Luminosity Calculator

Table of contents:
This calculator is for star-gazing. It calculates the light emitted by stars, and how bright they are relative to their distance from Earth. The calculator takes input for a star's radius, temperature, and distance, then outputs its luminosity and magnitude, both apparent and absolute. The inputs:

•	Radius - Can be miles, meters, kilometers, or sun radii (R), a common way to express the size of stars relative to the sun.
•	Temperature - Can be degrees Fahrenheit, Celsius, or Kelvin, though stars are typically measured in Kelvin - being the hottest objects in the universe, after all.
•	Luminosity - Expressed in solar luminosity, a standard scientific measure. But also can be megawatts.
•	Distance - Can be parsecs, light years, miles, meters, or kilometers. Parsecs and light years are the most commonly used units since galactic distances are so huge.

Proxima Centauri and Sirius

To pick an example, Proxima Centauri is our closest galactic neighbor. Its radius is 66,659 miles, its temperature is 3042 Kelvin, and its distance from us is 1.301 parsecs. Entering these, we discover it has a luminosity of 0.001827, has an apparent magnitude of 7.157, and an absolute magnitude of 11.59. It's a small red dwarf class star too faint to be seen with the naked eye.

The brightest star in the night sky is Sirius, AKA "the Dog Star," also a relatively close star to our own solar system. It has a radius of 739,600 miles and a temperature of 9940 Kelvin, so it's both bigger and brighter. It's luminosity, the calculator tells you, is 25.64.

Entering the distance from earth of 2.6 parsecs (just about twice the distance of Proxima Centauri), we get an apparent magnitude of -1.7073, and an absolute magnitude of 1.218. Sirius is easy to see with the naked eye; look for it in the Canis Major constellation visible from the southern hemisphere.

Star Jargon

For those new to star-gazing, let's define a few terms:

•	Luminosity - The brightness of an object. This is linked directly to temperature when it comes to stars; the hotter they burn, the brighter they are.
•	Absolute magnitude - This is also a measure of how bright the star is, with the lower end of the scale being brighter. It can even be a negative value like we had for Sirius.
•	Apparent magnitude - This is how bright the star is specifically when seen from Earth. As with absolute magnitude, this also runs with the brightest stars having the lowest value.

Additionally, the radius of a star accounts for some of its visibility as well. To illustrate an example, if you stand outside with a flashlight at night on a full moon and shine the flashlight in your face, it will appear brighter than the moon.

However, you can easily see the moon, while someone standing on the moon would not be able to see your flashlight at all because it is so small.

A Word About Light Years and AU

When we measure star distance in light years, we mean the distance a beam of light would take to travel in one year. A light year is equal to 9.46 trillion KM or 5.88 trillion miles. The speed of light is a well-studied constant, being about 300,000 km/s, so it's often used as a standard measure when computing galactic distance.

Because of the constant speed of light, we can even say with certainty that the light from our own sun takes 8 minutes and 20 seconds to reach Earth. Bear in mind that this also means that when you gaze upon Sirius, the light from that star takes nine years to reach Earth. So you're looking nine years into the past when you look at Sirius, and if it burned out all of a sudden, we wouldn't know about it for nine years!

Another unit commonly used to measure interstellar distances is the AU, the Astronomical Unit, which is roughly the distance from our own sun to Earth. An AU is equal to 150 million KM or 93 million miles.

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