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Science lesson plan · 11th grade (Year 12 in England) · 60 minutes

Orbits and orbital speed (v = 2Ï€r / T)

Space

CCSS NGSS.HS-ESS1-4CCSS NGSS.HS-PS2-4England: GCSE Physics: Space physics (orbital motion)

Objective and success criteria

Students will: Orbits and orbital speed (v = 2Ï€r / T).

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Earth's orbit, years and seasons; Scalars and vectors: distance vs displacement, speed vs velocity

Leads to: Newton's law of gravitation and field strength; Circular motion and centripetal force

Materials: Torch and ball for a Sun-Earth-Moon model, Space images, Mini whiteboards, A diagram or short video clip of the idea, Printed student sheet (below).

Warm-up · 6 min

  • Quick retrieval from earlier learning (Earth's orbit, years and seasons; Scalars and vectors: distance vs displacement, speed vs velocity). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. By how many degrees is Earth's axis tilted? (about 23.5° / 90° / 0° / 45°) → about 23.5°Prompt: It is less than a quarter of a right angle.
  2. Is mass a scalar or a vector quantity? (scalar (size only) / vector (size and direction)) → scalar (size only)Prompt: Does it make sense to give it a direction?
  3. A year is 365 days, plus one extra day every 4 years (a leap year). How many days are there in 4 years in a row? → 1461Prompt: How many leap days are there in 4 years?

Hook · 6 min

  • Ask why we see the Moon change shape over a month.
  • Share the objective: Orbits and orbital speed (v = 2Ï€r / T). Read the success criteria together.

I do: model it · 12 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: A polar weather satellite orbits at a radius of about 7200 km from Earth's centre, taking 101 minutes per orbit. What is its orbital speed, in km/s? (v = 2Ï€r ÷ T; give 1 decimal place)
  • Step 1: T = 101 × 60 = 6060 s
  • Step 2: 2Ï€ × 7200 = 45239 km
  • Step 3: 45239 ÷ 6060 = 7.47
  • Step 4: So the answer is: 7.5 km/s
  • Answer: 7.5 km/s
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 12 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. A polar weather satellite orbits at a radius of about 7200 km from Earth's centre, taking 101 minutes per orbit. What is its orbital speed, in km/s? (v = 2πr ÷ T; give 1 decimal place) → 7.5 km/sPrompt: Convert the period to seconds.
  2. The Moon takes about 27 days to orbit Earth, but the ISS takes about 90 minutes. Why the difference? (The ISS has no mass / The Moon orbits a different planet / The ISS orbits much closer, so it must move faster around a much shorter path / The Moon is pushed by the Sun) → The ISS orbits much closer, so it must move faster around a much shorter pathPrompt: Compare their distances from Earth.

You do: independent practice · 17 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 7 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. A satellite moves at a steady speed in a circular orbit. Why is it accelerating? (Its engines are always on / Its speed increases every orbit / It is not accelerating / Its direction is always changing, so its velocity changes) → Its direction is always changing, so its velocity changesPrompt: Velocity is a vector.
  2. A GPS satellite orbits at a radius of about 26560 km from Earth's centre, taking 718 minutes per orbit. What is its orbital speed, in km/s? (v = 2πr ÷ T; give 1 decimal place) → 3.9 km/sPrompt: Convert the period to seconds.

Watch out for

  • Everyday meanings of words getting in the way of the science meaning: define key words explicitly.
  • Remembering facts without the reason: ask "why?" and "what is the evidence?"

Support and stretch

Support

  • Review first: Earth's orbit, years and seasons.
  • Use concrete materials: torch and ball for a sun-earth-moon model.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Move on to: Newton's law of gravitation and field strength; Circular motion and centripetal force.
  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/science/grade-11.

Free lesson plan from eurekami.com/lesson-plan-builder

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Orbits and orbital speed (v = 2Ï€r / T)

Name

Date

Score/ 8

  1. Question 1

    A GPS satellite orbits at a radius of about 26560 km from Earth's centre, taking 718 minutes per orbit. What is its orbital speed, in km/s? (v = 2πr ÷ T; give 1 decimal place)

    Answerkm/s

  2. Question 2

    Orbits: which statement is NOT true?

    • A. Gravity provides the force that keeps planets and satellites in orbit.
    • B. A satellite in a circular orbit has a constant velocity.
    • C. Astronauts on the ISS feel weightless because they are in free fall around Earth.
    • D. The force on an orbiting object points towards the centre of the orbit.

  3. Question 3

    The Moon takes about 27 days to orbit Earth, but the ISS takes about 90 minutes. Why the difference?

    • A. The ISS has no mass
    • B. The ISS orbits much closer, so it must move faster around a much shorter path
    • C. The Moon orbits a different planet
    • D. The Moon is pushed by the Sun

  4. Question 4

    Why are geostationary satellites useful for TV broadcasts?

    • A. They pass over the poles
    • B. They do not move
    • C. They orbit very close to the ground
    • D. They orbit once every 24 hours, so they stay above the same point on Earth

  5. Question 5

    The International Space Station orbits at a radius of about 6780 km from Earth's centre, taking 92 minutes per orbit. What is its orbital speed, in km/s? (v = 2πr ÷ T; give 1 decimal place)

    Answerkm/s

  6. Question 6

    How does orbital speed change for a smaller (lower) stable orbit?

    • A. It must move slower
    • B. It must move faster
    • C. It stops
    • D. Speed does not depend on radius

  7. Question 7

    A satellite moves at a steady speed in a circular orbit. Why is it accelerating?

    • A. Its direction is always changing, so its velocity changes
    • B. It is not accelerating
    • C. Its speed increases every orbit
    • D. Its engines are always on

  8. Question 8

    A geostationary satellite orbits at a radius of about 42160 km from Earth's centre, taking 1436 minutes per orbit. What is its orbital speed, in km/s? (v = 2πr ÷ T; give 1 decimal place)

    Answerkm/s

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Answer key: Orbits and orbital speed (v = 2Ï€r / T)

  1. 1. 3.9 km/s

  2. 2. B. A satellite in a circular orbit has a constant velocity.

  3. 3. B. The ISS orbits much closer, so it must move faster around a much shorter path

  4. 4. D. They orbit once every 24 hours, so they stay above the same point on Earth

  5. 5. 7.7 km/s

  6. 6. B. It must move faster

  7. 7. A. Its direction is always changing, so its velocity changes

  8. 8. 3.1 km/s