I
n the recent film release, “Gravity,” astronauts are left
stranded at the Hubble Space Telescope (HST) after
a pretty horrific accident. Since one of the astronauts
was wearing a Manned Maneuvering Unit (MMU), they
used the nifty apparatus to get to the International
Space Station (ISS). We like this movie, even though
many space blogs have been written about how
this feat is virtually impossible, simply because of the
different orbital heights and orbital inclinations.
The verdict: impossible!
So the question is whether there is a way to find out
if the accusation is true? I mean it’s not like there’s a
Pre-Calculus class out there in America that is actually
running a S.T.E.M. projec t that calculates Delta V, is
there? Well, guess what? There really is.
As it turns out, The Learning Community Charter
School (TLCCS), a High School in Albuquerque, NM,
has a Pre-Calculus class that is running a S.T.E.M. for the
Classroom Delta V project. They even have an app for
it! Moreover, they presented their findings to their class
on October 17, 2013.
Now the question is can we use their app to determine
the required Delta V that our hapless astronauts need?
Sure we can! Let’s plug in some numbers and find out
how.
Note: For this exercise, we will ignore the orbital
inclination and destination positioning. Uh...don’t ask.
The equations needed are a bit sticky, but they work
nicely, especially in a spreadsheet.
1.609 km, The HST orbital altitude is at 570 km and the
ISS orbital altitude is 330 km.
We’re now set to tackle the question. To
the Batmobile app!
Click this link to go the app: http://bit.ly/s4cGRAVITY
Here’s some technical terms to match what the
students had to work with: the periapsis is the lowest
point of an elliptical orbit, while the apoapsis is the
highest point.
Since the astronauts start at the higher orbital
altitude, and try to thwart their momentum instead of
applying an opposite thrust, we’ll only concentrate on
the Apoapsis Delta V.
First things first: if you what to change your orbital
altitude, you must know the orbital altitudes that you
want to change from and to. Looking up the particulars
of HST and the ISS, we get that the HST Orbital altitude is
354 miles and the ISS Orbital Altitude is 205 miles (your
mileage may vary, since their orbits are decaying).
Of course, we have to always first convert everything
to S.I. units for the app. Therefore, since one mile equals
For a more in-depth treatment of this high
school project by Joe Maness & Rich Holtzin
visit www.stemfortheclassroom.com.
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The link above is to a working copy of the Delta
V App that S.T.E.M. for the Classroom has created
for TLCCS students to use in their Pre-Calculus projects.
The inputs are: Periapsis: 330 and Apoapsis: 570 (we
can ignore the On-Station Time).
The output is: Apoapsis Delta V is 0.070 kps, or 70
mps. Not much of a change needed, huh? But can the
MMU handle it?
The MMU is rated at 24.4 mps. Since 24.4 is no where
near 70, we therefore can safely conclude that the
MMU does not have the capability of reaching the ISS
from the Hubble.
Too bad this kind of stuff isn’t taught at a High School
somewhere, huh? Oh wait. There is a High School out
there somewhere that is trying their best to provide
students with relevant math topics after all. This entire
lesson was taught at TLCCS, and will continue to be
taught, along with other innovative and fun S.T.E.M.
stuff geared for Pre-Algebra, Algebra 1 and Algebra
2 classes.
Besides, wouldn’t this lesson be better than wasting
time on Standardized Tests? Isn’t this a better way of
getting students to a deeper level of understanding in
mathematics and critical thinking?
By the way, the movie has great human drama and
has got some great special effects. However, what’s
projected on the screen simply ain’t happening. Our
students proved as much given all the above.
www.RocketSTEM.org