`a_"rad" = (4*pi^2* r )/ "T" ^2`

Enter a value for all fields

The Orbital Radial Acceleration calculator computes the radial or centripetal acceleration (a_rad) of an orbiting body given the period (T)  and the radius (R). 

INSTRUCTIONS: Choose units (e.g. milliseconds or years) and enter the following:

• (T) Period of Orbit
• (r) Radius of Orbit

Radial Acceleration (a_rad): The calculator returns the centripetal acceleration in meters per seconds squared (m/s²).  However, this can be automatically converted to other acceleration units (e.g. feet / meters squared) via the pull-down menu.

The Math / Science

The formula for orbital radial acceleration based on orbit radius and period is:

    `a_(rad) = (4*pi^2*R)/T^2`

where:

• a_rad = Orbital Radial Acceleration
• R = Radius of Orbit
• T = Period of Orbit

Astronomy Calculators

• 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
  • (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
• 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
• Luminosity and other Formulas
  • Distance from absolute and apparent magnitude
  • Radius from Speed and Period
  • Speed of Circular Motion
  • Hubble Time
  • Luminosity from Mass