We're going down, I'm yelling timber

I suppose this is my last entry concerning my spacefaring adventures, but worry not, for I still have things to say! It turns out, this planet is really fucking boring, there¡¯s absolutely no one and nothing here, and it¡¯s cold as fuck, so I¡¯m gonna write the rest about my amazing and non-faulty landing that got me exactly where I wanted, then I¡¯m going to write about something that is relatively cool.

So, landing. It was pretty uneventful to be honest. I dropped down and deployed my parachute and fell down at a leisurely pace. I mean, I didn't even land close to my intended landing site, but as long as I'm down, who cares, right? (I care, but not enough to fix it)

On top of there not being much to write about, the video software didn't work properly either, so the best I can do is a bunch of cool pictures of my landing across the planet:

So; the one thing I did: calculate the force of some kind of landing engine if that became necessary

You see, if I had been landing on an asteroid or some planet with ridiculously light atmosphere, I might have needed more than a parachute to slow down. I didn't need that, but I did the calculations anyways because I was bored on the trip. Sue me.

the trick is that we want no acceleration; we want to be going downwards at a steady pac. That's why we want the upwards force to be equal and opposite to the downward force:

The downward force is pretty much just gravity:\(F_G\), which should be countered by the parachute drag:  \(F_D \). Since we're working with the assumption that \(F_D \) is not enough we have to add some other force, \(F_L \), to adjust. This can be added by some really big rocket that spews out hot rocket fuel, but since the atmosphere is made out of mostly methane and oxygen, I decided to instead use cold, compressed air just to be safe.

so adding the new term, we say that

    \(F_G = F_D + F_L\)

We can then define \(F_L \) by saying

    \(F_L = F_G - F_D\)

    \(F_L = G\frac{Mm}{r^2} - \frac{\rho_0Av_{safe}^2}{2}\), where \(v_{safe}\) is the safe speed, the speed we want to be landing with

    \(F_L = \frac{\rho_0A}{2}(\frac{2GMm}{r^2\rho_0A} - v_{safe}^2)\)

We could leave it at this, or we could recognize that one of the terms actually becomes the function for terminal velocity that we made earlier! (check my last post if ya wanna)

    \(F_L = \frac{\rho_0A}{2}(v_{term}^2 - v_{safe}^2)\)

So for the actual landing. I set some guidelines for how I wanted to do the landing, and made a simulation after that:

I would not:

• let the frictional forces from the air exceed 250000N, as that would tear my lander apart
• let the landing velocity exceed 3m/s, as that would blow up my lander
• land too far away from my originally planned landing site (I completely gave up on that one)
• fail at getting good footage (video fucked, but pictures happened, so I've got that going for me at least)

I made a simulation that dropped the lander off from my satellite (essentially fired it from a cannon just fast enough that it would lose all velocity in relation to the planet and fall straight down) and continually checked the drag force it was experiencing to see if everything suddenly broke until it was eventually just above the surface where I checked the speed to see if everything would break.

According to my simulation everything worked out, so I tried it out properly:

While it didn't burn apart, the strange thing was that I hit the surface with 0.8m/s, which means that I probably fucked up when calculating the density, and it is actually much denser than I expected. Might also not be made of lot sof methane and oxygen, so I might have just been able to use conventional thrusters, and I should also probably not try to breathe out there, just in case there's a bunch of noxious gases that I didn't know were there.

I'm pretty sure I ended up on the other side of the planet, though. meh, doesn't really matter, as long as I landed and got some hella cool pictures doing it.