Orbital maneuvers are crucial for spacecraft to change their paths in space. Delta-v , the change in velocity needed for these maneuvers, is key. It affects how much fuel is needed and what missions are possible.
The Hohmann transfer is a smart way to move between circular orbits. It's fuel-efficient but takes time. Gravity assists use a planet's pull to change a spacecraft's speed and direction, making far-off missions possible without extra fuel.
Orbital Maneuvers and Transfers
Concept of delta-v in maneuvers
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Represents change in velocity needed for orbital maneuver
Quantifies the impulse required to perform a maneuver like changing the orbit of a satellite or spacecraft
Measured in m/s or km/s (Δ v \Delta v Δ v of 1 km/s means changing velocity by 1 km/s)
Directly proportional to propellant required
Higher Δ v \Delta v Δ v maneuvers need more propellant mass (Tsiolkovsky rocket equation )
Limited by propellant capacity of spacecraft (Falcon 9, Space Shuttle)
Determines practicality and affordability of maneuver
High Δ v \Delta v Δ v maneuvers may be infeasible or cost-prohibitive
Minimizing Δ v \Delta v Δ v is a key objective in mission planning (Hohmann transfers, gravity assists)
Drives spacecraft design and mission planning
Propellant tanks and engines sized based on anticipated Δ v \Delta v Δ v needs
Mission trajectories optimized to reduce total Δ v \Delta v Δ v
Hohmann transfer for orbit changes
Two-impulse maneuver between coplanar circular orbits
Utilizes an elliptical transfer orbit tangent to initial and final orbits
Requires prograde burn at periapsis to raise apoapsis, then prograde burn at apoapsis to circularize
Most propellant-efficient method for circular orbit transfers
Minimizes Δ v \Delta v Δ v compared to other transfer strategies (one-tangent burn, fast transfers)
Enables larger payload mass for a given rocket or longer satellite lifetimes
Commonly used for LEO to GEO transfers
Satellites often launched into LEO parking orbit, then use Hohmann transfer to reach GEO
Also used for transferring between Lagrange points (SOHO mission)
Longer transfer durations than alternative methods
Half-orbit period of the elliptical transfer orbit (usually several hours to days)
May be undesirable for time-sensitive missions or crewed flights
Energy requirements of orbital transfers
Orbital maneuvers change orbital energy (ϵ = − μ / 2 a \epsilon = -\mu/2a ϵ = − μ /2 a )
Increasing orbital altitude increases energy and requires positive Δ v \Delta v Δ v (prograde burn)
Decreasing altitude decreases energy and requires negative Δ v \Delta v Δ v (retrograde burn )
Plane changes require large amounts of energy
Δ v \Delta v Δ v depends on inclination change and orbital velocity (Δ v = 2 v sin ( Δ i / 2 ) \Delta v = 2v\sin(\Delta i/2) Δ v = 2 v sin ( Δ i /2 ) )
Most efficient at nodes where orbital planes intersect
Costly in terms of propellant (i.e. inclination changes in LEO)
Combined plane and altitude changes can be more efficient
Reduces total Δ v \Delta v Δ v compared to separate maneuvers
Bi-elliptic transfers combine plane change with apoapsis burn (Moulton transfer )
Gravity assists for interplanetary missions
Technique using a planet's gravity to alter spacecraft trajectory and speed
Spacecraft exchanges momentum with planet during close flyby
Can significantly change velocity without using propellant
Enables missions to distant targets with less propellant
Reduces launch energy and Δ v \Delta v Δ v requirements
Allows smaller launch vehicles or larger payloads (New Horizons mission to Pluto)
Velocity change depends on flyby geometry
Prograde flybys (in direction of planet's motion) increase spacecraft velocity
Retrograde flybys (opposite to planet's motion) decrease spacecraft velocity
Multiple gravity assists can enable complex trajectories
Voyager grand tour of outer solar system (Jupiter, Saturn, Uranus, Neptune)
Cassini mission used Venus-Venus-Earth-Jupiter gravity assists to reach Saturn