As you near the surface you must shut down the engine and then quickly pulse it several times to keep your velocity above -5 m/s (but never above 0 m/s) during the last few metres of descent. Only a few lines of code are needed to implement the core simulation. (this is Newton's second law). Then at the end of the simulation loop add the statements of the form: We are going to assume that this thrust is a constant. Version 1. Determine the neutral gravitation point between the Earth and the Moon, and plan to reach this point with a small positive velocity. A simple implementation of the above model is given in the QBASIC source code It it thus necessary to fire almost as soon as you pass the 1.7 km mark or it will be too late.

The first is where the lander is in free fall and its acceleration a = -g where g is the value of the lunar gravitational acceleration.
Log in sign up. We assume that initially the craft is in free fall. The simulation itself also requires a lot more programming skill. The simplest type of analog indicator is a bar graph. There are several simple modifications that can be made to the basic lunar lander presented here to explore other aspects of spaceflight.

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In actual practice, when the rocket engine is fired for lift-off, the spacecraft velocity is slowly built up. At the end of these calculations we print out the current time, height, velocity and fuel, until the lander hits the lunar surface. To improve the simulation one can add 'meters' showing the parameters of height, velocity and fuel in analog format. The aim of the simulator of course, is to soft land the spacecraft on the lunar surface before the fuel runs out (ie f = 0 ). However, in practice, this situation can never be achieved, and even if it could, would result in death for astronauts - people don't like the very high accelerations necessary to achieve this. To implement the simulation we consider the motion of the lander in small segments of time Δt. The equations that we must compute for each small amount of time are: If an atmosphere was present, the equations would become more complicated. We also have to choose the acceleration that the engine produces. In this state the astronauts inside will be weightless. Without the graphics of todays computers, the modest requirements of this simulation could be implemented on the earliest PC's and even the early simple programmable calculators.

Although it is not important for our simulation, A = T / m where T is the thrust produced and m is the mass of the spacecraft. The mission is not simple, your little spaceship is attracted by the lunar gravity and if you go too fast, you will crash on the surface, simply. Be prepared however, in a real-time simulation such as this to take quite some time to reach that point! 4 comments. There is of course a minimum time and a minimum amount of fuel that you need to land softly on the lunar surface. Especially in situations where parameters are changing rapidly the eye-brain combination responds better to an analog presentation than a digital one. Lunar lander. More sophisticated additions would be to have a central screen displaying an image of the lunar surface, and have this move in response to a 2D joystick which would impart a velocity in the north-south and east-west directions. Because this is directed down toward the lunar surface and we have taken the positive direction of all our vectors to be up, the acceleration of the craft is negative or toward the surface of the moon. The first phase involves allowing the spacecraft to descend in free fall toward the surface. A basic program is presented and discussed as a core around which a more interesting simulation might be developed. At the end of the simulation the array can be written to a file where it can then be plotted at leisure. The lander has limited fuel f = F and the rate of using the fuel is directly proportional to the time that the engine is on.

In this first condition, the spacecraft will accelerate toward the lunar surface, the velocity will increase in a negative direction and the height will decrease. Thus for an optimum flight we allow the spacecraft to descend a distance of 8.4 km until it is 1.6 km above the lunar surface, at which time we fire the engines until we hit the lunar surface with zero velocity.

Our presentation here is devoted to explaining the educational side of the simulation - the physics and mathematics involved. This is because although they are being acted upon by lunar gravity they are falling at an acceleration that that gravitational force produces. One of the earliest 'space' games was known as 'lunar lander'.

Well, in the case of the Moon we are helped by the Earth.

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