Wouldn’t when we land on the moon, the earth would still be in motion bc of the orbit, and so whenever we exit the orbit of the moon (Which was orbiting the earth) the earth would still be in a constant orbit moving at high speeds, how did we calculate and intercept earth in said orbit.
In: Planetary Science
My knowledge of this comes from KSP (Kerbal space program) which is a game where you make your own space program, and it has surprisingly realistic orbital mechanics. Search for videos on “how to get from Kerbin to the Mun and back” if you want to see a demonstration of something similar to going from the Earth to the Moon and back in real life. (Although skip the parts irrelevant to you, like rocket building).
Firstly, there is no “dead zone”. You’ll always be dominated by some nearby large mass, whether that’s the moon, the Earth, or the Sun. Most of the time, you’re going to be orbiting something, unless you’re going so fast that you’re just doing a bit of a flyby (but your path is going to be bended by the nearby big mass object anyway).
Imagine we are in orbit around the moon. We have a nice circular orbit at the moment. It is well calculated and well understood. If I start to increase my velocity in my direction of travel (we call this direction “prograde”), which is kind of parallel to the moon’s surface, using my rocket engines, then this orbit is not going to be circular anymore. At this point, it becomes an ellipse.
Due to the fun nature of how orbits work if I increase my velocity (in the prograde direction) at one point in the orbit, then the opposite side of the orbit will start to elongate. Like becoming more oval shaped. This “elliptical” orbit is also well understood. The maths for it nice and predictable. The point where we are currently in the orbit is called the periapsis – the point in the orbit closest to the moon. The opposite side of the orbit is called the apoapsis – the point in the orbit furthest from the moon. Remember these words. So far we are still orbiting the Moon, just with a more elliptical orbit.
To get from the Moon to the Earth, we need to make this orbit more and more elliptical – increase that apoapsis (point furthest from the moon) more and more until the apoapsis is now in the Earth’s sphere of influence, instead of the moon.
We also have to worry about direction here – I can’t just increase my apoapsis at some random point in the orbit and expect it to be okay. I need to make sure that my apoapsis actually meets up with Earth. It is not as simple as making the apoapsis the point that is nearest to Earth at the time I turn my rocket engines on, because as we know the moon is orbiting Earth, so by the time we get to that apoapsis the Earth will be somewhere else. Fortunately, the solution is just to do the whole maneuver later in our orbit around the moon. Like, imagine you are throwing a football to a friend, but that friend is moving in a circle around you. You throw it to where they will be (off to the side) instead of where they are right now (straight ahead). This concept works the same for orbits.
Once we have our elliptical orbit set up where the apoapsis is pretty close to where Earth will be relative to the moon, we simply turn off our engines and wait until we get near to that apoapsis. Depending on the exact specifics, we may now be caught in a new orbit – a highly Elliptical one around Earth, or we may be just doing a bit of a flyby where we bend around the Earth a bit. Regardless, when we get into Earth’s orbit there will be a new periapsis (the point in the orbit closest to Earth). Here, we can do a “retrograde” burn – that means face away from our direction of travel (which would be parallel to Earth) and fire our rockets. This will lower the apoapsis (which is also a new apoapsis – different to the one we had in our orbit around the moon), and make the orbit less elliptical, eventually even near circular if we burn those rockets long enough. From there we can do another retrograde burn until our periapsis (now at the opposite side of our orbit) intersects with Earth’s atmosphere. We can travel along that path and let the atmosphere slow us down, and activate our parachutes, and land close to where we intended.
There are definitely other ways we could do maneuvers to go from the moon to Earth, of varying efficiencies, but this is one of them!
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