Answer key: Stellar Magnitude Worksheet
For teachers. This page is hidden from search engines and not linked from student pages, but it is not password-protected, so please don’t share the link with students. Student worksheet: Stellar Magnitude Worksheet.
Goal: Use the logarithmic magnitude scale to compare how bright stars and other objects look from Earth.
Completed results table
| Setting | Flux A / Flux B | Brighter object |
|---|---|---|
| Five magnitudes (A 1, B 6) | 100× | Object A |
| One magnitude (A 1, B 2) | 2.51× | Object A |
| Equal (A 2, B 2) | 1× | Equal |
| Sirius vs Polaris (A −1.46, B 1.98) | 23.77× | Object A |
| Swapped (A 6, B 1) | 0.01× | Object B |
Answers
Which is brighter, a star of magnitude 1 or a star of magnitude 6? By how many times?
The magnitude 1 star, by exactly 100 times. Smaller magnitudes mean brighter objects.
How many times brighter is a one-magnitude difference? Show that five such steps make 100.
About 2.512 times. 2.512 × 2.512 × 2.512 × 2.512 × 2.512 ≈ 100, because 2.512 is the fifth root of 100.
How many times brighter does Sirius (−1.46) look than Polaris (1.98)?
About 23.8 times: 10^(0.4 × (1.98 − (−1.46))) = 10^1.376 ≈ 23.8.
What happened to the ratio when you swapped the two magnitudes? Explain.
It became 0.01, the reciprocal of 100: Object A is now the fainter one and delivers one hundredth of Object B’s light.
The full Moon has a magnitude of about −12.7, and the faintest stars you can see from a dark site are about magnitude 6. About how many times brighter is the full Moon?
About 30 million times: 10^(0.4 × 18.7) ≈ 3.0 × 10⁷.
Does a star’s apparent magnitude tell you how much light it actually gives off? Explain.
No. Apparent magnitude measures how bright a star looks from Earth, which depends on its distance and on dust as well as its true power. Absolute magnitude, the brightness it would have at 10 parsecs, compares true power.