What is the eccentricity of this transfer orbit?
A spaceship travelling in an unoccupied part of Earth's orbit changes its velocity in order to make a rendezvous with Vesta. Its position vector in heliocentric ecliptic coordinates for the departure burn is
x₁ = −0.09273216409680376 AU
y₁ = +0.9790543154949219 AU
z₁ = 0.0
The position of the rocket at the time of arrival is
x₂ = −0.1329822455259632 AU
y₂ = −2.149578487312375 AU
z₂ = +0.08086760107675305 AU
Assume that the transfer orbit has its aphelion at the arrival position and calculate the eccentricity of the transfer orbit.
- 1 year ago
All right, folks. It's only linear algebra, and not much of that. The answer is
e = 0.3748484811736179
Feel free to check.