Compare orbital speeds using both radius and period
Interpret orbital data without assuming that a larger path always means greater speed.
Extended only (Supplement); Physics 0625, 2026–2028. Use supplied distances, periods and stated orbital models. Drawings are not to scale. Written practice is self-checked.
Before you begin
- Use ratios and proportional reasoning.
- Calculate orbital average speed.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which quantity combines radius and period to rank circular-model speeds?
What you will learn
- Interpret orbital data without assuming that a larger path always means greater speed.
- Rank orbital averages from a consistent radius-period ratio, with model limits explicit.
Compare the ratio r/T
For the same circular model, v is proportional to r/T. A larger radius increases path length, but a longer period increases elapsed time. Both quantities matter. Comparing only radii or only periods can therefore rank speeds incorrectly.
For two model orbits, vB/vA = (rB/rA)/(TB/TA), since the common factor 2π cancels. Keep units consistent before forming the ratios. This comparison is kinematic; a real gravitational system also constrains which radii and periods occur together.
Separate a data comparison from an orbit law
If radius doubles and period triples, speed becomes two thirds of the original value. If both double, the calculated average speed is unchanged. These are statements about supplied models, not an assertion that every body orbiting the same star can freely choose any period.
For actual planets farther from the Sun, orbital periods increase sufficiently that their typical orbital speeds decrease. The Solar System sequence explains that trend through gravity. Here the task is to evaluate stated radius-period pairs and detect unit or reference mistakes.
Pause and explain
Radius and period both double in a supplied circular model. How does average speed change?
Worked example
Model A has radius r and period T. Model B has radius 2r and period 3T. Compare average speeds.
Show the worked solution
- Use v = 2πr/T for each model.
- Divide B by A: (2r/3T)/(r/T).
- Cancel common quantities to obtain 2/3.
Answer Model B has two thirds of model A’s average speed.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Model B has three times A’s radius and six times A’s period. Find vB/vA.
Give me a hint
Compare the radius factor with the period factor.
Compare my reasoning
- Write the speed ratio as (3r/6T)/(r/T).
- Cancel r and T.
- Evaluate 3/6 = 1/2.
vB/vA = 0.5.
Look for these in your work
- Use both factors.
- State a dimensionless ratio.
Model A has r = 10000 km, T = 2 h. Model B has r = 15000 km, T = 4 h. Which average speed is larger?
Give me a hint
Convert both models consistently or compare their common-unit r/T values.
Compare my reasoning
- A has r/T = 5000 km/h.
- B has r/T = 3750 km/h.
- The shared factor 2π makes A’s average speed 4/3 of B’s.
A is faster; vA/vB = 4/3.
Look for these in your work
- Use matching units.
- Do not rank by radius alone.
A spreadsheet doubles a period from one day to two days but leaves the orbit radius fixed. What should its calculated speed do?
Give me a hint
Apply the inverse dependence on period at fixed radius.
Compare my reasoning
- The circumference is unchanged.
- The elapsed time doubles.
- Distance divided by time halves.
The calculated average speed should halve.
Look for these in your work
- Hold radius fixed.
- Treat this as a supplied model comparison.
Common mistakes
- A longer path need not mean a greater speed.
- Do not compare periods in different units.
- Supplied kinematic pairs are not a complete gravity law.
What can you explain now?
Radius and period both double in a supplied circular model. How does average speed change?
Compare with the explanation
It stays the same
The doubled path length is divided by a doubled traversal time, leaving their ratio unchanged.
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Make it stick
Rank orbital averages from a consistent radius-period ratio, with model limits explicit.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.