Predicting Orbits with Mathematical Models — Drills · Grade 9 Science

Chapter: Earth, Moon & Solar System

What these drills covers

By the end of Predicting Orbits with Mathematical Models you should be able to:

8 questions, numeric, multiple choice and written answer, each with a worked explanation.

Vocabulary used: semimajor axis, orbital period, astronomical unit.

Problem 1

For a = 1 AU around the Sun, find P.
Answer and explanation

1 Earth year

P² = 1, so P = 1.

Problem 2

A solar orbit has P = 8 years. Find a using a³ = P².
Answer and explanation

4 AU

a³ = 64, so a = 4.

Problem 3

A satellite completes an orbit every 90 minutes. How many orbits in 24 hours?
Answer and explanation

16 orbits

1,440 / 90 = 16 orbits per day.

Problem 4

A planet moves fastest in its orbit when it is
  1. furthest from the Sun
  2. closest to the Sun
  3. at the midpoint
  4. at the same speed throughout
Answer and explanation

closest to the Sun

It sweeps equal areas in equal times, so it moves faster when nearer.

Problem 5

A moon orbits every 7 days. How many complete orbits in 42 days?
Answer and explanation

6 orbits

42 / 7 = 6 orbits.

Problem 6

A model that predicts an eclipse to the minute is valuable mainly because
  1. it looks impressive
  2. its predictions can be checked against observation
  3. it is simple
  4. it uses mathematics
Answer and explanation

its predictions can be checked against observation

Testability is what distinguishes a scientific model from a description.

Problem 7

Explain why a model that fits past data may still fail to predict the future.
Answer and explanation

A model can be tuned to reproduce a record without capturing the processes that generated it, so it fits the past by construction and has no reason to hold beyond it. The test of a model is prediction of data it was not fitted to, which is why successful forecasts of new observations count for far more than agreement with the data used to build it.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the data, mechanism, or calculation that supports it.
  • Include units, conditions, or limits where relevant.

Problem 8

Why are orbits described as ellipses rather than circles?
Answer and explanation

Measurement shows planetary distances from the Sun vary through the year, which a circle cannot produce. An ellipse with the Sun at one focus matches the observed positions and speeds, including the speeding up when closer. Most planetary orbits are only slightly elliptical, so a circle is a usable approximation for rough work but fails when precise positions are needed.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the data, mechanism, or calculation that supports it.
  • Include units, conditions, or limits where relevant.

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