Editing Relativistic Doppler effect (section)

==== One object in circular motion around the other ====
[[File:Transverse Doppler effect scenarios 5.svg|thumb|300px|Figure 5. Transverse Doppler effect for two scenarios: (a) receiver moving in a circle around the source; (b) source moving in a circle around the receiver.]]

Fig.&nbsp;5 illustrates two variants of this scenario. Both variants can be analyzed using simple time dilation arguments.<ref name=Morin/> Figure&nbsp;5a is essentially equivalent to the scenario described in Figure&nbsp;2b, and the receiver observes light from the source as being blueshifted by a factor of <math>\gamma</math>. Figure&nbsp;5b is essentially equivalent to the scenario described in Figure&nbsp;3, and the light is redshifted.

The only seeming complication is that the orbiting objects are in accelerated motion. An accelerated particle does not have an inertial frame in which it is always at rest. However, an inertial frame can always be found which is momentarily comoving with the particle. This frame, the [[Proper reference frame (flat spacetime)|''momentarily comoving reference frame'' (MCRF)]], enables application of special relativity to the analysis of accelerated particles. If an inertial observer looks at an accelerating clock, only the clock's instantaneous speed is important when computing time dilation.<ref name=Misner>{{Cite book|last1=Misner | first1 = C. W. | last2 = Thorne | first2 = K. S. | last3 = Wheeler | first3 = J. A|title=Gravitation|year=1973|page=163|publisher=Freeman|isbn=978-0716703440}}</ref>

The converse, however, is not true. The analysis of scenarios where ''both'' objects are in accelerated motion requires a somewhat more sophisticated analysis. Not understanding this point has led to confusion and misunderstanding.