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    Academy lesson

    Orbital transfers

    Hohmann and bi-elliptic transfers, plane changes, gravity assists and launch windows.

    Advanced 13 min read
    Δv₁ (prograde)Δv₂inner orbit r₁target orbit r₂transfer ellipseaₜ = (r₁ + r₂)/2

    Hohmann transfer

    To move between two circular coplanar orbits, a Hohmann transfer uses an ellipse tangent to both. Two burns — one at departure, one at arrival — give the minimum two-impulse Δv for radius ratios below about 11.94. The transfer takes half the ellipse's period.

    Plane changes are expensive

    Changing inclination by Δi at speed v costs Δv = 2v·sin(Δi/2). At low Earth orbit speed, a 28.5° change costs about 3.8 km/s — as much as reaching geostationary altitude. Plane changes are therefore made where the spacecraft is slowest, often combined with the apogee burn.

    Launch windows and gravity assists

    Interplanetary Hohmann-like transfers require the target planet to arrive where the spacecraft does. For Earth to Mars, windows recur every synodic period of about 26 months. Gravity assists exchange momentum with a planet to change heliocentric speed and direction without propellant.

    Knowledge check

    1. An Earth-to-Mars Hohmann transfer takes about:
    2. Where is a plane change cheapest?