So we have varied the starting velocity, and we have seen what can happen if the starting velocity
is just slightly increased from the circular trajectory, we get such an orbital trajectory.
If we increase it by another factor of one point twenty five, approximately then the velocity is so
large that we can even leave the gravitational field of the Earth.
Roughly speaking, of course, it's always in the gravitational field, but then the force or the influence
by the Sun is larger than the influence by the Earth.
So what happens if we set an intermediate velocity where it is oval?
This elliptical trajectory trajectory hits or intersects the trajectory of the Moon.
So then we may get a so-called moon encounter where the object is so close to the moon that the motion
is mostly affected by the Moon, even though the Moon is much lighter than the Earth.
But due to the small distance, it's then strongly affected and there really funky stuff can happen
so.
I have just copied here a few lines of code from our previous examples.
And now I can just change it once again, so I will change here.
The starting velocity and though I will, we have one point twenty five.
We had one point five zero and now I take one point three four.
So here, of course, since this is a very sensitive maneuver, when we want to hit the Moon, it's
very sensitive to this velocity.
So if you changed as a tiny bit, it can give different results, of course.
And I think the time period we can check if this is OK.
And then I also fixed here the X limit and the Y limit as we had before.
So instead of speaking, I just press shift enter and here we see our results.
So we see here the trajectory of the Earth around sorry, the moon around the Earth and the spaceship
around the Earth.
And one thing that we can notice if we zoom in a bit more, if we could, for example, use here year
two to zoom in a bit.
What we can see, then, is that the trajectory is not always on the same oval.
It is a bit shifted, so we see that there was some influence of the Moon already.
So since our spaceship is in the vicinity of the Moon, the trajectory has been shifted a bit.
But this effect is really not so large.
So then let me increase this to a few months.
So I will simulate here to zero point three years.
And you see at the point where we almost hit the moon here, we will have an earth escape, where the
spaceship will leave the Earth and we'll go on a trajectory around the sun.
And the cool thing about this is that we achieved this with a lower velocity compared to the 1.5 that
we had before for the Direct Earth Escape.
So this was here 1.5 B orbits, and now we can get qualitatively the same result.
We leave the sphere of influence by just using a lower starting velocity.
So this is really useful for some maneuvers because you can save a lot of fuel.
You don't have to accelerate to such a high velocity.
You basically get something like a slingshot where you approach the moon.
And since you are so close to this object, you get an additional acceleration and then you get thrown
out of the rotation around the Earth.
So that's a cool trick, and we can use this for leaving, leaving Earth and maybe traveling to Mars
one day.
But what's also really nice is that we are here pretty close to the Moon, we can actually check the
distance here.
This will be the distance spaceship to the Moon.
And so we have to use here nine, 12 and six and nine.
And you see, in the beginning, we are not so far, we always roughly oscillate here, but you see
it's not really a nice oscillation, which means there is also stuff going on in the beginning and we
oscillate approximately twice and then we are here very, very close to zero.
So you see, this is really such a kink where we almost hit the moon.
And since we are so close, we get thrown out of the trajectory and then we leave the moon and we also
leave the Earth.
And now the idea is we approached Moon here pretty closely.
What happens if we break at this point of time?
Can we achieve a moon orbit?
And of course we can.
And of course, this is also how it's done in reality, how you get to the moon orbit and from there,
how you land on the moon by just breaking even more.