`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

The Astronomy Calculator Suite includes functions that are useful for studying astronomy and include the following:

• Kepler's 3^rd Law formula                             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
• Small Angle Formula        Small Angle Formula    α = S / D
  • (α) - angle
  • (D) - distance to astronomical object
  • (S) - size or diameter of astronomical object
• Flux and Magnitude formulas
  • Change in Magnitude from Flux Ratio
  • Flux Ratio from Magnitudes
• Telescope formulas
  • Resolving Power of a Telescope
  • Magnification of a Telescope
• 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
• 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
• 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 provides the distance from the Earth to numerous astronomical bodies (e.g. Sun, Moon, planets, stars, Milky Way's Center and Edge, Andromeda Galaxy)
  • Astronomical Distance Travel Time Calculator computes the time to travel to distant parts of space at different velocities.
  • 3D Vector Calculator
  • Drake Equation Calculator
  • Seager Equation Calculator
  • Friedman Equation Calculator
  • Lagrange Points L1 and L2
  • Schwarzschild Radius
  • Hill Sphere Radius
  • Escape 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