Try to land InSight on Mars (without exploding)

NASA has just parked its InSight lander on Mars. Yes, March is a big problem because many missions on Mars have not succeeded. So it's no wonder that Mars missions thrill me.

For this particular mission, the lander, protected by a heat shield, used the atmosphere of Mars to slow down. After that, he deployed a quick parachute to further reduce speed. Finally, the landing gear detached from the parachute and made the last part of the trip using rockets to control its descent.

Now, for the real question, though: could you be responsible for landing InSight? And if you did a manual landing, would the robot survive? Let's find out.

Before entering the game, let's examine basic physics. To keep it manageable, I focus on the part of the landing propelled by a rocket. During the descent of the spacecraft, two forces act on it. There is the descending gravitational force and an upward force of the probe rockets. The gravitational force depends solely on the local gravitational field and the mbad of the spacecraft. On Mars, this gravitational field is a little lower than on Earth, with a value of about 3.71 Newtons per kilogram (against 9.8 N / kg on Earth). This gravitational field is essentially of constant strength as long as you are near the surface of Mars.

Although the gravitational field is constant, the mbad of the spacecraft is not. By using his rockets, he loses mbad (because the engine of the rocket works by drawing fuel). This means that the gravitational force also changes a bit – but of course, the whole spacecraft is not made of fuel. The total mbad of the fuel is only about 16% of the total mbad.

The changing mbad of spacecraft also affects its motion. According to the principle of momentum, the total force (gravitational plus rocket) is equal to the rate of change over time of the momentum. However, momentum is defined as the product of mbad and velocity. Thus, a constant net force on the spacecraft will mean a momentum that changes at a non-constant rate as the mbad changes. Yes, it becomes complicated.

Well, let's move on to action. Here is how it works.

• Start with the fully powered vehicle 50 meters above the ground.
• You must adjust the thrust of the rocket
• . The change of speed of the rocket depends on the amount of thrust.
• The variation of the fuel mbad also depends on the amount of thrust of the rocket.
• You want the rocket to reach the ground while it is moving at less than 1 m / s (it should actually be slower).

That's all. Click "Run" to begin and then adjust the slider down for rocket thrust. The program also displays the vertical speed and the amount of fuel remaining. It is essentially a dimensional version of the clbadic video game Lunar Lander.

It is more difficult than it seems. The problem is that we often think of a direct link between force and movement, so that a greater force speeds it up. Aha! Not so fast. In reality, a greater force makes a bigger CHANGE in motion. As the undercarriage goes down, you need to increase the force to prevent it from accelerating as it falls. But if you give it too much thrust, the LG slows down so much that it starts to accelerate in the opposite direction. It's not a landing, it's a take-off.

Let's move on to some homework. See if you can bring the undercarriage to the ground (safely) in the shortest time. Now, try to create an algorithm for the magnitude of the thrust (not controlled by the user) that makes the landing as short as possible. It'll be fun.

Still more beautiful cable stories