AP Calc BC Parametric & Polar Simulations Unit 9 Vectors

Project: Finding Neptune

April 11, 2026

1 simulation

Unit: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (AP Calc BC Unit 9)
Topics: Derivatives of parametric and vector-valued functions, Velocity, speed, and acceleration along a curve
In this project, students investigate deviations in Uranus’s orbit, mirroring the real analysis that led to the discovery of Neptune in 1846. They use parametric and polar equations to model Uranus’s orbit, computing its velocity vector and speed at different points, and then model how Neptune’s gravity pulls Uranus off its predicted path by analyzing its deviation vector and when it changes most rapidly. At the end of this project, students write a short report recommending where a telescope should be pointed to find Neptune based on their calculations.