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Astronomy & space · University

Kepler period with a central mass ratio

Use the approximate AU-year-solar-mass two-body model with negligible companion mass.

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Method and conditions

Use the approximate AU-year-solar-mass two-body model with negligible companion mass.

P(years) = sqrt(a(AU)³/M(solar masses))

Worked examples

A negligible-mass companion has semimajor axis 14 AU around a star of 2.5 solar masses. Use P²=a³/M in AU, years and solar masses. Find P. Round the final result to 4 decimal places if needed. Answer in years.

Compute sqrt(14³/2.5) under the stated two-body scaling.

33.13 years

A negligible-mass companion has semimajor axis 26 AU around a star of 0.2 solar masses. Use P²=a³/M in AU, years and solar masses. Find P. Round the final result to 4 decimal places if needed. Answer in years.

Compute sqrt(26³/0.2) under the stated two-body scaling.

296.4456 years

Try it

  1. A negligible-mass companion has semimajor axis 7 AU around a star of 3.5 solar masses. Use P²=a³/M in AU, years and solar masses. Find P. Round the final result to 4 decimal places if needed. Answer in years.

  2. A negligible-mass companion has semimajor axis 1 AU around a star of 1.1 solar masses. Use P²=a³/M in AU, years and solar masses. Find P. Round the final result to 4 decimal places if needed. Answer in years.

Check your work

Answers and marking notes
  1. 9.8995 years

    Compute sqrt(7³/3.5) under the stated two-body scaling.

  2. 0.9535 years

    Compute sqrt(1³/1.1) under the stated two-body scaling.

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