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Star brightness and magnitude questions
Apparent magnitude ranks how bright a star looks on a scale inherited from ancient astronomy, in which brighter means a smaller number. Add the parsec, a distance defined from the Earth's orbit, and one logarithmic equation converts between how bright a star looks and how bright it actually is.
20 original questions · 56 marks · the star brightness and magnitude notes · Astrophysics
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State which way the apparent magnitude scale runs, and the apparent magnitude of the dimmest stars visible to the naked eye.
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Brighter objects have smaller, and then negative, magnitudes; the scale runs backwards (1). The dimmest naked-eye stars are about magnitude +6 (1).Define the parsec, and state its relationship to the light year.
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One parsec is the distance at which one astronomical unit, the mean Earth-Sun distance, subtends an angle of one arcsecond (1). 1 pc = 3.26 light years (1).State the brightness ratio corresponding to one step of apparent magnitude, and to five steps, and explain why the scale is built from ratios rather than equal differences.
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One magnitude step is a received-intensity ratio of 2.51 (1); five steps are exactly 100 (1). The eye judges brightness roughly logarithmically, so the equal-feeling steps of the ancient scale correspond to equal ratios of intensity (1).Define the astronomical unit and the light year.
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The astronomical unit is the mean distance from the Earth to the Sun (1). The light year is the distance light travels through a vacuum in one year (1).A star lies exactly 10 pc from Earth. State the relationship between its apparent and absolute magnitudes.
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They are equal: at d = 10 pc, m − M = 5 log(10/10) = 0 (1).State what is meant by the distance modulus of a star, and what it is used to find.
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The difference m − M between the apparent and absolute magnitudes (1). Since m − M = 5 log(d/10), it gives the star's distance in parsecs (1).Star P has apparent magnitude 2.0 and star Q has apparent magnitude 7.0. Calculate how many times brighter P appears than Q.
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P is the brighter, having the smaller number, by 2.51(7.0 − 2.0) = 2.515 (1)
= 100 times (1)Sirius has apparent magnitude −1.5 and lies 2.64 pc from Earth. Calculate its absolute magnitude.
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M = m − 5 log(d/10) (1)
= −1.5 − 5 log(0.264) (1)
M = +1.4 (1)A star has absolute magnitude +0.6 and lies 25 pc away. Calculate its apparent magnitude.
A star's apparent magnitude is 8.5 and its absolute magnitude is 1.0. Calculate its distance in parsecs.
Two stars have the same absolute magnitude. One lies 5.0 pc away, the other 50 pc. Calculate the difference in their apparent magnitudes and the ratio of their apparent brightnesses.
A star radiates a total power (luminosity) of 3.2 × 1028 W. Calculate the radiant flux received by a detector 4.1 × 1017 m away. Assume no light is absorbed on the way.
A pulsating star used as a standard candle has a known luminosity of 7.8 × 1029 W. The radiant flux received from it is 6.2 × 10−13 W m−2. Determine its distance in metres, and in parsecs (1 pc = 3.08 × 1016 m).
Star V appears 16 times brighter than star W. Calculate the difference between their apparent magnitudes.
A star lies 42 light years away and has apparent magnitude 5.0. Calculate its distance in parsecs and its absolute magnitude.
The Sun's apparent magnitude is −26.7 and Sirius's is −1.5. Estimate how many times brighter the Sun appears than Sirius.
Explain why apparent magnitude alone cannot tell you how luminous a star really is, and what absolute magnitude does about the problem.
A red dwarf has absolute magnitude +7.5 and lies 3.5 pc from Earth. The naked-eye limit is apparent magnitude +6. Deduce whether the star is visible to the naked eye.
Star T has absolute magnitude −2.0 and lies 250 pc away. Star U has absolute magnitude +1.0 and lies 15 pc away. Deduce which star appears brighter in the night sky.
The mean Earth-Sun distance is 1.50 × 1011 m, and one arcsecond is 1/3600 of a degree. Show that one parsec is about 3.1 × 1016 m.
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
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