So you see, when we take our standards, starting values for the radius and for the velocity we get
are a stationary orbit.
This is what a satellite is supposed to move on, but we can, of course, try out different starting
values.
So, for example, we could think what happens if our spaceship just accelerates here very quickly and
changes to velocity to a certain value.
What will happen to the trajectory, and I don't know, don't know if you are aware of this, but what
will happen is we will go to an oval trajectory.
And first of all, I want to show you this elliptical orbit and then you see here the other four cases
that we will analyze thereafter.
So I copy here from our previous cell just what we had written down.
And we do not need to redefine starting conditions for the Sun, the Earth and the Moon, of course,
but just for the spaceship.
And then this is really everything that we had before as well.
So the first thing that I want to try out here is the elliptical orbit.
And for this, I will just increase the velocity.
So, for example, one point twenty five times we orbit.
And then I will use this plot here instead.
So let me copy this and plot it instead of this one.
And now we can run it.
So, OK, now it takes already maybe three seconds.
And you see, this is the solution.
So we have propagated this for a single year and this is what happens.
So the Moon is still moving on the rather circular trajectory and it is not really affected by the spaceship,
of course.
It's not, not at all the fact that because we disregarded this interaction and the spacious space Soviet
spaceship itself moves on the elliptical trajectory around the Earth, which is positioned here.
So you see, it can be pretty close and it can be pretty far from the Earth and it gets closer to the
moon at points.
But still, I do not really see much of an influence of the Moon to the spaceship.
But this will come sooner or later.
So the next thing I want to analyze is something we did before, so let me scroll up and let me copy,
for example, this one where we analyzed the distance from the Sun to the Earth over time.
And you guessed it already, I want to do the same thing now for our overall trajectory to see how oval
it actually is.
So our right systems space ship to Earth.
Earth and then this is the time we can leave it as it is.
And here we have to use to spaceship.
So the order here doesn't matter that this is the Earth, so is supposed to be the spaceship, this
is nine to 12.
And we give it the color purple like like we used for the spaceship previously.
And you see, this is how the distance changes over time.
So you see the the the period of this oscillation is very small.
There are many amount of these oscillations.
So maybe like we decrease the time to one month.
So I divide by 12.
And now you see how it goes.
So in a month, we have one two three four five six seven eight and almost nine constellations.
So one of these oscillations or one of these periods, takes maybe three or four days.
And you see that the distance changes pretty much.
So here we have meters 10 to the power of eight.
So this would be 10 to the power of five kilometers.
So we go from from 40k to 140 K and the radius and of course, our starting radius.
We find up here this one we had.
So this was yeah, this was 4.2 times 10 to the power of two.
So this was forty two thousand kilometers.
OK, so that's probably the minimum point here.
And that corresponds to this point on the trajectory.
OK, so now we have analyzed the motion of the spaceship around the Earth.
We could, of course, do the same thing with respect to the Moon.
But what we can also do is we can analyze the velocity.
So velocity
of the spaceship.
With respect to the Earth
in meters per second, I hope it's not too long.
Let's see.
And we have to plot now here just the velocities.
So we basically have to add here 12 of these indices.
So plus 12, 12, 12, 12, 12.
And this is the velocity.
So when the spaceship is closest to the Earth, 42000 kilometers, then the velocity is actually the
largest.
It's almost four K, so four kilometers per second.
And then when the spaceship goes far away from the Earth, when it is in this point here, then the
velocity is the smallest.
It's only 1000 meters per second, which is, of course, still extremely fast, but not so fast.
It's a factor of four decrease here for the velocity.
So it moves very fast here and very slowly here, and this is really what happens also in reality.
OK, so now we have analyzed this elliptical motion and we have analyzed the trajectory and the trend
of the coordinate and the velocities.
And next, we will go ahead and further tune the starting velocity.
We will further increase it.
And then we will see what happens when we increase it here.
And the the overall, the elliptical trajectory will get larger and larger, and at some point we may
encounter the Moon and let's see what happens when we see when we get an encounter with the moon or
even higher.
We get a direct earth escape.