Final answer:
A spaceship traveling to Mars will follow an elliptical orbit, which appears nearly circular due to the low eccentricity of Mars's orbit. The spacecraft, once it escapes Earth's gravity, coasts to Mars in a heliocentric orbit, with its path adjusted slightly by on-board thrusters. Precise timing is crucial to align with Mars's orbit upon arrival.
Step-by-step explanation:
On its way to Mars, a spaceship will follow an elliptical orbit, which is a characteristic path in space under the influence of gravity. This applies to any object in space, including spacecraft, planets, stars, and galaxies. An ellipse's size and shape are defined by its semimajor axis and its eccentricity.
Johannes Kepler, using Tycho Brahe's data, concluded that Mars has an elliptical orbit with the Sun at one focus, which has a relatively low eccentricity of about 0.1, making it appear almost circular.
For interplanetary travel, once a spacecraft escapes Earth's gravity at the required escape speed—approximately 11 kilometers per second—it predominantly coasts to its destination while following a heliocentric orbit. The spacecraft's trajectory is tweaked using on-board thrusters for minor adjustments.
Crucial to the journey is the precise timing to ensure that when the spacecraft reaches Mars's orbit, the planet is actually there. Missions to Mars are therefore planned around orbital mechanics considering both Earth's and Mars's positions in their respective orbits.