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Measuring the Universe

# Animated circles

If we assume that a planet is traveling in a perfect circle, how could we simulate this motion? First, let's assume that our circle is centered at coordinates (0, 0) and has a radius, r.

Planet radius r away from the center of the circle (0,0)

How can we simulate the motion of a planet orbiting around the perimeter of a circle?

Sweeping a planet around the circumference

Notice the position of the planet is based on the distance from the center (radius r) and the angle it has swept around the circle (0 to 360 degrees). These are known as polar coordinates.

However, in order to draw this planet we need to define the planet's position using x,y coordinates. These are known as cartesian coordinates

Cartesian coordinates of the planet's position (x,y)

The length of the triangle is x, the height is y, the hypotenuse is r and the angle at the origin is the planets current angle around its orbit. Now we just need to find the distance of x and y using basic trigonometry:

x = r * cos(θ)

y = r * sin(θ)

To animate the motion of a planet we can increment the angle θ by one degree at each frame and the planet will move around the origin in a circle. Your turn!

Next we can try animating our own planet in the upcoming challenge.