Saturday , October 1 2022

Try landing InSight on Mars (Without Exploding)


NASA just parked its InSight farmer on Mars. Yes, Mars. This is quite a big deal, because some Mars missions did not. It's no wonder I'm super excited about missions to Mars.

For this mission, landowners, protected by heat shield, used the Mars atmosphere to slow down. Then a high speed parachute was used to further reduce the speed. Finally, the farmer unloaded from the parachute and traveled the last part of the journey using rockets to control his descent.

Now for the real question, but: Could you be responsible for the InSight landing? What happens if you made a manual landing, should the robot survive? Let's find out.

Before we enter the game, let's go over basic physics. To keep this manageable, I focus on the rocket-driven landing part of this mission. During the descent of the spacecraft there are basically two forces acting on it. There is the downward gravity and an upward force from the spacecraft's rockets. The gravity strength depends only on the local gravity field and the spacecraft mass. On Mars, this gravitational field is a bit lower than the Earth, valued at approximately 3.71 Newtons per kilo (compared to 9.8 N / kg on Earth). This gravitational field is essentially constant in strength as long as you are close to Mars.

Although the gravity field is constant, the mass of spacecraft is not. Because it uses its rockets, it loses mass (because the rocket engine works by firing fuel). This means that the gravity strength also changes a little bit, but of course the whole spacecraft is not made of fuel. The total mass of the fuel is only about 16 percent of the total mass.

The growing mass of spacecraft also has an impact on its movement. According to the momentum principle, the total force (gravitations plus rocket) is equal to the speed of change of momentum. However, the moment is defined as the product of mass and velocity. Thus, a constant power of space on the spacecraft means a momentum that changes at a non-constant pace since the mass changes. Yes, it will be difficult.

OK, let's jump into the game. This is how it works.

  • Start with the spacecraft fully drifted and 50 meters above the ground.
  • You can adjust the rocket support.
  • The change in rocket speed depends on the amount of compressive force.
  • The change in fuel mass also depends on the amount of rocket power.
  • You want the rocket to reach the ground when traveling less than 1 m / s (it should actually be even slower).

That's all. Click "run" to start and then adjust the slider at the bottom of the rocket support. The program also shows vertical speed and amount of fuel left. This is basically a dimensional version of the classic video game Lunar Lander.

This is harder it seems. The problem is that we often think of a direct connection between power and motion so that a greater power makes it faster. A ha! Not so fast. In fact, a greater force makes a greater change in movement. When the farmer moves down, you need to increase the power to prevent it from falling quickly when it falls. But if you give it too much power, the landlord lowers so much that it actually begins to accelerate in the opposite direction. It does not land – it's over.

Now for some homework. See if you can get the farmer to the ground (safe) for a minimum of time. Try creating an algorithm for power (not user-controlled) that makes the shortest possible landing. It'll be fun.

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