Editing Circular orbit (section)

==Circular acceleration==
[[:wikt:transverse|Transverse]] acceleration ([[perpendicular]] to velocity) causes a change in direction. If it is constant in magnitude and changing in direction with the velocity,  [[circular motion]] ensues. Taking two derivatives of the particle's coordinates concerning time gives the [[centripetal acceleration]]

:<math> a\, = \frac {v^2} {r} \, = {\omega^2} {r}  </math>

where:
*<math>v\,</math> is [[Kinetic energy|the orbital velocity]] of the orbiting body,
*<math>r\,</math> is [[radius]] of the circle
*<math> \omega \ </math> is [[angular speed]], measured in [[radian]]s per unit time.
The formula is [[Dimensionless quantity|dimensionless]], describing a ratio true for all units of measure applied uniformly across the formula. If the numerical value <math> \mathbf{a}</math> is measured in meters per second squared, then the numerical values <math>v\,</math> will be in meters per second, <math>r\,</math> in meters, and <math> \omega \ </math> in radians per second.