Earth, Moon & Solar System — Extension · Earth & Space Science, Grade 9
Model sky patterns, seasons, tides, and predictable orbital motion.
Test an Orbital Relationship
Investigate
Does doubling orbital size double the orbital period?
Plan three teaching sessions: define the model and comparison; run or analyze repeated supplied/collected records; then graph, explain, revise and submit the notebook. These independent home-study routes do not certify the school’s mandated investigations or laboratory minutes.
Materials
- Calculator with square root
- Graph paper
- Supplied ideal orbital data
Before you begin
This is a paper-and-data investigation. Use supplied illustrative data or teacher-approved observations. Do not enter hazardous sites to collect evidence.
Plan a fair test
Compare semimajor axis a in AU and period P in years for bodies orbiting a Sun-mass star. Neglect the orbiting body’s mass and interactions; do not apply the same numerical equation to arbitrary central masses.
Method
- Predict the period at twice Earth’s semimajor axis.
- Calculate a³ and P² for every row.
- Graph P versus a and describe its shape.
- Calculate P for a = 2 AU and compare with the initial prediction.
- Explain how a straight-line graph of P² versus a³ tests the model.
- State the assumptions and one reason a real observation may differ slightly.
Open the investigation data (illustrative)
Illustrative data created for this activity; these are not measurements from an actual site or an official reference table.
| Semimajor axis a (AU) | Period P (years) |
|---|---|
| 1 | 1 |
| 4 | 8 |
| 9 | 27 |
| 16 | 64 |
Analyze and explain
- What is P at 2 AU under this model?
- Why is gravity required even if speed in a circular orbit stays constant?
- Would the table apply unchanged to moons orbiting Earth?
- Identify the system boundary, units and conditions held comparable.
- Explain how the graph or figure supports the mechanism rather than merely repeat its trend.
- State one uncertainty or scale limitation and design a follow-up comparison that could challenge the explanation.
What a strong explanation includes
- Tests the stated orbital relationship for table rows
- Calculates the requested period with units
- Explains inward acceleration as a change in velocity direction
- States dependence on central mass and units
- Keep observations separate from model-generated or supplied illustrative records.
- Explain a revision using the evidence and a stated model limitation.
Parent / teacher guide: discuss after the investigation
The table gives equal P² and a³. At 2 AU, P = √8 ≈ 2.83 years, not 2. Gravity provides net inward acceleration; inertia is not an outward force balancing it. Earth’s smaller mass requires a different numerical constant for its moons. The model neglects interactions and small mass contributions. A complete notebook also specifies the boundary, measurement units and matched conditions. Describe a mechanism connecting the pattern to the claim, then state a limitation and an additional comparison. Supplied illustrative outcomes are not a claim about your collected results; differences must be interpreted rather than corrected to match the example.
Compare this model with the learner’s actual evidence. Different measurements can support a different conclusion; check the reasoning and limitations, not matching wording.
Extend the chapter investigation by evaluating its evidence and proposing a better test.
Problem 1
Answer and explanation
The table gives equal P² and a³. At 2 AU, P = √8 ≈ 2.83 years, not 2. Gravity provides net inward acceleration; inertia is not an outward force balancing it. Earth’s smaller mass requires a different numerical constant for its moons. The model neglects interactions and small mass contributions. A complete notebook also specifies the boundary, measurement units and matched conditions. Describe a mechanism connecting the pattern to the claim, then state a limitation and an additional comparison. Supplied illustrative outcomes are not a claim about your collected results; differences must be interpreted rather than corrected to match the example.
Problem 2
Answer and explanation
The table gives equal P² and a³. At 2 AU, P = √8 ≈ 2.83 years, not 2. Gravity provides net inward acceleration; inertia is not an outward force balancing it. Earth’s smaller mass requires a different numerical constant for its moons. The model neglects interactions and small mass contributions. A complete notebook also specifies the boundary, measurement units and matched conditions. Describe a mechanism connecting the pattern to the claim, then state a limitation and an additional comparison. Supplied illustrative outcomes are not a claim about your collected results; differences must be interpreted rather than corrected to match the example.
Problem 3
Answer and explanation
The table gives equal P² and a³. At 2 AU, P = √8 ≈ 2.83 years, not 2. Gravity provides net inward acceleration; inertia is not an outward force balancing it. Earth’s smaller mass requires a different numerical constant for its moons. The model neglects interactions and small mass contributions. A complete notebook also specifies the boundary, measurement units and matched conditions. Describe a mechanism connecting the pattern to the claim, then state a limitation and an additional comparison. Supplied illustrative outcomes are not a claim about your collected results; differences must be interpreted rather than corrected to match the example.
Problem 4
Answer and explanation
The table gives equal P² and a³. At 2 AU, P = √8 ≈ 2.83 years, not 2. Gravity provides net inward acceleration; inertia is not an outward force balancing it. Earth’s smaller mass requires a different numerical constant for its moons. The model neglects interactions and small mass contributions. A complete notebook also specifies the boundary, measurement units and matched conditions. Describe a mechanism connecting the pattern to the claim, then state a limitation and an additional comparison. Supplied illustrative outcomes are not a claim about your collected results; differences must be interpreted rather than corrected to match the example.
Problem 5
Answer and explanation
The table gives equal P² and a³. At 2 AU, P = √8 ≈ 2.83 years, not 2. Gravity provides net inward acceleration; inertia is not an outward force balancing it. Earth’s smaller mass requires a different numerical constant for its moons. The model neglects interactions and small mass contributions. A complete notebook also specifies the boundary, measurement units and matched conditions. Describe a mechanism connecting the pattern to the claim, then state a limitation and an additional comparison. Supplied illustrative outcomes are not a claim about your collected results; differences must be interpreted rather than corrected to match the example.
Problem 6
Answer and explanation
The table gives equal P² and a³. At 2 AU, P = √8 ≈ 2.83 years, not 2. Gravity provides net inward acceleration; inertia is not an outward force balancing it. Earth’s smaller mass requires a different numerical constant for its moons. The model neglects interactions and small mass contributions. A complete notebook also specifies the boundary, measurement units and matched conditions. Describe a mechanism connecting the pattern to the claim, then state a limitation and an additional comparison. Supplied illustrative outcomes are not a claim about your collected results; differences must be interpreted rather than corrected to match the example.