Measurement of (1036) Ganymed rotation axis

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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

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)


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.