An ellipse between inner and outer orbits
For an outward heliocentric transfer, the ellipse has perihelion near the starting orbit and aphelion near the destination orbit, with the Sun at a focus. The spacecraft follows the outward half of the ellipse.
A vehicle departing Earth already shares Earth’s orbital motion around the Sun. A suitable increase in heliocentric speed raises orbital energy and aphelion; simply reaching space vertically does not create this interplanetary trajectory.
Matching velocities at both ends
In the ideal outward transfer, an initial increase enters the ellipse and another adjustment at the outer end matches the destination circular orbit. Entering orbit around Mars additionally requires the appropriate Mars-relative capture conditions; heliocentric matching and planetary orbit insertion are distinct.
For an inward transfer, reducing heliocentric energy lowers perihelion toward the inner planet’s distance. Motion may continue in the original prograde direction: deceleration is a change measured in a specified frame, not a reversal straight toward the Sun.
A moving target and an idealized model
The destination planet must occupy the encounter region when the spacecraft arrives. Departure timing therefore depends on planetary positions, while flyby, capture and landing impose different arrival requirements.
The model is useful for understanding propulsion and travel-time tradeoffs, not a universal optimum for every mission. Real inclinations, eccentricities, arrival dates, gravity assists and sustained low thrust can lead to other trajectories.
References: [1]