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Astronomy & space · University

Distance from an unextinguished distance modulus

This simplified model neglects extinction. Apparent and absolute magnitudes must use the same band.

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Method and conditions

This simplified model neglects extinction. Apparent and absolute magnitudes must use the same band.

d(pc) = 10^((m−M+5)/5)

Worked examples

A star has apparent magnitude 9 and absolute magnitude 4 in one band. Neglect extinction. Find distance in parsecs. Round the final result to 4 decimal places if needed. Answer in pc.

The distance modulus is 5. Rearrange m−M=5 log₁₀(d/10 pc).

100 pc

A star has apparent magnitude 11 and absolute magnitude 0 in one band. Neglect extinction. Find distance in parsecs. Round the final result to 4 decimal places if needed. Answer in pc.

The distance modulus is 11. Rearrange m−M=5 log₁₀(d/10 pc).

1584.8932 pc

Try it

  1. A star has apparent magnitude 12 and absolute magnitude 4 in one band. Neglect extinction. Find distance in parsecs. Round the final result to 4 decimal places if needed. Answer in pc.

  2. A star has apparent magnitude 19 and absolute magnitude -2 in one band. Neglect extinction. Find distance in parsecs. Round the final result to 4 decimal places if needed. Answer in pc.

Check your work

Answers and marking notes
  1. 398.1072 pc

    The distance modulus is 8. Rearrange m−M=5 log₁₀(d/10 pc).

  2. 158489.3192 pc

    The distance modulus is 21. Rearrange m−M=5 log₁₀(d/10 pc).

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