to stars in the galaxy NGC Why use distance modulus instead of distance?

### Brightest Stars: Luminosity & Magnitude

I can think of two reasons, though they really boil down to the same thing. Often, one determines the distance to a distant object by assuming that it is identical to some nearby object whose distance is known, and comparing the apparent brightness of the two objects. In this case, the quantities actually observed are the two apparent magnitudes; so using distance modulus is natural. In the magnitude system, Hipparchus grouped the brightest stars and called them first magnitude, slightly fainter stars were second magnitude, and the faintest stars the eye could see were listed as sixth magnitude.

If you notice, the magnitude system is therefore backwards—the brighter a star is, the smaller its magnitude. Our eyes can detect about a factor of difference in brightness among stars, so a 1st magnitude star is about times brighter than a 6th magnitude star. We have preserved this relationship in the modern magnitude scale, so for every 5 magnitudes of difference in the brightness of two objects, the objects differ by a factor of in apparent brightness flux.

If object A is 10 magnitudes fainter than object B, it is x or 10, times fainter. If object A is 15 magnitudes fainter than object B, it is x x or 1, times fainter. So, the magnitude of a star depends on distance. The closer the star is to us, the brighter its magnitude will be. That is, the apparent magnitude of a star is its magnitude measured on Earth.

However, astronomers use the system of absolute magnitudes to classify stars based on how they would appear if they were all at the same distance. If we know the distance to that star and calculate what its apparent magnitude would be if it were at a distance of 10 pc, we call that value the absolute magnitude for the star. If a star is precisely 10 pc away from us, its apparent magnitude will be the same as its absolute magnitude.