Space Propulsion - IAP/TU Wien

Space Propulsion
Spiraling up
dv
dt
=
T
m
+
g
equation of motion for S/C of mass m,
propelled by thrust T
r
r
2
v
ε = +U 2
() r
∞
∞
FG
() ( r) dU
U r = −∫
dr = −∫
g( r)
dr = − g( r)
m
dr
⎤ dv dU
() ( r) dr ⎛ ⎞
⎥ = + = ⎜
dv
r v
v − g() ⎟
⎡ 2
dε
d v
= ⎢ + U
r
dt dt ⎢ 2 ⎥ dt dt ⎜
⎣ ⎦ dr ⎝ dt
⎠
Specific energy = spec. kinetic energy +
+ potential
potential energy and its gradient
time derivative of specific energy
dε
=
dt
T
v
m
=
T
v
m
acc. to assumption, always v II T; inner
product replaced by magnitudes