This is an experience of calculating BVRI photometric magnitudes of Uranus, from my observations of December 9th, 2018. With no experience at the time, I took as much star spectra as I could, in Pisces, at a declination as close as possible to that of Uranus. Here is a strip from the Sky Chart software where I have identified the targets:

In yellow is the G2V star that has been used to calculate the reflectance spectrum of Uranus (read on my blog). In blue is a B9 star that looked interesting because as any blue star it can provide a spectrum very easy to correct. It was also very close to Uranus. In red, finally, are stars that looked interesting for photometry:

1) They are provided with BVRI catalogue magnitudes, and not variable

2) They are of not too far from Uranus's color, or the Sun (cool stars F to G)

Among them, HD11592 looked as the most interesting, because of its proximity to Uranus and similar declination (this is indeed the star that served me as reference to calculate a spectrum in absolute flux). HD3088 is found as well at a very close declination but was far in term of right ascension, and was so observed a few hours before the planet, an interval of time that could facilitate any change in atmospheric transparency that would bring inaccuracy in the measurements. Finally, HD3861 and HD7047 cumulate both problem, far in RA and at a significantly lower declination. None the less, I have used all four stars to calculate the magnitudes, just in order to make some tests and it was interesting.

Method used to calculate the magnitudes of Uranus

I have used my experimental method of a complete photometric spectrum and I have explained here how were calculated the transformation coefficients. Here is the data from the reference stars:

The equation of differential photometry is the one proposed by the AAVSO in their CCD manual:

Vuranus = (v_uranus - v_star)+Tv_bv * (Tbv * (b_ura - v_ura)) + Vstar

It is adapted for each BVRI band. Here are the results. Uranus was supposed to be of V = +5,8 at the time of observation (but the other color bands are unknown):

(The spectrum in absolute flux is just for illustration: the magnitudes are calculated with an ADU spectrum as explained in a previous article).

The V and B mag values look quite consistent, with very few variations. The R and I magnitudes are more inaccurate. It is not easy to know why it is so. In general, R and I photometry looks to be a more uncertain world than V and B.

It is also interesting to note that the two stars found at the same declination than Uranus (11592 and 3088) both give close values, even identical for B and V, and that the two stars found at a lower declination (and then a thicker airmass) look to show that Uranus is somewhat brighter, at least in V and I. One explanation would be the difference in airmass but I can't be sure of that at this time of my learning curve.

This work will be repeated during the coming 2019 apparition.

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