`v = (2*pi* "r" )/ "T" `

Enter a value for all fields

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`  

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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

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Astronomy Calculators

Kepler's 3rd Law           T² = (4π • R³)/(G • M) (M) Mass of the system.  (T) Period of the orbit. (R) Separation distance between the two objects. (G) Universal Gravity Constant	Flux and Magnitude Change in Magnitude from Flux Ratio Flux Ratio from Magnitudes
Small Angle Formula         α = S / D (α) Angle (D) Distance from Size and Angle (S) Size of astronomical object	Telescope formulas Resolving Power of a Telescope Magnification of a Telescope Luminosity Luminosity from Stellar Mass
Mass formulas Mass from Luminosity Mass from Acceleration and Radius Mass from Speed and Separation Mass of extra-solar planet from mass of star, radius of star orbit and radius of exoplanet orbit Mass of extra-solar planet from mass and velocity of star and velocity of planet Black Hole Mass Calculator Black Hole Event Horizon Calculator	Other Formulas Distance from absolute and apparent magnitude Radius from Speed and Period Speed of Circular Motion Hubble Time Galaxy Recession Velocity Luminosity from Mass Hubble's Law Exoplanet Calculator  Orbital Radial Acceleration Distance to Barycenter Sakuma-Hattori Equation Astronomical Distance Calculator  Astronomical Travel Time Calculator  3D Vector Calculator Drake Equation Calculator Seager Equation Calculator Friedman Equation Calculator Lagrange Points L1 and L2 Schwarzschild Radius Hill Sphere Radius Escape Velocity Barycenter Distance
Relative Size Formulas Relative Size from Relative Temperature and Luminosity Relative Temperature from Relative Size and Luminosity Relative Luminosity from Relative Temperature and Size
Wavelength Formulas Velocity from shift in Wavelength and Unshifted Wavelength Wavelength Shift from Wavelength and Speed Blackbody Wavelength from Temperature Blackbody Temperature from Peak Wavelength Photon Energy from Wavelength Photon Wavelength from Energy Redshift Galaxy Recession Velocity

• 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