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Illustration 3.6: Circular and Noncircular Motion

Please wait for the animation to completely load.

A planet (green) orbits a star (yellow) as shown in the two animations. Restart. One animation depicts the uniform circular motion of a planet and the other one depicts the noncircular motion of a planet (position is given in 103 km and time is given in years). This Illustration will compare the two motions by focusing on the velocity and the acceleration of the planet in each of the animations.

Start the uniform circular motion animation and watch the planet's motion. How would you describe the motion of the planet (consider velocity and acceleration)? The speed of the planet is certainly a constant since the motion of the planet is uniform. But using our usual xy coordinates, the velocity certainly changes with time. Recall that the term velocity refers to both the magnitude and direction. However, if we use the radial and tangential directions to describe the motion of the planet, the velocity can be described as tangential and the acceleration can be described as being directed along the radius (the negative of the radial direction). Click here to view the velocity vector (blue) and the black line tangent to the path. Click here to view the acceleration vector (red), too. Notice that the acceleration vector points toward the star at the center of the circle.

Start the noncircular motion animation and watch the planet's motion. How would you now describe the motion of the planet (consider velocity and acceleration)? The speed of the planet is certainly no longer a constant since the motion of the planet is no longer uniform. Again using our usual xy coordinates, the velocity certainly changes with time since now both the direction and the magnitude change. However, if we use the radial and tangential directions to the path of the planet, the velocity can be described as tangential and the acceleration can be described as being directed along the radius. Click here to view the velocity vector (blue) and click here to view the acceleration vector (red), too. Notice that the velocity and the acceleration are no longer perpendicular for most of the orbit of the planet.

Notice that between points A and C the planet is speeding up, and between points C and A the planet is slowing down. This means that at points A and C the tangential component of acceleration is zero. It turns out that for a planet orbiting a star (if there are no other planets or stars nearby) the acceleration of the planet is directed exactly toward the star whether the motion of the planet is uniform or not.

Illustration authored by Aaron Titus and Mario Belloni.

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