Lesson Worksheet: The Mass-Luminosity Relation Physics

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

Q1:

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

StarLuminosity 𝐿⊙Mass 𝑀⊙
Sirius A25.42.06
Procyon A6.931.50
Tau Ceti0.5200.783
Beta Arietis23.02.34
Eta Cassiopeiae1.230.970
Epsilon Herculis64.02.60

Which star is most likely to have the shortest lifetime?

  • AEpsilon Herculis
  • BEta Cassiopeiae
  • CSirius A
  • DProcyon A
  • ETau Ceti

Which star is most likely to have the longest lifetime?

  • AEta Cassiopeiae
  • BBeta Arietis
  • CProcyon A
  • DEpsilon Herculis
  • ETau Ceti

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

  • ASirius A
  • BEpsilon Herculis
  • CTau Ceti
  • DEta Cassiopeiae
  • EProcyon 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?

  • ALonger than that of the Sun
  • BEqual to that of the Sun
  • CShorter than that of the Sun

Q3:

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

Q4:

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

Q5:

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

Q6:

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?

  • AGreater than that of the Sun
  • BEqual to that of the Sun
  • CLess than that of the Sun

Q7:

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

StarEpsilon Apodis48 LibraeDelta Antliae AEta Hydrae69 Orionis
Luminosity 𝐿⊙1,6101,1002002,680596
  • AEpsilon Apodis
  • BDelta Antliae A
  • C48 Librae
  • D69 Orionis
  • EEta Hydrae

Q8:

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

Star53 Aquarii A8 Draconis4 Scorpii57 Persei A9 Ceti
Mass (𝑀)⊙1.011.562.641.281.09
  • A57 Persei A
  • B8 Draconis
  • C4 Scorpii
  • D53 Aquarii A
  • E9 Ceti

Q9:

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

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 longer lifetime
  • BA shorter lifetime

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