# Calculating absolute magnitude

In summary, Sirius A has an apparent magnitude of -1.5 and is located at a distance of 2.6 pc, while the sun has an apparent magnitude of -26.8 and is located at a distance of 1 AU. To find Sirius's absolute magnitude, we can use the equation m-M=5lg(d)-5. To calculate how many times brighter Sirius is than the sun, we can divide Sirius's absolute magnitude by the sun's absolute magnitude. The units for distance, "d", should be in parsecs (pc) for the first equation. Flux refers to the rate of flow of energy through a given surface and is typically measured in units of energy per unit time per unit area.
Sirius A has an apperant magnitude of -1.5, and his distance from us is 2.6 pc. the sun has an apperent magnitude of -26.8 and a distance of 1 AU.
what is Sirius's absolute magnitude?
how meny times is Sirius brighter then the sun?

m1-m2=-2.5lg(f1/f2)
this is the equation I'm supposed to use, its the one they gave me.
i think it is much more oppropriate to use:
m-M=5lg(d)-5
and then just dividing to find how much brighter he is.

so, what unit does the distance "d" needs to be in? and how do i calculate the answers with the first equation?
and what is flux? i couldn't get a clear explanation anywhere.

The distance "d" in the second equation should be in parsecs (pc). To calculate the absolute magnitude of Sirius, we can use the second equation as follows:

m-M=5lg(d)-5
m-(-1.5)=5lg(2.6)-5
m+1.5=5(0.415)-5
m+1.5=2.075-5
m+1.5=-2.925
m=-4.425

So, Sirius's absolute magnitude is approximately -4.425.

To calculate the ratio of Sirius's brightness to the Sun's, we can use the first equation as follows:

m1-m2=-2.5lg(f1/f2)
-4.425-(-26.8)=-2.5lg(f1/f2)
22.375=-2.5lg(f1/f2)
-8.95=lg(f1/f2)
f1/f2=10^-8.95

So, Sirius is approximately 10^-8.95 times brighter than the Sun.

The term "flux" refers to the amount of energy that passes through a given area in a given amount of time. In this context, it refers to the amount of energy emitted by a star that reaches Earth. The equation m1-m2=-2.5lg(f1/f2) takes into account the flux of the two stars, as the apparent magnitude is a measure of the flux received from the star.

## 1. What is absolute magnitude and how is it different from apparent magnitude?

Absolute magnitude is a measure of the intrinsic brightness of a celestial object, while apparent magnitude is a measure of how bright an object appears to us on Earth. Absolute magnitude takes into account the distance of the object, while apparent magnitude does not.

## 2. How is absolute magnitude calculated?

Absolute magnitude is calculated using the formula M = m - 5(log(d/10)), where M is the absolute magnitude, m is the apparent magnitude, and d is the distance to the object in parsecs. This formula takes into account the inverse square law of light, which states that the brightness of an object decreases with distance.

## 3. What is the significance of absolute magnitude in astronomy?

Absolute magnitude allows astronomers to compare the true brightness of different celestial objects, regardless of their distance. This is important for understanding the properties and evolution of stars, galaxies, and other astronomical objects.

## 4. How is absolute magnitude used to classify stars?

Stars are classified based on their spectral type and luminosity, which is determined by their absolute magnitude. This classification system, known as the Hertzsprung-Russell diagram, helps astronomers to study the properties and life cycles of stars.

## 5. Can absolute magnitude change over time?

Yes, the absolute magnitude of a star can change over time as it evolves. For example, as a star runs out of fuel and expands into a red giant, its absolute magnitude will increase. However, the absolute magnitude of a star at a certain point in time can still be determined by its initial mass and age.

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