How does orbital size relate to period in a simplified solar system?
Submit: An evidence record, explanation and revision.
Related lesson: Astronomy: Stars and Galaxies
This is a teacher-led extension beyond the short lesson. The task supplies a performance opportunity; completion alone does not certify mastery, full NGSS coverage or state alignment.
Teacher review guideBuild the idea
For a small object orbiting a Sun-mass central body, T²=a³ when T is in Earth years and a is in astronomical units. Here a is the ellipse’s semimajor axis, not its instantaneous distance. Kepler’s equal-area rule implies faster motion near the central body than farther away. The model neglects other bodies and assumes the central mass dominates.
Science / engineering practice
Using mathematics and computational thinkingCore idea
Orbital motion follows mathematical relationshipsCrosscutting concept
Scale, proportion and quantityEvidence and model inputs
Original orbit cases: circular-like model A, a=1 AU; elliptical model B, a=4 AU, perihelion=2 AU and aphelion=6 AU. An equal-time area diagram should show larger arc travel near perihelion. These are hypothetical orbits around a Sun-mass object.
Keep actual observations, published findings and invented model cases labeled separately. If a source or required equipment is unavailable, pause that part with a teacher; do not invent results.
Materials and preparation
Paper, graph paper or spreadsheet, and the linked readings.
Grade-level scope
Two bodies and algebra only; no calculus or many-body simulation.
Do the work
- Check that B’s semimajor axis is (2+6)/2=4 AU.
- Calculate each period using T=√(a³).
- Sketch B with the star at a focus, not at the ellipse center.
- Draw equal-area wedges for equal times and explain the relative speed.
- Predict the effect of a=9 AU and state why the same numerical unit relation needs modification for a different central mass.
Learner worksheet
Write on paper or type here and print. Entries stay in this page’s memory and are lost when you leave or reload; they are not saved or submitted.
Check your reasoning
- What are periods for a=1 and a=4?
- What is the period for a=9?
- Where is motion faster on B?
- Is a always the current star–object distance?
Teacher review guide
Review the actual deliverable and discuss the reasoning. For each criterion, use 0 when evidence is absent or fundamentally incorrect, 1 when partly supported with a material error or omission, and 2 when accurate, supported and complete for the stated task. Maximum 8 points is a task score, not a proficiency certification. Give feedback and allow revision.
- Uses the correct quantities and units.
- Computes period predictions algebraically.
- Connects ellipse geometry and equal-area motion.
- States central-mass and two-body assumptions.
Answer guidance for the reasoning checks
What are periods for a=1 and a=4?
1 year and 8 years.
What is the period for a=9?
27 years.
Where is motion faster on B?
Near perihelion.
Is a always the current star–object distance?
No. It is the semimajor axis.
Access, support and extension
Offer read-aloud support, labeled diagrams, larger print or an oral/recorded explanation while preserving the scientific reasoning. A partner or teacher can handle physical manipulation while the learner plans, records and interprets. Use a teacher-provided measured dataset only when its provenance and limitations are explicit; it does not replace conducting an investigation when that is the assessed practice. For greater independence, remove prompts and ask learners to compare a second explanation or test another justified revision.
Sources and standard reference
- Official NGSS HS-ESS1-4 performance expectation — inspect the practice, core idea, crosscutting concept and assessment boundary.
Instructional text and hypothetical cases are original. Linked source readings supply published evidence where specified. Teachers should judge fit with their course and state requirements.