# Dimensionless units

David Berry dsb at ast.man.ac.uk
Fri Feb 18 08:00:35 PST 2005

```Martin,

> >         It would seem reasonable that a unit conversion scheme should be
> > able to determine the conversion from Jy/sr to Jy/arcmin**2 without needing
> > UCDs. The conversion is obviously just a simple scaling factor - no need
> > for any extra physics or UCDs or anything. But since these two units have
> > the same MLT dimensions, how can the conversion be determined on the basis
> > of a dimensional analysis alone? Introducing Angle as a dimension along
> > with Mass, Length and Time could do it.
>
> Hi David
>
> I understood that a scaling factor was part of the dimension-based unit
> converters (we can't do any unit conversions otherwise?)  So converting
> from Jy/sr to a dimension equation will give the same result as converting
> Jy/arcmin^2 to a dimension equation, as the scaling values used for radians
> and arcmins will be different.

But the scaling factor as I understand it is just the ratio of the units
you want, to the SI units implied by the dimensional analysis. That is,
The DIMEQ for "Jy" is "MT-2", implying SI units of kg/s/s, and the
corresponding SCALEQ value of 1.0E-26 means that 1 Jy is 1.0E-26 kg/s/s/.
But since angle does not enter into the dimensional analysis, neither will
it enter into the scaling factor. So I would expect Jy/sr and Jy/arcmin**2
to have the same scale factor.

> However you can, in principal, ask a dimension-based unit converter to
> convert from Jy/sr to Jy, and it will not be able to tell you that this is,
> at first glance, just silly.

Is this progress, given that a straightforward string parsing system could
tell you this?

David

```