Microworld
Title Page:
Rocket Science 101
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Microworld:
Rocket
Science 101: (All in One)
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Author:
James
White
Your
Mission, Rocket Fans, should you choose to accept it, is to dock the Space
Shuttle with the "Novi Mir" Space Station. You will learn right
away the first lesson of space flight. In Space, flying is coasting. Let momentum,
inertia, and gravity do most of the work. You should use your engines only
when you have to make course corrections. Continually move the cursor near
the blue Shuttle avatar to fire the rockets. You will see and hear the engines
light. The shuttle velocity will slowly change as you correct the course.
But keep moving the cursor near the center of the Earth when you want to coast!
That is very important.
Finally,
you must approach within 250 Kilometers of the Station before you hand the
job over to the pilot to dock. If your velocity does not match closely enough
to the Station's velocity, you will hear a short message from Arnold.
What
does this simulation teach? The equations we use to guide the Shuttle Craft
and the Space Station are Newton's equations, with fairly realistic choices
of parameters (the Earth's radius and mass, the gravitational force, the initial
velocity and position of the Shuttle, and so on). All
units are in Kilometers, Seconds, and Kilograms (Metric). The Space station
begins in circular orbit around the Earth at altitude 3000 Km. and moving
with speed 6.52 Km/sec. The satellite has its (constant) speed determined
by these items: The centrifugal acceleration, which is
must be equal to the gravitational acceleration, which is:
Thus,
you may work out for yourself the speed of the Space station before you begin
this simulation. For that, you will need to know that we use
for EarthMass*GravConstant.
We also use 
for the radius of the
Earth. For the mass of the Earth, we take:
The
total energy of the Space Station (and also that of the Shuttle when it is
coasting) is given by the formula:
This
is the Kinetic energy + Potential Energy. For the Shuttle, it varies in time
because of the energy of motion supplied by the rockets. In order to dock,
the Shuttle's energy/mass must be roughly equal to that of the Satellite.
Why?
The
Space Station will move in the clockwise sense in the left screen. That is
the same sense of direction that the Shuttle starts with. You view the process
in 3 dimensions from the forward window of the Shuttle in the right Graph3D
object. This is slightly unrealistic, because, while you can see the Earth
and fixed stars, we have to "magnify" the Space Station so that
you can see it as you approach it from a distance initially of roughly 6000
Km. So imagine that you are viewing the Space Station through a powerful telescope.
Be
sure to
read the Interaction Instructions below the Portal to learn how to handle
your Spacecraft before you start, Captain, and have a good mission!
Author: James E. White
Author Email: mathwrig@gte.net
Topics: Flying Spacecraft, Newton's Laws of Motion, Second-order differential equations, Gravitation, Centrifugal acceleration, simulations with 3D models
Suggested Use: Visualization of laws of gravitation and inertia
Number of Pages: 2
Animation:Yes
Grade Level:10-16
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