Pulsar Topocentric Calculator

Estimates the topocentric (observed) pulse frequency for a selection of strong pulsars, given the observer's Latitude and Longitude, and UTC time. See below for instructions. Also be sure to read the Notes for caveats.

Pulsar Topocentric Pulse Frequency Calculator
UTC (DD/MM/YYYY hh:mm:ss):
Observatory Latitude (dd mm ss.s):   N   S  
Observatory Longitude (dd mm ss.s):   E   W  
Pulsar RA (hh mm ss.s):
Pulsar DEC (±dd mm ss.s):
Pulsar Type:
   
Calculate
   
Barycentric Pulse Frequency (Hz):
 Topocentric Radial Velocity (±km/s):
Topo Frequency Doppler Shift (±ppm):
Topocentric Pulse Frequency (Hz): (±2 ppm)
Topocentric Pulse Period (ms): (±2 ppm)
 
Binary Pulsar Information: Orbital Doppler Shift is automatically included in the output results above
Orbital Period (days):

 

Maximum Orbital Doppler (±ppm):
Orbital Radial Velocity (±km/s):
Orbital Doppler Shift (±ppm):
 


Presets
   
Set Pulsar:
Set City/Town/Observatory:
   

Instructions: Via the drop-down 'Preset' menus provided, set the target pulsar to one of the relevant pulsar candidates for amateur observers. Pulsar candidates are limited to the pulsar drop-down list entries as they need to be associated with their individual ephemeris parameters. (Note: other pulsars can be added if requested via the email address in 'Contact').

The latitude/longitude for a selection of main cities/towns/observatories can be selected from the 'Presets' menu, or can be manually entered in free format sexagesimal  - (note: preset public observatory locations are exact, but the location accuracy of preset private stations is limited to the closest town to preserve privacy). Only fields highlighted in green are editable.

Time (UTC) can be set by the 'UTC Now' button or entered manually in the format of DD/MM/YYYY hh:mm:ss (observe format exactly).

Available Calculations: Two different calculation modes are provided...

  1. "Now" shows a single result for the set UTC date/time.
     
  2. "Day:xm" opens a new window with a table covering 24 hours starting from hour/minute 00:00 of the set UTC date with an increment of 'x' minutes (options for 1, 5 and 15 minute increments).  The fields are MJD, UTC Date and Time, Orbital Radial Velocity (km/s) and Orbital Doppler Shift (ppm).
     
  3. "100 Days" opens a new window with a table covering 100 successive days starting from the set UTC date at the fixed time of 00:00 UTC each day. The fields are MJD, UTC Date and Time, Orbital Radial Velocity (km/s) and Orbital Doppler Shift (ppm).

 The tables can be printed - just be sure to enable 'background graphics' to print the highlighting.

Doppler Effect: For +ve velocities (moving away) the period Doppler shift is +ve. Conversely, for -ve velocities (moving towards) the period Doppler shift is -ve.

Derived from: Old FORTRAN code ("DOP") to C# to Javascript plus JS code from many sources. Please report errors or discrepancies with other sources.

Pulsar Ephemeris Data: ATNF Pulsar Database (Manchester, R. N., Hobbs, G.B., Teoh, A. & Hobbs, M., AJ, 129, 1993-2006 (2005)) - except where later epoch data is available.

J0437-4715 Orbital Data: "Precision timing of PSR J0437−4715: an accurate pulsar distance, a high pulsar mass and a limit on the variation of Newton’s gravitational constant": J. P. W. Verbiest, M. Bailes, W. van Straten, G. B. Hobbs, R. T. Edwards, R. N. Manchester, N. D. R. Bhat, J. M. Sarkissian, B. A. Jacoby and S. R. Kulkarni.

Notes:

  • Pulsar timing is referenced to a barycentric (centre of gravity of all objects in the solar system) frame of reference. If use is made of the pulsar parameters from, say, the ATNF Pulsar Database, a velocity correction is needed to convert to a topocentric (earth-based observer) pulse timing for accurate epoch-folding.  Strictly speaking, the calculation above is the correction from heliocentric (centre of the sun), but the difference (< 0.05 ppm) between barycentric and heliocentric frames of reference is negligible for amateur purposes and in any case the difference is less than the accuracy of the algorithm.
     
  • Binary Pulsars: some pulsars are in binary systems (e.g. J0437-4715) which means that the binary orbital Doppler must be added to the period calculated here. The orbital Doppler value for the date/time is calculated and applied to the period to arrive at the actual topocentric period. The light blue highlighted fields are only active when a binary pulsar has been selected from the drop-down list.

    Note: Currently there is only one candidate (J0437-4715) - being the strongest binary pulsar and possessing and almost perfectly circular orbit making calculation of orbital a simple solution of a sinusoidal function. Binary pulsars with eccentric orbits require a more complex solution.
     
  • The young Vela and Crab pulsars are 'glitchers'. Vela can suddenly spin-up in frequency by as much as 3 ppm - although this happens, on average, only every 2.5 years. In the case of Vela, the calculation here adds in the average glitch behaviour to produce a result which, over time, has minimal excursions from the actual spin frequency. Consequently, the result will swing either side (±1.5 ppm) of the actual spin frequency dependent on when the last glitch has occurred. Note that the TEMPO Vela result can be more than 3 ppm out depending on whether the TEMPO ephemeris data used is updated after the last glitch(es).  For the Crab pulsar no glitch correction is applied, but the ephemeris data will be updated periodically (once or twice a year) to the latest Jodrell Bank data while it is available. Note that both pulsars are slowing down quite rapidly - the Vela pulsar by about 3.3 ppm/month, and the Crab Pulsar even more so at about 32 ppm/month.
     
  • Note that the precision in the results exceeds the accuracy.  This deviation from mathematical purity is a programming decision which avoids the need to provide a variable number of significant digits depending on the period calculated.
     
  • While the calculation of a pulsar topocentric correction velocity is exactly the same as the calculation of radial velocities associated with VLSR, it excludes the velocity of the sun.  Therefore, this calculator is not suitable for determining doppler correction for emission lines (HI, CH3OH, OH, etc) - which requires the sun velocity.