mdf@ziebmef.uucp (Matthew Francey) (04/21/89)
First, I would like to thank Mr. Yee for posting the "press kit". Real
information is always like a breath of fresh air...
But there seems to be a problem. The IUS described in the kit does not seem
capable putting Magellan into an Earth-escape trajectory.
Here is the IUS as described:
mass at ignition 15160kg (excludes Magellan)
total mass at ignition 20750kg (includes Magellan)
1st stage: burn time 150s thrust 187000N fuel 9700kg
burn rate 65kg/s
exhaust velocity 2.88km/s
2nd stage: burn time 108s thrust 80000N fuel 2700kg
burn rate 25kg/s
exhaust velocity 3.20km/s
Here is how it is used:
initial orbit is 297x297km (6675x6675km from geocentre)
orbital speed is 7.73km/s.
first stage burn
the delta-V comes to 2.88*ln(20750/(20750-9700)) = 1.81km/s
1st stage separate
an unknown mass is jettisoned. See below...
wait 150s
from the 1st stage burn, the resulting orbit has a semi-major
axis of 14000km, and an eccentricity of 0.523. Assuming that
the IUS/Magellan is at the perigee of this orbit
then at the end of the 150s wait, IUS/Magellan
is now 6730km from the geocentre, and its speed is 9.49km/s.
second stage burn
the escape velocity at this point (6730km) is 10.88km/s.
So, the IUS must now supply a velocity increment of at least
1.39km/s. From this, we can calculate the >minimum< mass of
the jettisoned 1st stage. Sparing the details, it comes to
3390kg.
And this is the problem. The inert (non-fuel) mass of the IUS at launch is
15160 (total IUS) - 9700 (total 1st stage fuel) - 2700 (total 2nd stage fuel)
= 2760kg.
It seems that a piece of Magellan will have to be disposed of as well.
Can someone explain this away? Perhaps the engines on the IUS have a strange
thrust curve? Maybe the data in the press-kit was incorrectly/badly rounded?
NASA has made a horrible mistake? I can't use a calculator?
--
Name: Matthew Francey Address: N43o34'13.5" W79o34'33.3" 86m
mdf@ziebmef.UUCP uunet!utgpu!{ontmoh!moore,ncrcan}!ziebmef!mdf