Astronomy Kepler Semi-Major Axis Ratio

Inverse of Wave 1 Kepler period ratio. Distinct from synodic period.

a1 = a2 × (T1/T2) to the power 2/3.

Tip: Keep “Period T1” and “Period T2” on the same basis (period, units, and population) before calculating Astronomy Kepler Semi-Major Axis Ratio.

Cluster: Astronomy hub · Parallax distance · Kepler period · Physics hub · Percentage guide

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

Enter periods T1, T2 and reference semi-major axis a2.

Target orbital period
Reference orbital period
Reference orbit size

Semi-major Axis a1

Understanding Astronomy Kepler Semi-Major Axis Ratio

How we calculate. a1 = a2 × (T1/T2) to the power 2/3. 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 Semi-Major Axis Ratio case uses period t1 8 and period t2 1. Enter the same figures below to reproduce the worked path.

What is Astronomy Kepler Semi-Major Axis Ratio?

Inverse of Wave 1 Kepler period ratio. Distinct from synodic period.

  • Same central mass
  • Matching T units
  • a units follow a2

The Formula

Kepler Semi-Major Ratio
a1 = a2 × (T1 ÷ T2)^(2/3)

Worked Example

Scenario: T1 = 8 yr; T2 = 1 yr; a2 = 1 AU.
Step 1: (8/1)^(2/3) = 4
Step 2: a1 = 1 × 4 = 4
Answer: Semi-major axis a1 is 4 AU.

Common Use Cases

  • Homework: find a from periods
  • Study: pair with Wave 1 T1 tool
  • Lab: scaled systems

Pro Tips

  • Keep T1/T2 unitless
  • Not synodic
  • Not binary mass solver

Limitations: Astronomy Kepler Semi-Major Axis 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

Same as Wave 1 Kepler period?

Inverse. Wave 1 solves for T1; this page solves for a1.

Same as synodic period?

No—synodic combines two periods without semi-major axes.

Authoritative References

For astronomy study concepts, consult:

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