The primary goal of interplanetary trajectory design is to find the most energy-efficient path between two celestial bodies, considering factors such as propellant consumption and mission duration.

Hohmann transfer orbits are elliptical orbits that connect two circular orbits in the same plane and are commonly used for interplanetary transfers due to their energy efficiency.

Lambert's problem involves finding a trajectory that satisfies specific boundary conditions, such as the initial and final positions and velocities of the spacecraft. Solving this two-point boundary value problem is computationally challenging.

The vis-viva equation is a fundamental equation in orbital mechanics that relates the spacecraft's velocity to its position in an orbit, allowing for the calculation of orbital parameters and energy.

Jupiter's massive gravitational field makes it an ideal gravitational assist point for spacecraft traveling to the outer planets, providing a significant boost in velocity and reducing the overall energy requirements.

Low-thrust propulsion systems, such as ion thrusters, offer significantly improved fuel efficiency compared to traditional chemical propulsion systems, enabling longer mission durations and more ambitious interplanetary exploration.

Powered swing-by trajectories involve using a spacecraft's propulsion system during a gravitational assist maneuver to modify the trajectory and reduce the overall transfer time, making them suitable for missions with tight time constraints.

Hohmann transfer orbits are designed to minimize the propellant requirements for interplanetary transfers by utilizing a two-impulse maneuver that follows an elliptical trajectory.

The transfer time in a Hohmann transfer orbit is primarily determined by the semi-major axis of the elliptical transfer orbit, which defines the overall size and duration of the trajectory.

Bi-elliptic transfer orbits offer reduced transfer times compared to Hohmann transfer orbits by utilizing two elliptical orbits with different semi-major axes, allowing for faster transfers at the expense of increased propellant consumption.

Earth is frequently used as a gravitational assist point for spacecraft traveling to Mars due to its proximity and favorable orbital alignment, providing a significant boost in velocity and reducing the overall energy requirements.

Low-energy trajectories are designed to minimize the propellant requirements for interplanetary missions by utilizing efficient transfer orbits and gravitational assist maneuvers, enabling more ambitious and cost-effective missions.

The eccentricity of an orbit determines the spacecraft's velocity at a given point in its orbit, with higher eccentricities resulting in higher velocities at periapsis and lower velocities at apoapsis.

Designing interplanetary trajectories for missions to the outer planets presents the challenge of long transfer times due to the vast distances involved, requiring careful planning and consideration of various trajectory design techniques to optimize mission efficiency.