If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## NASA

### Unit 2: Lesson 3

Orbital mechanics

# Circular orbits

## 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 left parenthesis, 0, comma, 0, right parenthesis 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, comma, 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:
\begin{aligned} x = t \times cos(\theta) \\ y = t \times sin(\theta) \\ \end{aligned}
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.
✏️ The program below is an almost-working simulation of a planet orbiting around a star. Find the line of code that is currently commented out, remove the slashes, and watch it go!

## Want to join the conversation?

• Who came up with cartesian coordinates?
• Rene Descartes came up with the Cartesian Coordinate System. He was a brilliant mathematician but a flawed philosopher because he tried to apply math to philosophy.
• i dont understand this i dont like this part in math
• You don't need to know how to code a circular orbit for this lesson.
(1 vote)
• Great Article!
But how can i achieve this for a elliptical orbit?

Thanks ! :D
• Why! why does this have to be so haaardddd!
(1 vote)
• Could there be any chance the Mr. Khan could make a video for these concepts because it is a bit confusing just reading it.
(1 vote)
• what is t in the equation(x = t x cos (0)) ?
(1 vote)
• I think there may be a typo in the description before the equation. Here, _t_ should be the radius of the circle.
(1 vote)
• It'd be useful to provide quick definitions of cosine and sine in the article. In a right angled triangle, the cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse. In a right angled triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.
(1 vote)
• How/what would you define x and y as?
(1 vote)
• Is there a quicker way to do this
(1 vote)