# 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 Answer

Relevance

- 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.

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