# NED's Calculators

## Introduction

Most redshifts for extragalactic objects are published as "heliocentric" redshifts -- that is, the earth's rotational and orbital motions have been removed from the measured velocity. It is often necessary to further "correct" the redshifts for other motions: Galactic rotation, peculiar motion of the Galaxy within the Local Group, "infall" of the Local Group toward the center of the Local Supercluster, and motion within the reference frame defined by the 3K microwave background radiation. This calculator enables you to make these corrections as needed. NED has several pre-defined apex vectors that you may use, or you may input your own apex vector.

NOTICE: Conversions between redshift and apparent velocity, and decomposition of an observed redshift into its physical components, are currently computed using traditional approximations (see Huchra 2008) applicable for low redshifts. Results accurate at all redshifts, accounting for cosmological effects (see Davis et al. 2019), are planned for a future NED update.

## Data Entry

Enter the input coordinates in decimal degrees or in sexagesimal units. Input is checked by a software interpreter, and re-formatted for display. The best way to gauge these interpreters is to test them; they will post an error message if the input is not interpretable.

Examples of supported coordinate formats are

• 09h55m52.7s +69d40m46s
• 09:55:52.7 +69:40:46
• 09 55 52.7 +69 40 46
• 148.969687d 69.679383d

Select the input coordinate systems that you want to use. It may be one of the following:

• Equatorial (default)
• Galactic
• Supergalactic

The equinox may be any date between AD 1500.0 and AD 2500.0. If you do not prepend a "B" (Besselian dates) or "J" (Julian dates) to the equinox, the calculator will use Besselian dates for equinoxes before 1990.0, and Julian dates for equinoxes after 1990.0.

Enter the redshift you wish to correct in velocity units of km sec-1.

If you wish to use one of NED's pre-defined apex vectors, choose the one defining the reference frame to which the redshift is currently referred by clicking on the "From" button and choosing one of the reference frames named there. Do the same for the "To" button, choosing the reference frame to which you wish to correct the redshift.

If your redshift is currently referred to a velocity frame for which NED does not provide an apex vector, click the radio button and enter your apex vector (coordinates and coordinate system, and velocity) in the boxes provided.

## Results

Click on "Calculate" to run the calculator. It will replace the input page with a new page showing your input parameters, the type of correction you requested, and the apex vector used, as well as the output velocity. If the calculator does not recognize some aspect of your input, it will display an error message. In this case, use your browser's "Back" button to return to the input page to correct the input.

## Notes

NED converts velocities from one reference frame to another using the standard equation

Vcon = V + Vapex [sin(b) sin(bapex) + cos(b) cos(bapex) cos(l - lapex)]

where l and b are the object's longitude and latitude, V is its unconverted velocity, and the apices (with Galactic coordinates) of the various motions are given as

 Conversion lapex bapex Vapex Source Heliocentric to Galactocentric (GSR) 87.8 deg +1.7 deg 232.3 km/sec RC3 Heliocentric to Local Group 93 deg -4 deg 316 km/sec AJ 111, 794, 1996 Heliocentric to 3K Background 264.14 deg +48.26 deg 371.0 km/sec ApJ 473, 576, 1996

Courteau and van den Bergh AJ 118, 337, 1999 have a recent review of the solar motion with respect to the Local Group.

## Introduction

This is an easy-to-use coordinate transformation, precession, and position angle calculator provided for your convenience. It is flexible enough to convert accurately between Besselian and Julian equinoxes, taking the epoch of observation into account when needed. It assumes that Besselian dates refer to the FK4 system, that Julian dates refer to the FK5 system, and makes the appropriate transformations. Though the International Celestial Reference Frame (ICRF) is not explicitly supported, the FK5 optical system is consistent with ICRF to within the known errors of the FK5 system (see e.g. Ma et al. AJ 116, 516, 1998).

The coordinate calculator also returns the foreground Galactic extinction at your input position using the Schlafly & Finkbeiner 2011 (ApJ 737, 103, 2011) recalibration of the Schlegel, Finkbeiner & Davis 1998 (ApJ 500, 525, 1998; SFD98) extinction map. The original SFD98 extinction values are also returned for comparison purposes. See this FAQ page for more information and cautions on using the extinction values returned by the calculator.

## Data Entry

Select the input and output coordinate systems that you want to use. They may be any of the following:

• Equatorial (default)
• Ecliptic
• Galactic
• Supergalactic

The input and output equinoxes may be any date between AD 1500.0 and AD 2500.0. If you do not prepend a "B" (Besselian dates) or "J" (Julian dates) to the equinox, the calculator will use Besselian dates for equinoxes before 1990.0, and Julian dates for equinoxes after 1990.0.

If you know the epoch of the observation (between AD 1500.0 and AD 2500.0), enter that in decimal years. The default epoch, 1950.0, is adequate for all but high-precision conversion between the FK4 and FK5 systems.

Enter the input coordinates in decimal degrees or in sexagesimal units. Input is checked by a software interpreter, and re-formatted for display. The best way to gauge these interpreters is to test them; they will post an error message if the input is not interpretable.

Examples of supported coordinate formats are

• 09h55m52.7s +69d40m46s
• 09:55:52.7 +69:40:46
• 09 55 52.7 +69 40 46
• 148.969687d 69.679383d

The position angle (default is 0 degrees) is optional. Enter it in decimal degrees if you need to precess it.

## Results

Click on "Calculate" to run the calculator. It will replace the input page with a new page showing your input parameters as well as the output. If the calculator does not recognize some aspect of your input, it will display an error message. In this case, use your browser's "Back" button to return to the input page to correct the input.

## Notes

Different systems may be used for input and output; for example, equatorial B1950.0 coordinates on the FK4 system may be precessed and transformed to ecliptic J2000.0 coordinates on the FK5 system.

Position angles are in degrees, measured from north through east.

The precession and coordinate conversion routines were written by J. Bennett who has also provided extensive documentation on them.