So you see, we started from the typical velocity of satellites on this circular orbit around Earth,
and then we increase the velocity at this point and give rise to such an elliptical trajectory.
So of course, when we increase not a lot of T here, this radius will get larger and larger.
And now we may encounter the moon or if we go even higher, we will leave the gravitational field of
the Earth.
I mean, we will never really leave it, but it has one of our dependence, so it becomes basically
not negligible.
And this is what we want to analyze next.
The direct earth escape where the spaceship leaves basically hit the Earth.
So I will just copy what we have here and paste it here.
And now we have a look once again at the velocity and I try to bits.
It is already sufficient if we just briefly increase the velocity here and we can go, for example,
to 1.5 feet orbit.
And when they're on it, you see, this is here to position off the Earth.
This is here the moon trajectory and this trajectory of our spaceship.
So we start from Earth and then be straightforwardly leave it.
And what happens then is we will enter the fields of the Sun.
Of course, we are always in the field of the Sun.
But now the effect of the gravity of the sun is larger than the effect of the gravity of the Earth.
So then the motion will be more effected by the Sun than the Earth.
So for this reason, let's re plot this whole thing here.
Let's go ahead and copy this and make a new figure.
And this time we will not subtract here.
The Earth coordinates, so we will not put it in the reference systems.
The system of the Earth bump in the reference system of the Sun.
So we would have to subtract you the coordinates of the Sun.
But since they are basically zero, we don't have to do it.
I mean, we have seen they're not exactly zero, but we can neglect really this effect.
So for the green, we have the moon and then the spaceship, and now I want to remind the Sun and the
Earth from before.
So this would be zero and one and three and four, and the colors were blue and red.
And when I plot this, we see this is now what happens here, the Sun.
And I think actually it was a red and blue.
Yes.
So this is here to sun.
And then we have here the moon and the Earth, and we see the spaceship is moving on a different trajectory.
So of course, now we should increase the simulation time and I will simulate here not one month, but
I will now simulate here for years.
So our first plot, which was with respect to the Earth, changed to this one.
We have here the Earth and also the Moon, which is not really visible anymore, but you have to zoom
in here to see it.
And in this coordinate frame, the satellite will spiral away from the Earth, which is clear it's not
anymore in a circle which is spiral away.
And in the coordinate system of the Sun.
This is what happens.
We see blue and green are here.
Actually, we can only see green, but we know that the moon and the Earth in the very similar trajectory.
So this here to circle with the larger radius and this is here the motion of our spaceship.
And it's pretty interesting that at some point the spaceship will come back to the Earth and to the
Moon.
They don't have to be here at the same time, necessarily, but at least the possibility exists that
they re-enter the orbit.
And it turns out that this happens already after two of these oscillations here or two of these rotations
around the Sun rather to see.
So we can find this out by increasing the simulation time even more.
And I will simulated here for 16 years, which is four times the time that we had before.
And of course, now it takes a bit longer.
And you see, this is here to plot in the coordinate system of the Earth.
It's no bit confusing, to be honest, because here is the Earth and the moon in the center, and then
the satellite starts basically leaving this trajectory and then coming back, it seems.
And it's, of course, much better to see on this trajectory.
We go in this circle and then we on the larger circle and then eventually we come back to this point.
So here on this whole path, there always is the possibility that the spaceship re-enters to orbit around
the Earth and to figure out if this is happening or not.
We will now use a different plot and I will basically take this plot here and I will just fix here to
plot range to this area so that we can really see what's going on in the vicinity of the Earth.
So I would right, Pulte thoughts.
Excellent, excellent.
And I will use three times the radius of Earth and Moon.
So in positive and a negative direction.
And of course, I will use the same for the wide range.
So plotted out why Lim?
And now we can see what's going on here.
So at first we start from the Earth or very close to the Earth, and then we have so high velocity that
we basically leave the Earth and the Moon and we move on this trajectory and then we move around the
sun once and twice, maybe and even more times, we don't know.
And eventually we come back very, very close to the Earth and we will almost hit it.
And then we will leave it again.
So at this point, it would in principle be possible to break or basically to use a booster and boost
along the opposite direction and decrease the velocity so that we re-enter here.
The orbits of coasters would cost an enormous amount of energy, but in principle it's possible to do.
So the last thing that I want to analyze is, of course, to time dependence here.
So I will plot the distance of our spaceship with respect to the Earth.
And I think we have done this already here, so I can just copy this.
Go to the bottom and look at it.
And we see we have simulated for 16 years.
Of course, I have tested this before, so I know that it is a good time range to simulate and we see
that the distance increases with some additional fluctuations.
And then we are here for the furthest apart and we get closer and we get once again further apart.
And then we are here almost at zero.
This is where we almost hit the Earth.
So this is this point that we see here.
So I think this is really an interesting discussion because just by increasing the starting velocity,
we get such an interesting physics and such a very different behavior.
So instead of having this oval trajectory, which is always the same around the Earth, we instantly
leave the Earth and then we basically circle around the sun on a different trajectory.
But then eventually, after two rotations after 16 years, we reenter here and we almost hit the Earth.
So that's pretty, pretty nice.
Physics are pretty interesting.
OK, so the next thing I want to analyze is the surface cable, like we just did, we escaped the orbit,
but I want to show you that it's even possible with the lower velocity by using a trick, by using the
so-called moon and copter.