That baseball (spacecraft) follows a nice parabolic curve, and can be
described using a quadratic equation:
h = at2 + v0t + h0
where
• a is a constant = -4.9
• v0 is the initial velocity
• h0 is the initial height
Analysis
The SS2 parabolic spaceflight profile shows that the rocket engine
cutoff is at a certain Mission Elapsed Time (MET) and height above
Mean Sea Level (MSL). This is equivalent to the state a baseball is in at
the moment a player releases it into the air.
Plugging
that
information
into
the
quadratic
equation
allows us to calculate the time the spacecraft reached
maximum altitude, and the maximum altitude itself. All we have to do
is find the vertex of the parabola, since that is the point of maximum
height. Once we find the time at maximum altitude, we can finally use
that calculate the maximum altitude.
-v0
vertext = –––
2a

and
vertexh = a(vertext)2 + v0(vertext) + h0
where
• vertext is the time (after rocket burnout) at maximum height
• vertexh is the maximum height
Example
Let’s suppose that the SS2 rocket burnout time is at 110 min MET at
an altitude of 135,000 ft MSL with a velocity of 2,600 mph. Will it reach
space, which is to say, will it go above 62 miles?
First, as always, we must convert our input into S.I. Units:
v0 = 135,000 ft = 41,148 m
h0 = 2,600 mph = 1,162 mps
Space = 62 mi = 100 km = 100,000 m
So,
Time of Maximum Altitude = Rocket Burnout Time + vertext = 111.98 min
Maximum Altitude = vertexh = 110,027 m
Conclusion
As a result of the spacecraft breaking the 100,000 m barrier, the space
tourists aboard this particular parabolic spaceflight would have all
proudly earned their Astronaut Wings.
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