# Doppler Effects

A ground-based observatory is not operating in a non-inertial frame of reference - that is, from an outside point of view it is moving at a variable velocity.  Depending on the longitude, latitude and time of day, the relative velocities of ground-based observatories in the direction of an observed object are different for different locations.  These different velocities cause a doppler shift on the observed pulse period of the pulsar which is unique to each observatory at any point in time.  Pulse periods thus measured by an ground-based observatory are termed 'topocentric'.

In order to 'normalise' the time of arrival of pulses (which also means the stated period of the pulse) to facilitate exchange of data between observatories, topocentric observations are corrected to an inertial frame of reference.  This frame of reference is taken to be the Solar System Barycentre - the centre-of-mass point around which the Sun and its planets revolve.  This inertial frame of reference actually moves slowly in time as the planets orbit (and so is not a 100% true-blue inertial frame of reference) with the bulk of the 'wobble' coming from the effects of Jupiter (1/1000th the mass of the Sun and 2.5 times the combined mass of all the other planets).

For amateur pursuits this 'wobble' can be ignored as it takes many years and only causes ~0.05 ppm doppler shift.

It is important to note that the periods quoted in pulsar data (e.g. the ATNF Pulsar Catalogue) are 'barycentric'.

In the pursuit of detecting known pulsars, the observational data received will be 'topocentric'.  In order to convert predictions expressed in barycentric form into the topocentric equivalent for the purpose of epoch folding at the correct period to reveal a pulse, other orbital effects must be taken into account.  The annual orbit around the Sun of the Earth produces significant doppler shift on the pulse period of a pulsar, depending on the orientation the observed pulsar w.r.t to the axis of the Earth's orbit around the Sun.  The magnitude of the diurnal doppler shift is dependent on the product of the cosine of the declination of the pulsar and the cosine of the latitude of the observatory. For Vela the annual doppler shift caused by the Earth's orbit around the Sun has a range of ~ ±48 ppm.  The diurnal doppler shift for Vela for HawkRAO (latitude -34) is ~ ±1 ppm.  There is a small monthly doppler caused by the Earth/Moon barycentre, but this only amounts to ~ ±0.02 ppm and can be ignored for amateur purposes.

Failure to take these doppler effects into account can prevent finding the correct folding period - hence a failure to detect a pulsar signal.  Most amateurs (and professionals) use some version of TEMPO to calculate the current topocentric period of the observed pulsar for their individual observatories.