Fizziks! - A Fun Physics game
Provided by The Problem Site!

Gravitational Forces - Fizziks Tilt Game

Do you know how to calculate the force due to gravity between two bodies? It is directly proportional to the masses of the two bodies, and inversely proportional to the square of the distance between the two bodies. In other words, with more massive objects, the force due to gravity is greater, and as the objects get further apart, that force gets smaller at a fairly rapid rate.

There's also this funky thing called the gravitational constant (G = 6.67300 × 10^-11 m³ kg^-1 s^-2) included in the equation, so the total force could be written like this:

F = G×m₁m₂ / r².

Playing Fizziks Tilt

In the Fizziks Tilt game, some levels contain planets. Obviously, knowing that the force on the ball gets larger the closer you get to the planet, in most cases (if possible) you'll want to keep your distance.

In some cases, planets can help you out. If the level has a corner, and there is a planet on the inside of that corner, the gravitational force will help you make the corner without using as much energy.

The calculation is done as a series of approximations. Remember that at every instant in time, the gravitational force is changing, based on the changing distance between the two objects. Since your computer deals in discrete units of time (the amount of processor time it takes to make everything move around the screen), the game calculates the force at one moment in time, and makes the approximation that this force will remain constant until the next time it "gets around to" calculating the force again.

Thus, while the movement of the marble is a very good simulation of real gravitational attraction, it is not perfect.

The error in approximation becomes most clear when the marble gets closest to the planet. This makes perfect sense: when the marble is closer, the forces are larger, and therefore the marble moves a greater distance in a unit of time, meaning that by the next time the computer gets around to calculating forces, the marble is off course.

But, since you can't get very close to a planet without colliding with it, the approximation errors are insignificant.

Sample Level With Planets

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