Astronomy Kepler Period Ratio

Written by Aarav Sharma, Mathematics Editor Reviewed by Vikram Sen, Technical Reviewer Last updated: June 1, 2026 Last verified: June 1, 2026 · Methodology · Accuracy policy

Kepler’s third-law ratio form. Distinct from Physics period-from-frequency.

T1 = T2 × (a1/a2) to the power 1.5.

Tip: Keep “Reference Period T2” and “Semi-major Axis a1” on the same basis (period, units, and population) before calculating Astronomy Kepler Period Ratio.

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For two orbits about the same central mass, (T1/T2)² = (a1/a2)³.

Enter reference period T2 and semi-major axes a1, a2 in matching units.

Period T1

Understanding Astronomy Kepler Period Ratio

How we calculate. T1 = T2 × (a1/a2) to the power 1.5. The form uses the same arithmetic as the worked examples on this page. See our methodology and accuracy policy.

Real-world scenario: A typical Astronomy Kepler Period Ratio case uses reference period t2 1 and semi-major axis a1 4. Enter the same figures below to reproduce the worked path.

What is Astronomy Kepler Period Ratio?

Kepler’s third-law ratio form. Distinct from Physics period-from-frequency.

Same central mass
Matching a units
T units follow T2

The Formula

Kepler Period Ratio

T1 = T2 × (a1 ÷ a2)^(3/2)

Worked Example

Scenario: T2 = 1 yr; a1 = 4 AU; a2 = 1 AU.

Step 1: (4/1)^(1.5) = 8

Step 2: T1 = 1 × 8 = 8

Answer: Period T1 is 8 years.

Common Use Cases

Homework: planetary periods
Study: AU–year solar examples
Lab: scaled orbits

Pro Tips

Keep a1/a2 unitless ratio
Not for binary mass solutions
Don’t use Physics wave period tool

Limitations: Astronomy Kepler Period Ratio results are educational astronomy study aids—not navigation, mission planning, or professional observing advice. Confirm constants and units with your textbook or instructor.

FAQ

Does this find central mass?

No—this ratio form assumes the same central mass and solves for T1.

Same as Physics period 1/f?

No. That page is wave/circuit period; this is orbital Kepler scaling.

Authoritative References

For astronomy study concepts, consult:

OpenStax Astronomy — free textbook reference
NASA — mission and outreach context
IAU — astronomical constants and naming