The shape of the lesson
By the end of the lesson, learners can
- Speed around the loop: Change the orbital radius and period and watch the orbital speed that results.
- Circumference over time: The distance for one orbit is the circumference 2 pi r, and dividing by the period gives the speed.
- Formula: v = 2(pi)r / T.
- Units: r in metres, T in seconds, v in m/s.
- Rearrange: to find r or T when needed.
One picture every idea returns to
An orbiting body moves at v = 2 pi r divided by T, the circumference of the orbit divided by the time for one orbit. Planets closer to the Sun travel faster and take less time to go round.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Once around, divided by time.. A planet on a circular orbit travels the whole way round in one period. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Speed around the loop | Change the orbital radius and period and watch the orbital speed that results. Project tab 5 of the lab (Orbital speed) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Circumference over time | The distance for one orbit is the circumference 2 pi r, and dividing by the period gives the speed. Model the worked example Worked example on the board, one line at a time. | Round Table |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 15 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Circumference over time, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Round Table
One sheet travels round the team. Each student adds one line of working or one idea and passes it on, so the solution is built four hands at a time and every contribution is visible.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Use the full circumference 2 pi r, not just the radius, and keep r in metres and T in seconds. | Planets further from the Sun move more slowly and take longer to orbit. |
Orbital speed: worksheet
6 questions, 15 marks. Written in the style of the papers; no past paper question is reproduced.
Write down the equation for orbital speed, and state what each symbol means.
A planet orbits a star in a circle of radius 6.0 x 10 to the 10 m, with a period of 2.0 x 10 to the 7 s. Calculate its orbital speed.
A satellite moves at 7500 m/s in a circular orbit of radius 7.0 x 10 to the 6 m. Calculate its period.
Two satellites have the same period, but one orbits at twice the radius of the other. Compare their orbital speeds.
Explain why a satellite with a longer period, at the same orbital radius, moves more slowly.
The Moon orbits the Earth at a radius of about 3.8 x 10 to the 8 m with a period of about 2.4 x 10 to the 6 s. Estimate its orbital speed.
Answer key and marking notes
- v = 2(pi)r / T. ✓
- r is the orbit radius, T is the period (time for one orbit), v is the orbital speed. ✓
- v = 2(pi)r / T = 2 x (pi) x (6.0 x 10 to the 10) / (2.0 x 10 to the 7)
v = 1.9 x 10 to the 4 m/s (about 19000 m/s)
- T = 2(pi)r / v = 2 x (pi) x (7.0 x 10 to the 6) / 7500
T = 5900 s (to 2 significant figures)
- Speed is proportional to radius when the period is the same. ✓
- The one at twice the radius moves at twice the speed. ✓
- It travels the same distance (2(pi)r) round the orbit. ✓
- But it takes a longer time, so its speed (distance / time) is smaller. ✓
- v = 2(pi)r / T = 2 x (pi) x (3.8 x 10 to the 8) / (2.4 x 10 to the 6)
v = 1000 m/s (about 1.0 x 10 to the 3 m/s)
3 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
A planet moves in a near-circular orbit of radius 4.5 × 1012 m with an orbital period of 9.0 × 109 s. What is its orbital speed? (v = 2πr ÷ T)
- Aabout 3.1 × 103 m/s
- Babout 5.0 × 102 m/s
- Cabout 1.6 × 103 m/s
- Dabout 2.0 × 103 m/s
A satellite orbits at a speed of 1.0 × 104 m/s in a circular orbit of radius 6.0 × 1011 m. What is its orbital period? (rearrange v = 2πr ÷ T)
- Aabout 3.8 × 108 s
- Babout 6.0 × 107 s
- Cabout 1.9 × 108 s
- Dabout 1.7 × 108 s
Compared with the inner planets, the outer planets of the Solar System have:
- Alarger orbits, longer periods, and slower orbital speeds
- Bsmaller orbits and faster speeds
- Cthe same orbital speed as the inner planets
- Dlonger periods but faster speeds
Quiz key
v = 2πr ÷ T = 2π × (4.5 × 10¹²) ÷ (9.0 × 10⁹) = 2π × 500 ≈ 3.1 × 10³ m/s. Option B forgets the factor of 2π and C uses π instead of 2π.
T = 2πr ÷ v = 2π × (6.0 × 10¹¹) ÷ (1.0 × 10⁴) = 2π × 6.0 × 10⁷ ≈ 3.8 × 10⁸ s. Option B drops the 2π and C uses π instead of 2π.
Outer planets have larger orbital radii, so they travel further and take much longer to complete an orbit, and they move more slowly. Neptune, for example, takes about 165 Earth years for one orbit.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.