Space Propulsion - IAP/TU Wien
Space Propulsion - IAP/TU Wien
Space Propulsion - IAP/TU Wien
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<strong>Space</strong> <strong>Propulsion</strong><br />
Spiraling up<br />
time required to spiral up from r 0 to r<br />
assumption: T = const.<br />
•<br />
m = T / I dm/dt = const. •<br />
( )<br />
sp<br />
m = m0 − m t − t 0<br />
ΔV<br />
=<br />
t<br />
∫<br />
t0<br />
T<br />
m<br />
dt =<br />
T<br />
m<br />
0<br />
t<br />
∫<br />
t0<br />
m<br />
1−<br />
m<br />
dt<br />
•<br />
( t − t0<br />
)<br />
0<br />
⎡<br />
T<br />
⎢<br />
m<br />
= − ln 1−<br />
•<br />
m<br />
⎢ m0<br />
⎣<br />
⎤<br />
•<br />
( t − t0<br />
)<br />
⎥ ⎥ ⎦<br />
Δ V<br />
=<br />
μ −<br />
r<br />
0<br />
μ =<br />
r<br />
μ ⎛<br />
⎜1<br />
−<br />
r<br />
0 ⎝<br />
r<br />
0<br />
r<br />
⎞<br />
⎟<br />
⎠<br />
τ =<br />
t<br />
− t<br />
0<br />
=<br />
m<br />
•<br />
⎤⎫<br />
μ ⎞<br />
⎟<br />
m<br />
⎥⎪<br />
⎠ ⎦⎪<br />
⎭<br />
0<br />
sp<br />
1 exp<br />
m<br />
• ⎨ − −<br />
⎬ =<br />
0<br />
−<br />
⎢ ⎜<br />
−<br />
r0<br />
r ⎟ T ⎥ T<br />
m<br />
⎧<br />
⎪<br />
⎪<br />
⎩<br />
⎡<br />
⎢<br />
⎣<br />
⎛<br />
⎜<br />
⎝<br />
μ<br />
I<br />
−( vc,0<br />
−vc,1<br />
)/<br />
Isp<br />
[ 1 e ]