Answers

- M101, M87, NGC 5248, NGC 4085, IC1410
- 6.31 times brighter
- (m
_{2}- m_{1}) = 2.5log_{10}(3) ; (m_{2}- m_{1}) = -1.19, so the star's brightness varies by 1.19 magnitudes

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Comparing the magnitudes of different objects

### Some examples to try

### In this Chapter

When Hipparchus first invented his magnitude scale, he intended each grade of magnitude to be about twice the brightness of the following grade. In other words, a first magnitude star was twice as bright as a second magnitude star. A star with apparent magnitude +3 was 8 (2x2x2) times brighter than a star with apparent magnitude +6.

In 1856, an astronomer named Sir Norman Robert Pogson formalized the system by defining a typical first magnitude star as a star that is 100 times as bright as a typical sixth magnitude star. In other words, it would take 100 stars of magnitude +6 to provide as much light energy as we receive from a single star of magnitude +1. So in the modern system, a magnitude difference of 1 corresponds to a factor of 2.512 in brightness, because

2.512 x 2.512 x 2.512 x 2.512 x 2.512 = (2.512)^{5} = 100

*Magnitude scale. Image credit: Alice Hopkinson, LCO *

A fourth magnitude star is 2.512 times as bright as a fifth magnitude star, and a second magnitude star is (2.512)^{4} = 39.82 times brighter than a sixth magnitude star.

The following table shows how the difference in apparent magnitude between two stars (m_{2} - m_{1}) corresponds to the ratio of their apparent brightnesses (b_{1}/b_{2})

Apparent magnitude difference (m_{2} - m_{1}) |
Ratio of apparent brightness (b_{1}/b_{2}) |
---|---|

1 | 2.512 |

2 | (2.512)^{2} = 6.31 |

3 | (2.512)^{3} = 15.85 |

4 | (2.512)^{4} = 39.82 |

5 | (2.512)^{5} = 100 |

10 | (2.512)^{10} = 10^{4} |

20 | (2.512)^{20} = 10^{8} |

This relationship can also be shown by the equation:

(m_{2}- m_{1}) = 2.5log_{10}(b_{1}/b_{2})

1. Put these galaxies in order of magnitude from brightest to faintest:

- NGC 4085: m = 12.94
- M101: m = 8.30
- M87: m = 9.60
- IC1410: m = 15.94
- NGC 5248: m = 10.97

2. How much brighter is a magnitude +2 star than a magnitude +4 star?

3. A variable star periodically triples its light output. By how much does the apparent magnitude change?

- Magnitude and Color
- Apparent magnitude
- What is absolute magnitude?
- Units for Distance and Size in the Universe
- Stellar Parallax
- What is distance modulus?
- Cepheid Variable Stars, Supernovae and Distance Measurement
- Comparing the magnitudes of different objects