Ganymed

Measurement of (1036) Ganymed rotation axis

The document summarizing the technique used can be accessed here.
Preliminary determination of rotation period has been done by Raoul Behrend with Courbrot software, see here.

Contributors are:
- Maurice Audejean (mpc B92)
- Jerome Caron (mpc C70)
- Francois Kugel (mpc A77)
- Emmanuel Conseil

Preliminary results

Measurement in	June-July 2011	August 2011	September 2011
from / to	21 June / 13 July	09 Aug / 01 Sept	08 Sept / 01 Oct
nb of nights	13	7	10
nb of Fourier harmonics	6	6	6
period (days)	0.428976	0.429330	0.429756
3-sigma uncertainty (days)	0.000025	0.000035	0.000024

Assumptions:
Results obtained with a Python equivalent of Courbrot software:
- simple script (~150 lines of code) thanks to the routine scipy.optimize.curve_fit which completely manages the least square fitting
- fit with a Fourier series at order 6. Fitting parameters are: period + 12 Fourier coefficients (cos and sin) + magnitude offsets to shift each measurement individually
- copy-paste of MPC ephemeris in a text file to get the distance asteroid / Earth. The propagating time of light is subtracted from the measuring times (small impact)
- scipy.optimize.curve_fit also gives the covariance matrix, the period uncertainty is thus also known (sigma=sqrt(variance))

The uncertainty on the period directly depends on the uncertainty of the magnitude measurements.
The magnitude error is estimated as the quadratic sum of two terms: (1) the rms noise of the obtained magnitude curve, (2) a value of 0.02 that represents all other errors (atmospheric effects, color of reference stars, interfering star when measuring flux, etc). The resulting period uncertainty is then multiplied by 3 to get a 3-sigma value.

June-July 2011:


Measurements (magnitude vs Julian date)	Lightcurve (magnitude vs rotation phase)

August 2011:


Measurements (magnitude vs Julian date)	Lightcurve (magnitude vs rotation phase)

September 2011:


Measurements (magnitude vs Julian date)	Lightcurve (magnitude vs rotation phase)

Updates

Dephasing (added 05 sept 2011):
If we keep the fit calculated with the June-July measurements, and put the August-September data on it we obtain the figure below. The shift is evident despite the slight change of shape of the lightcurve: as the period gets longer, the same magnitudes occur a bit later than initially expected.