A spacecraft follows a hyperbolic trajectory around a planet whose centre is taken as…
MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices
Problem
A spacecraft follows a hyperbolic trajectory around a planet whose centre is taken as the origin. The path lies along the x-axis and has eccentricity 2. At its closest approach (the periapsis) the spacecraft is 7000 km from the planet’s centre.
(i) Taking the periapsis as a vertex, find the values of a and c for the hyperbolic orbit.
(ii) Determine the length of the semi-conjugate axis b and hence write the equation of the trajectory.
(iii) Using the equation obtained in part (ii), calculate the distance of the spacecraft from the planet’s centre when its x-coordinate is 10000 km.