How do you find the brightness ratio of stars?

Answer 1

The brightness ratio of stars is typically expressed using a magnitude scale. The magnitude scale is a logarithmic scale that measures the brightness of celestial objects, including stars. The lower the magnitude value, the brighter the object. Conversely, higher magnitude values indicate fainter objects.

The magnitude scale is defined such that a difference of 5 magnitudes corresponds to a brightness ratio of exactly 100. In other words, a star that is 5 magnitudes brighter than another star is 100 times brighter. Similarly, a star that is 10 magnitudes brighter is 100 x 100 = 10,000 times brighter, and so on.

To find the brightness ratio (R) between two stars with different magnitude values (m1 and m2), you can use the following formula:

R = 100^( (m2 - m1) / 5 )

Where:

R = Brightness ratio between the two stars.

m1 = Magnitude of the first star.

m2 = Magnitude of the second star.

For example, if Star A has a magnitude of 2 and Star B has a magnitude of 6, you can calculate the brightness ratio as follows:

R = 100^( (6 - 2) / 5 )

R = 100^(4/5)

R ≈ 2.511

So, Star B is approximately 2.511 times dimmer than Star A.

It's important to note that the magnitude scale is relative, and negative magnitudes indicate exceptionally bright objects (e.g., the Sun, which has an apparent magnitude of approximately -26.74), while positive magnitudes represent progressively fainter objects. Additionally, the magnitude of a star can be influenced by various factors, such as distance, intrinsic brightness, and interstellar dust extinction.