options: A Hohmann transfer orbit requires the least possible propellant and delta-v; this is half of an elliptical orbit with aphelion and perihelion Spacecraft flight dynamics is the application of mechanical dynamics to model how the external forces acting on a space vehicle or spacecraft determine its flight path. These forces are primarily of three types: propulsive force provided by the vehicle's engines; gravitational force exerted by the Earth and other celestial bodies; and aerodynamic lift and drag (when flying in the atmosphere of the A slightly more complicated altitude change maneuver is the bi-elliptic transfer, which consists of two half-elliptic orbits; the first, posigrade burn sends the spacecraft into an arbitrarily high apoapsis chosen at some point r b {\displaystyle r_{b}} away from the central body. At this point a second burn modifies the periapsis to match the radius of the final desired orbit, where a third, retrograde burn is performed to inject the spacecraft into… A Hohmann transfer orbit requires the least possible propellant and delta-v; this is half of an elliptical orbit with aphelion and perihelion tangential to both planets' orbits, with the longest outbound flight time equal to half the period of the ellipse. This is known as a conjunction-class mission. There is no "free return" option, because if the spacecraft does not enter orbit around the destination planet and instead completes the transfer orbit, the departure planet will not be in its original position. Using another Hohmann transfer to return requires a significant loiter time at the destination planet, resulting in a very long total round-trip mission time. Science fiction writer Arthur C. Clarke wrote in his 1951 book The Exploration of Space that an Earth-to-Mars round trip would require 259 days outbound and another 259 days inbound, with a 425-day stay at Mars. Incre Orbital mechanics are used to calculate flight in orbit about a central body. For sufficiently high orbits (generally at least 190 kilometers (100 nautical miles) in the case of Earth), aerodynamic force may be assumed to be negligible for relatively short term missions (though a small amount of drag may be present which results in decay of orbital energy over longer periods of time.) When the central body's mass is much larger than the spacecraft, and other bodies are sufficiently far away, the solution of orbital trajectories can be treated as a two-body problem. This can be shown to result in the trajectory being ideally a conic section (circle, ellipse, parabola or hyperbola) with the central body located at one focus. Orbital trajectories are either circles or ellipses; the parabolic trajectory represents first escape of the vehicle from the central body's gravitational field. Hyperbolic trajectories are escape trajectories with excess velocity, and will be covered under Interplanetary flight below. Elliptical orbits are characterized by three elements. The semi-major axis a is The time period for a complete orbit is dependent only on the semi-major axis, and is independent of eccentricity: A Hohmann transfer orbit is the simplest maneuver which can be used to move a spacecraft from one altitude to another. Two burns are required: the first to send the craft into the elliptical transfer orbit, and a second to circularize the target orbit. To raise a circular orbit at v 1 {\displaystyle v_{1}} , the first posigrade burn raises velocity to the transfer orbit's periapsis velocity: A slightly more complicated altitude change maneuver is the bi-elliptic transfer, which consists of two half-elliptic orbits; the first, posigrade burn sends the spacecraft into an arbitrarily high apoapsis chosen at some point r b {\displaystyle r_{b}} away from the central body. At this point a second burn modifies the periapsis to match the radius of the final desired orbit, where a third, retrograde burn is performed to inject the spacecraft into the desired orbit. While this takes a longer transfer time, a bi-elliptic transfer can require less total propellant than the Hohmann transfer when the ratio of initial and target orbit radii is 12 or greater. Burn 1 (posigrade): A Hohmann transfer orbit requires the least possible propellant and delta-v; this is half of an elliptical orbit with aphelion and perihelion tangential to both planets' orbits, with the longest outbound flight time equal to half the period of the ellipse. This is known as a conjunction-class mission. There is no "free return" option, because if the spacecraft does not enter orbit around the destination planet and instead completes the transfer orbit, the departure planet will not be in its original position. Using another Hohmann transfer to return requires a significant loiter time at the destination planet, resulting in a very long total round-trip mission time. Science fiction writer Arthur C. Clarke wrote in his 1951 book The Exploration of Space that an Earth-to-Mars round trip would require 259 days outbound and another 259 days inbound, with a 425-day stay at Mars. Increasing the departure apsis speed (and thus the semi-major axis) results in a trajectory which crosses the destination planet's orbit non-tangentially before reaching the opposite apsis, increasing delta-v but cutting the outbound transit time below the maximum. A gravity assist maneuver, sometimes known as a "slingshot maneuver" or Crocco mission after its 1956 proposer Gaetano Crocco, results in an opposition-class mission with a much shorter dwell time at the destination. This is accomplished by swinging past another planet, using its gravity to alter the orbit. A round trip to Mars, for example, can be significantly shortened from the 943 days required for the conjunction mission, to under a year, by swinging past Venus on return to the Earth.