Worksheet: The Mass-Luminosity Relation

In this worksheet, we will practice estimating the mass and the lifetime of a star given its luminosity.

Q1:

Star A has a luminosity 2.92 times that of Star B. Both stars are main sequence stars. Which star is likely to have a greater mass?

  • AStar B
  • BStar A

Q2:

4 Sagittarii is a main sequence star with a mass 3.23 times that of the Sun. Is 4 Sagittarii likely to have a lifetime that is shorter than, longer than, or equal to that of the Sun?

  • AEqual to that of the Sun
  • BShorter than that of the Sun
  • CLonger than that of the Sun

Q3:

6 Equulei is a main sequence star with a luminosity 59 times that of the Sun. Is 6 Equulei’s mass greater than, less than, or equal to that of the Sun?

  • ALess than that of the Sun
  • BEqual to that of the Sun
  • CGreater than that of the Sun

Q4:

The given table shows the luminosities of five main sequence stars. Which star is likely to have the greatest mass?

Star Epsilon Apodis 48 Librae Delta Antliae A Eta Hydrae 69 Orionis
Luminosity  𝐿  ⊙ 1,610 1,100 200 2,680 596
  • ADelta Antliae A
  • B48 Librae
  • CEpsilon Apodis
  • D69 Orionis
  • EEta Hydrae

Q5:

1 Persei is a binary star system containing two main sequence stars: 1 Persei A and 1 Persei B. 1 Persei A has a luminosity 2,190 times that of the Sun. 1 Persei B has a luminosity 3,310 times that of the Sun. Which of the two stars is likely to have the shortest lifetime?

  • A1 Persei B
  • B1 Persei A

Q6:

Alpha Persei is a main sequence star with a mass 8.5 times that of the Sun. Is Alpha Persei likely to have a higher luminosity than, a lower luminosity than, or the same luminosity as the Sun’s?

  • AA lower luminosity
  • BA higher luminosity
  • CThe same luminosity

Q7:

Star A has a mass 0.8 times that of Star B. Both stars are main sequence stars. Which star is likely to have a higher luminosity?

  • AStar B
  • BStar A

Q8:

The given table lists the masses of five main sequence stars. Which star is likely to have the lowest luminosity?

Star 53 Aquarii A 8 Draconis 4 Scorpii 57 Persei A 9 Ceti
Mass ( 𝑀 ) ⊙ 1.01 1.56 2.64 1.28 1.09
  • A57 Persei A
  • B4 Scorpii
  • C9 Ceti
  • D53 Aquarii A
  • E8 Draconis

Q9:

The given table lists the masses and luminosities of six main sequence stars.

Star Luminosity  𝐿  ⊙ Mass  𝑀  ⊙
Sirius A 25.4 2.06
Procyon A 6.93 1.50
Tau Ceti 0.520 0.783
Beta Arietis 23.0 2.34
Eta Cassiopeiae 1.23 0.970
Epsilon Herculis 64.0 2.60

Which star is most likely to have the shortest lifetime?

  • ASirius A
  • BProcyon A
  • CTau Ceti
  • DEpsilon Herculis
  • EEta Cassiopeiae

Which star is most likely to have the longest lifetime?

  • ABeta Arietis
  • BEta Cassiopeiae
  • CEpsilon Herculis
  • DProcyon A
  • ETau Ceti

Which star has properties most similar to those of the Sun?

  • AEpsilon Herculis
  • BTau Ceti
  • CProcyon A
  • DEta Cassiopeiae
  • ESirius A

Q10:

The figure shows a graph of the luminosity of a number of main sequence stars against their mass cubed. The red line is a line of best fit, showing how the luminosity of main sequence stars is approximately proportional to their mass cubed.

Would a main sequence star that appears in the top right section of the graph have a longer or shorter lifetime than a main sequence star that appears in the bottom left section of the graph?

  • AA shorter lifetime
  • BA longer lifetime

Q11:

The figure shows a graph of the luminosity of a number of stars against their mass cubed. Most of the data points on the graph represent main sequence stars. The data point marked by the green circle represents a star that is not a main sequence star.

Which of the following statements about the star marked by the green circle are true?

  1. The star has a mass less than that of the Sun.
  2. The star has a mass greater than that of the Sun.
  3. The star has a luminosity more than one million times that of the Sun.
  4. The star has a luminosity more than one thousand times that of the Sun.
  5. The star has a luminosity less than that of the Sun.
  • AII and V
  • BI and V
  • CI and IV
  • DII and III
  • EII, III, and IV

Which of the following types of stars is the star marked by the green circle likely to be?

  • AAn O-type star
  • BA red giant
  • CA neutron star
  • DA brown dwarf
  • EA white dwarf

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