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 Earth or other body, such as Mars or Venus). The principles of flight dynamics are used to model a vehicle's powered flight during launch from the Earth; a spacecraft's orbital flight; maneuvers to change orbit; translunar and interplanetary flight; launch from and landing on a celestial body, with or without an atmosphere; entry through the atmosphere of the Earth or other celestial body; and attitude control. They are generally programmed into a vehicle's inertial navigation systems, and monitored on the ground by a member of the flight controller team known in NASA as the flight dynamics officer, or in the European Space Agency as the spacecraft navigator. Flight dynamics depends on the disciplines of propulsion, aerodynamics, and astrodynamics (orbital mechanics and celestial mechanics). It cannot be reduced to simply attitude control; real spacecraft do not have steering wheels or tillers like airplanes or ships. Unlike the way fictional spaceships are portrayed, a spacecraft actually does not bank to turn in outer space, where its flight path depends strictly on the gravitational forces acting on it and the propulsive maneuvers applied.
Basic principles A space vehicle's flight is determined by application of Newton's second law of motion:
F = m a , {\displaystyle \mathbf {F} =m\mathbf {a} ,}
where F is the vector sum of all forces exerted on the vehicle, m is its current mass, and a is the acceleration vector, the instantaneous rate of change of velocity (v), which in turn is the instantaneous rate of change of displacement. Solving for a, acceleration equals the force sum divided by mass. Acceleration is integrated over time to get velocity, and velocity is in turn integrated to get position. Flight dynamics calculations are handled by computerized guidance systems aboard the vehicle; the status of the flight dynamics is monitored on the ground during powered maneuvers by a member of the flight controller team known in NASA's Human Spaceflight Center as the flight dynamics officer, or in the European Space Agency as the spacecraft navigator. For powered atmospheric flight, the three main forces which act on a vehicle are propulsive force, aerodynamic force, and gravitation. Other external forces such as centrifugal force, Coriolis force, and solar radiation pressure are generally insignificant due to the relatively short time of powered flight and small size of spacecraft, and may generally be neglected in simplified performance calculations.
Propulsion The thrust of a rocket engine, in the general case of operation in an atmosphere, is approximated by:
F = m ˙ v e = m ˙ v e-opt + A e ( p e − p amb ) {\displaystyle F={\dot {m}}\;v_{e}={\dot {m}}\;v_{\text{e-opt}}+A_{e}(p_{e}-p_{\text{amb}})}
where,
m ˙ {\displaystyle {\dot {m}}} is the exhaust gas mass flow
v e {\displaystyle v_{e}} is the effective exhaust velocity (sometimes otherwise denoted as c in publications)
v e-opt {\displaystyle v_{\text{e-opt}}} is the effective jet velocity when pamb = pe
A e {\displaystyle A_{e}} is the flow area at nozzle exit plane (or the plane where the jet leaves the nozzle if separated flow)
p e {\displaystyle p_{e}} is the static pressure at nozzle exit plane
p amb {\displaystyle p_{\text{amb}}} is the ambient (or atmospheric) pressure The effective exhaust velocity of the rocket propellant is proportional to the vacuum specific impulse and affected by the atmospheric pressure:
v e = g 0 ( I sp-vac − A e p amb m ˙ ) {\displaystyle v_{e}=g_{0}\left(I_{\text{sp-vac}}-{\frac {A_{e}\,p_{\text{amb}}}{\dot {m}}}\right)}
where:
I sp-vac {\displaystyle I_{\text{sp-vac}}} has units of seconds
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