 The magazine of the Melbourne PC User Group Saturn V - Apollo 11: Part 7 - From Moon Orbit To Earth Atmosphere Ken Holmes |
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Orientation
We will revert to the axes we chose in Part 2; these were fixed in space and, at earth launch, the
sun was on the -y axis apparently moving at 1 degree per day anticlockwise. Angles are measured
anticlockwise from the +x axis, so the sun was at 270 degrees. The moon was at 294.5 degrees; after
119 hours the moon had moved to the +x axis and this is when we will start this program. For
convenience, we will place the CM/SM on the x axis on the moon far side in its 112 km altitude
circular orbit. Apollo 11 fired the Service Module engine to leave the moon 135 hours after the
earth launch, so, in Figure 10, there are 8 orbits by the CM/SM in the "pigtail" during the
intervening 16 hours; during this time it was also reunited with the Ascent Module.
We need to consider both earth and moon gravity during the return journey so the common code in
Listing 7 is identical
to that in Listing
3, Part 3. We again use a SELECT CASE structure to handle the various phases; there are
other ways to structure the program, such as with SUBs, which some may prefer. Programming,
provided you are not in a team, does give you the autonomy to do it just as you prefer. The exact
start of the Trans Earth Injection burn, as in Listing 7, was adjusted by
trial and error to fire at the appropriate position in moon orbit, close to the centre of the far
side, to get the desired earth re-entry path. Note that the burn started a few minutes after the CM
emerged from the unlit side of the moon; this is a very sudden sunrise as, with no refracting
atmosphere, the edge of the shadow is sharp and the CM crosses it at orbital speed, so it provided
a comforting late timing reference. Note also that the sunlit hemisphere has moved about 5 degrees
in the 5 days since earth launch.
The required velocity relative to the moon, vrelmr, was also decided by T&E to get the desired
journey time of about 60 hours, as with Apollo 11. Slightly greater escape velocities can shorten
the journey time but also involve higher energy to be dissipated during re-entry. Other Apollos
varied trip times according to loads, fuel reserves, desired splashdown point on earth and
confidence acquired by experience. Enormous amounts of contingency planning were necessary to cope
with any departure from schedule; unexpected variations could require major changes to the rest of
the trip to fit in with external factors such as recovery vessels and weather in the possible
splashdown areas. The velocity change needed was very close to that which was taken off during the
retroburn to get into moon orbit. Disposal of fuel and the LEM had reduced mass from 44 tonnes to
17 tonnes and, still using hydrazine fuel in the SM engine, it was necessary to use 4.9 tonnes
during a 162 second burn to get the desired effect.
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The re-entry angle in the upper atmosphere is very
sensitive to these variables, and it is unlikely in practice to attain absolute accuracy so there
was a correction burn, at 24000 km from earth by the SM engine, to fine tune the angle. It is
critical that this angle lie between 2 and 6 degrees; if too shallow, the ship would skip off the
atmosphere and continue on a large orbit, possibly as far as the moon's orbit and lasting up to two
weeks; if too steep, it could dig in with extreme deceleration and thermal loading of the heat
shield - not to be contemplated. In sector 4, we simply adjusted the y component of velocity by
T&E to get 4 degrees in our program but this bears little relationship to the correction
actually used by Apollo 11. Figure 10 well illustrates the thin layer of atmosphere which was the
target. The SM had now served its purpose and, half an hour later, it was separated to perform its
own fiery re-entry. The CM still had numerous small thrusters which could apply small corrections,
principally to control attitude to line up the heat shield to the oncoming atmosphere.
Apollo 11 splashed down at 5.50 am local time at about 1500 km SW of Hawaii, ie. near dawn or on
the terminator (edge of sunlight); note that the sunlit hemisphere had moved 8 degrees during the 8
days since launch. The end point of this program, which we have adopted as the start of re-entry,
is still about 18 degrees or 2000 km back around the earth from splashdown.
Next month we will face up to this most dramatic phase of the trip, re-entry. Bear in mind that the
Apollos entered the atmosphere with a velocity close to escape velocity, ie. square root 2 times
earth orbitting velocity, so their specific kinetic energy (per unit mass) was twice that of
returning orbitters such as the shuttle. Although the simple cone with rounded base was obviously
stable in the base-first attitude, its "flying" and control properties were akin to those of a
brick once it had entered the atmosphere, and the plasma streaming from the heat shield cut out
communication links for several minutes - makes for short finger nails.
Reprinted from the May 2001 issue of PC Update,
the magazine of Melbourne PC User Group, Australia
