Effects of Precession and Nutation on Short (a few Hours) VLBI Experiments

Yukio Takahashi (takahashi(AT)nict.go.jp)

Kashima Space Research Center
Communications Research Laboratory
893-1 Hirai, Kashima, Ibaraki 314, Japan

Errors in VLBI measurements are caused by many reasons, such as noise, atmospheric scintillation, clock fluctuation, the pseudo delay by the calibration system, and inaccurate physical model. I investigated the effects of the differences of the precession and nutation parameters from the model on the station positions.

The theoretical delay model of the Wahr's nutation model (1980), and the Lieske's precession model (1976), which were adopted in IAU'80, was used. The precession error is included in the estimated nutation parameters. Therefore, I show only the difference of nutation parameters from the Wahr's model in Figure 1.


Figure 1. Differences of adjusted nutation parameters Delta psi (dpsi) and Delta epsilon (deps)) from IAU80 model.


The differences reach about -30 mas (mili arcsec) for nutation in ecliptic longitude, and -10 mas for the ecliptic obliquity prior to the end of 1995. The amplitude of the modification for the nutation model is a few mas for some periodical terms. The main reason for the differences is due to modification of the precession, which corresponds to the rate of ecliptic longitude of -3 mas/year. These differences affect the station positions as shown in the following equations.

where P, N are the rotation matrixes for precession and nutation. D is the diurnal rotation matrix, and W is the wobble. vector B is the baseline vector or station position vector. The effect of the differences of the precession and nutation parameters from the model on the wobble is similar to its effect on station position. I represented the station positions Delta X, Delta Y, Delta Z for the estimated nutation parameters Delta psi (ecliptic longitude) and Delta epsilon (ecliptic obliquity).

where omega is the angular velocity of the earth (1 cycle is about 23 hours and 56 minutes) and t is a time. H is the hour angle which changes diurnally.

There are two types of effects on the station positions (the wobble). One is an offset and another is a periodical term. Therefore, the station position changes with a period of 23 hours and 56 minutes. It is shifted by 4 minutes. When the observation time is shifted by about 4 minutes every day, the hour angle H is the same for every experiment. Therefore, the effects of the modification for the precession and nutation parameters on the positions are a bias. When the observation time is fixed, the mean station position during the experiment has an annual variation.


Figure 2. The image of the change in the mean station positions when experiments is conducted during 1 am to 6 am. The sine curve means the daily variation of station position caused by the modifications of the precession and nutation parameters. Abscissa is a time.


Figure 2 shows the image of the changes in the mean station positions when experiments are conducted during 1 am to 6 am. The sine curve means the daily variation of station position caused by the modifications of precession and nutation parameters (the abscissa is time). The variation is shifted by 4 minutes per day. The mean position during 1 am to 6 am is also changeable annually. If the schedule time is changed (for example from day to night), the estimated station position becomes discontinuous.

CRL has conducted the VLBI experiments of KSP (the Crustal Deformation Monitoring System for Tokyo Metropolitan Area) since 1995. These experiments are conducted during 5 hours every day. The time of experiments is nearly fixed. I investigated the effects of the differences of the precession and nutation parameters from the model on the station positions. In the data of KSP experiments, the annual variations and the discontinuity at the change of the observation time were appeared [Takahashi et al., 1996]. These variations may be caused by the differences of the nutation and precession parameters from the IAU80 model. The typical baseline length is about 100 km, and the differences for the ecliptic longitude of -40 mas and for the ecliptic obliquity of -10 mas correspond to about 20 mm in components of the station position. For an east-west baseline such as Kashima-Koganei, the amplitude of periodic variation is about 9 mm for Z component, while the effects on X,Y components are like a bias. The variation of Z components will be corresponding on north and vertical movements.

Reference

Takahashi, Y., J. Nakajima, T. Iwata, H. Takaba, L. Furuya, Y. Koyama, and N. Kurihara, VLBI Error and the Short Term Variation in VLBI, Proceeding of the Technical Workshop for APT and APSG 1996, pp.225-230, 1996.

Updated on June 9, 1997. Return to CONTENTS