Do maneuvers with the 20m radio telescope affect the gravimeter?

The 20m radio telescope consists of a parabolical dish and a counterweight. Depending upon whether the gravimeter "sees" this arrangement head-on or from the side, the gravity attraction is  maximum or minimum in these two respective extremes.

The mass distribution in the telescope can be approximated by a 245 ton dipole that rotates according to the pointing commands. These are frequent and may imply large slews especially during Geo-VLBI experiments.

The gravity attraction of the mass dipole is given by

where H, Hs,, and As is the height and northing of the antenna and the gravimeter, respectively, A and α the antenna pointing azimuth and altitude, M the total mobile masses seperated by distance d =  5 m, D = 80 m the distance between antenna and gravimeter, and  G is the constant of gravity. The height difference is 10 m.

From Geo-VLBI schedules
Exp. name       Year Day UT start       
Year Day UT stop
cl09sx1         2009 174 08:57:12        2009 216 08:48:43
eg040fon        2009 166 08:28:40        2009 166 22:30:27
ey008aon        2009 217 06:44:31        2009 218 08:06:25
f09m1on         2009 303 07:23:26        2009 303 10:50:46
r1385on         2009 180 16:30:09        2009 181 17:04:10
r1386on         2009 187 12:11:00        2009 188 17:06:23
rd0908on        2009 266 14:13:04        2009 267 17:57:06
rg001con        2009 184 11:36:36        2009 185 17:01:26
tl09c6          2009 230 12:04:50        2009 295 11:25:37
tl09x1on        2009 216 09:32:57        2009 217 07:46:34
we have extracted time series of pointing to radio sources, right ascension and declination, and transformed the angles to the horizontal system.

The gravimeter record was reduced from tides and atmospheric effects, was band-pass filtered (Fig.1), downsampled to 30 s intervals, and chopped to retain sections synchronous with the VLBI schedules (Fig.2)
A least-squares fit of the variable factors in Eq. 1 gave the following results:

  RESULTS: ADMITTANCES, LOCAL COPHASES                                                     

  SITE/FILE: gdrc.ts  lon/lat:    11.9260   57.3964

 Normalized Chi^2 of fit :  4.57D-04, R=   2.14D-02 , X_1 X_2 =  1.00  2.30, Nev= 4

 The error information below is compatible with a unit normalized Chi^2.
 <rslist>d> rmsu=  2.138407516121582E-002  weff=  1.00000000000000  rchi=  1.00064262960750

 SYMB  #b  Regression signal                         Admittance parameter +- 68.3% cfd

 PSIN  1 <>                               -0.000396 +-0.000343

 PCOS  2 <>                                0.001146 +-0.000357
 /     3 Linear [uGal]/(12717*8.33333D-03[h])              0.000058 +-0.000671
 /     3 Linear [uGal]/[year]                              0.004822 +-0.055471
 -W    4 Const  1.000D+00                                 -0.000003 +-0.000191

Remarkably,  1/2 arctan( PSIN/PCOS coefficients ), 1/2 arctan(-396/1146) = -9o, is not far away from the bearing of the gravity station from the telescope (-17o, Fig.3). However, the uncertainty of this angle is 35o, so the determination cannot be called sharp.

Fig. 1 - Band-pass filter for suppressing drift and microseisms. The filter was applied on both the pointing and the
gravity time-series before the least squares fit. The sample frequency, 1/30 Hz, is denoted by fs (1/30 Hz in the experiment).

The band-pass filter is of window-design type. The pass-band is Fourier-integrated in the frequency domain, and the time series is windowed using a Kaiser-Bessel window with design parameter 2.1 (Harris, 1982) and a taper length of 60.

Fig 2.a -The whole range of pointing and gravity time series. The ordinate units are really uGal - sorry. The best-fitting amplitude of the pointing time-series has been increased with a factor 300. Figure 2b shows a short sub-interval

Fig.2b - suggesting that there are more important noises than antenna pointing effects. This serie was filtered more narrow than specified in the text. The actual filter had an upper corner frequency of 0.2 fs, half of the one used in Figure 2a.

Fig 3 - The bearing angle of the gravity station as seen from the 20m radio telescope. This aerial photo (GoogleEarth) is too old to show the building of the gravity lab.