Screener: Predicting Orbital Motion
Part 1: Computational Representations
Scientists have discovered a new object at the edge of the solar system. Its orbit has an eccentricity of 0.8.
- Sketch the Orbit: Draw a star and the object’s path. Mark the location of the Sun.
- State a Prediction: At which point in the sketch will the object have the highest kinetic energy? Explain using the concept of gravitational potential energy.
Part 2: Mathematical Thinking
An asteroid is found orbiting the Sun at an average distance of 9 AU.
- Apply Kepler’s 3rd Law: Use the relationship $T^2 = a^3$ where $T$ is in Earth years and $a$ is in AU.
- Calculate: What is the orbital period of this asteroid in Earth years? ______
Part 3: Analyzing Evidence
The table below shows the orbital data for two different planets.
| Planet | Distance (AU) | Period (Years) | $a^3 / T^2$ |
|---|---|---|---|
| Planet X | 1.0 | 1.0 | 1.0 |
| Planet Y | 5.2 | 11.8 | ______ |
- Complete the table: Calculate the value for Planet Y.
- Evaluate: Does Planet Y follow the same mathematical pattern as Planet X? What does this tell us about the force governing both planets?
Part 4: Design Solution
A satellite needs to stay directly over the same spot on a planet (Geostationary Orbit). This requires a very specific orbital period.
Identify the Variable: If the planet’s mass were suddenly doubled, what would happen to the required distance (a) for the satellite to maintain the same orbital period (T)? Use your understanding of gravitational force to justify your answer.
(Space for student response)