Speed of Circular Motion

The Speed of Circular Motion calculator computes the speed (s) of a particle or point in uniform circular motion based on the radius (r) of the orbit and the period of rotation, T.

INSTRUCTIONS: Choose units and enter the following:

• (r) Radius defining Orbit of Circular Motion
• (T) Orbital Period of Rotation

Speed of Circular Motion (v): The calculator computes the velocity in meters per second.  However this can be automatically converted to numerous other velocity units via the pull-down menu.

Exercise: Choose Years as the units for period, and Astronomical Units as the unit for radius.  Then enter 1 as the value for both.  The resulting velocity is the speed that the Earth travels about the Sun.  Then use the pull-down menu to see the result in miles per hour (mph).

The Math

The angular frequency is the number of increments of `2*pi` radians (`2*pi` radians is one complete rotation) divided by the period of the rotation, outputting simply rotations per unit time.

The distance around the circular path is ` d = 2*pi*r` (`2*pi` radians is one complete rotation) and then  `v = d / T` is the velocity.

So, `v = (2*pi*r) / T`  

Exoplanet Functions:

• Separation from Mass and Period
• Speed of Circular Orbit
• Mass of Exoplanet from Mass and Speed of Star and Planet Speed
• Mass of Exoplanet from Stellar Mass and Radius around barycenter and planetary orbit radius
• Mass from Period and Separation
• Mass from Speed and Separation
• Radius from Speed and Period
• Speed from Delta Lambda and Lambda
• Distance from Apparent and Absolute Magnitude
• Flux Ratio from Magnitudes
• Planetary Temperature
• Goldilocks Zone

Astronomy Calculators

• Centripetal Acceleration as a function of tangential velocity and radius, CLICK HERE.
• Angular Frequency as a function of orbital period,.
• Radial Acceleration as a function of orbital period and radius, CLICK HERE.
• Acceleration in non-uniform Circular Motion, CLICK HERE.

¹

1. ^ Young, Hugh and Freeman, Roger.  University Physics With Modern Physics.  Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 89, eq 3.29