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 />
Δ<br />
V = v c , 0<br />
− v c , r<br />
ΔV<br />
v<br />
c,0<br />
= 1−<br />
r<br />
0<br />
r<br />
I sp<br />
>> ΔV<br />
τ =<br />
m<br />
0<br />
I<br />
sp<br />
T<br />
I<br />
−ΔV<br />
/ Isp<br />
sp ΔV<br />
/ Isp<br />
[ 1−<br />
e ] = m ( e −1)<br />
f<br />
T<br />
→<br />
m<br />
f<br />
ΔV<br />
T<br />
m<br />
p<br />
⎡ ⎛ V ⎞ ⎤<br />
m<br />
f ⎢ ⎜<br />
Δ<br />
= exp ⎟ −1⎥<br />
→ m<br />
⎢<br />
⎣<br />
I<br />
⎝ sp ⎠ ⎥⎦<br />
f<br />
ΔV<br />
I<br />
sp<br />
m<br />
∞<br />
= 100.<br />
5<br />
10<br />
100<br />
5x10<br />
τ ∞<br />
=<br />
−3<br />
5<br />
7809<br />
( e 1) 2 /10 − ≅ 11.7 [ kg]<br />
5<br />
7809<br />
( e 1) 2 /10 − ≅ 5.1 [ y]<br />
Example<br />
Electric propulsion: T = 5 mN, I sp<br />
= 10 5 m/s;<br />
Time and propellant mass required for spiraling<br />
up a 100 kg payload from 300 km LEO (v =<br />
7730 m/s) to escape velocity?