Trajectory Calculation Function | Dataford Interview Questions

Write a function to calculate the trajectory of a spacecraft given initial conditions for Impulse Space.

Assume ideal two-body motion around a point mass at the origin. Implement universal-variable Kepler propagation for a spacecraft's three-dimensional position and velocity. Return the state at each requested, nonnegative time.

Signature: def calculate_trajectory(initial_position, initial_velocity, mu, times):

Positions, velocities, mu, and times use consistent units. Return a list of objects containing time, position, and velocity. times is sorted in nondecreasing order, and valid inputs avoid collisions with the central body.

Constraints

initial_position and initial_velocity each contain exactly 3 finite real numbers
mu is a positive finite real number
The initial position magnitude is greater than zero
times contains between 1 and 1000 finite nonnegative values
times is sorted in nondecreasing order
Inputs avoid collision trajectories during the requested times
Use a floating-point tolerance of 1e-9 when comparing coordinates

Function Signature

def calculate_trajectory(initial_position, initial_velocity, mu, times):

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