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In this problem, we'll return the spaceship, so I'm very excited.
Now, similar to what we saw in units 1 and 2, we want our spaceship in this case
or it's actually a satellite to get into orbit.
However, this is a very special type of orbit. It's a geostationary orbit.
What this means is that once the satellite is in space at a certain distance away from the earth,
it will orbit the earth at exactly the same rate as that at which the earth rotates.
So the people on earth, it's going to look like this satellite isn't moving at all, which is pretty cool.
To show you how this happens, we have this lovely diagram right here,
which I warned you is not to scale.
In the center, we have the earth, and initially, the satellite is orbiting
at just 200 km away from the Earth's surface.
At a certain moment, in fact, at the moment when the rocket first crosses the x axis on this diagram,
the rocket is going to spit the satellite out, and this is going to repel the satellite away
from its original orbit and eventually out to the radius that needs to be at for geostationary orbit
so this red line right here then it's going to stay along this red path for as long as it needs to.
Now, the radius of geostationary orbit is 42,164 km.
Also, just an interesting tidbit, this transition orbit, this green curve right here,
is exactly half of an ellipse that is tangent to both of these circular orbits, the pink one and the red one.
Also, these orbits are both perfectly circular even though my drawing doesn't really show that.
So there are three tasks that we would like you to complete for this problem.
The first of these is to find out what the speed and radius of that initial smaller orbit is.
Remember, like I said, this is a circular orbit so that should make things a little bit simpler.
You probably have to use pencil and paper for this part of the problem.
Now, on the rocket and the satellite attached to it
cross the negative part of the x axis for the first time.
The rocket fires its engine to increase the speed of the satellite
by the amount given in the variable called boost.
This should remind you a lot at the last problem of unit 2.
So for your second task, we want you to figure out how to make this boost happen
and of course how to make it happen at the appropriate time.
Let's go back a bit in the code to get your last task.
This is going to be to figure out as you've done before.
What the correct magnitude of the boost velocity is?
We filled a dummy value of 42 just to sort out with,
and I've given you several different options to choose from.
One of these is the correct answer.
Once you completed the first two tasks, plug in each of these values for boost
and compare the path to see which one helps the satellite and the geostationary orbit.