Locate the Sun at a focus of an elliptical orbit
Read elliptical orbit geometry without placing the Sun automatically at the ellipse centre.
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
- Read centre and radius in a circle.
- Calculate distances along a number line.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How many foci does an ellipse have?
What you will learn
- Read elliptical orbit geometry without placing the Sun automatically at the ellipse centre.
- Interpret Sun-relative distances from the focus of an elliptical path.
Distinguish focus from centre
Planets, minor planets and comets have elliptical orbital paths in the syllabus model. An ellipse has two foci. The Sun is located at one focus, not at its geometric centre, except that an approximately circular orbit makes the focus and centre nearly coincide.
The Sun-to-object distance therefore changes along a visibly elliptical orbit. The nearest and farthest positions occur at opposite ends of its long axis relative to the Sun’s focus. Do not measure those distances from the ellipse centre instead.
Avoid unnecessary numerical orbit rules
A strongly stretched ellipse can make the difference between focus and centre clear in a diagram. Most planetary drawings exaggerate this shape for teaching; a comet’s orbit may be much more elongated. The drawing does not establish exact eccentricity or period unless numbers are supplied.
This objective requires the elliptical shape and focus location, not a general ellipse-circumference formula. The earlier 2πr/T expression is the syllabus’s average-radius model. It should not be treated as an exact local speed equation for every position on a strongly elliptical orbit.
Pause and explain
Where is the Sun in a non-circular elliptical orbit model?
Worked example
An ellipse diagram labels the centre at x = 0 and the Sun focus at x = −3 in arbitrary units. Its ends are x = −5 and +5. Find nearest and farthest Sun distances.
Show the worked solution
- Measure each end from x = −3.
- The nearer end is 2 units away.
- The farther end is 8 units away.
Answer Nearest 2 units; farthest 8 units.
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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.
On a non-circular ellipse, mark a centre and two foci, then place the Sun.
Give me a hint
Keep the three fixed geometric locations distinct.
Compare my reasoning
- Place the centre midway between the ends.
- Place the two foci on the long axis on either side.
- Place the Sun at one focus.
The Sun belongs at one focus, not the ellipse centre.
Look for these in your work
- Distinguish centre from focus.
- Use one of the two foci.
An ellipse’s ends are x = −10 and +10; the Sun focus is x = −6, all in model units. Find end separations.
Give me a hint
Measure each end from the Sun rather than from zero.
Compare my reasoning
- Near end distance is |−10 − (−6)| = 4.
- Far end distance is |10 − (−6)| = 16.
- Both distances use the same focus.
4 units near; 16 units far.
Look for these in your work
- Use absolute separations.
- Reference the Sun focus.
A nearly circular planet orbit shows the Sun close to its centre. Does that invalidate the focus rule?
Give me a hint
Consider the circular limiting case.
Compare my reasoning
- As the ellipse approaches a circle, its foci approach the centre.
- The Sun can consequently appear nearly central.
- The focus statement still applies to the approximate geometry.
No; focus and centre nearly coincide for an approximately circular orbit.
Look for these in your work
- Explain the limiting geometry.
- Avoid claiming every ellipse is central.
Common mistakes
- Focus and centre are different for a non-circular ellipse.
- Measure separation from the Sun focus.
- A schematic ellipse does not supply exact period or local speed.
What can you explain now?
Where is the Sun in a non-circular elliptical orbit model?
Compare with the explanation
At one focus
The orbital model places the Sun at one of the ellipse’s foci, away from the geometric centre.
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Make it stick
Interpret Sun-relative distances from the focus of an elliptical path.
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.