Light propagation in the field of a moving axisymmetric body: Theory and applications to the Juno mission

Given the extreme accuracy of modern space science, a precise relativistic modeling of observations is required. We use the time transfer function formalism to study light propagation in the field of uniformly moving axisymmetric bodies, which extends the field of application of previous works. We first present a space-time metric adapted to describe the geometry of an ensemble of uniformly moving bodies. Then, we show that the expression of the time transfer functions in the field of a uniformly moving body can be easily derived from its well-known expression in a stationary field by using a change of variables. We also give a general expression of the time transfer function in the case of an ensemble of arbitrarily moving point masses. This result is given in the form of an integral that is easily computable numerically. We also provide the derivatives of the time transfer function in this case, which are mandatory to compute Doppler and astrometric observables. We particularize our results in the case of moving axisymmetric bodies. Finally, we apply our results to study the different relativistic contributions to the range and Doppler tracking for the Juno mission in the Jovian system.

Figure 1

Representation of different contributions on the range (left panels) and range rate (right panels) between Juno and Earth over one year. The contributions represented are the lower order contribution (the actual value of the observables) and the corrections produced by the Shapiro due to the monopole of the Sun.

Figure 2

Representation of different contributions on the range (left panels) and range rate (right panels) between Juno and Earth over one year. The contributions represented are the corrections produced by the Shapiro due to the monopole of Jupiter (top panels) and the contributions due to the velocity of Jupiter (bottom panels).

Figure 3

Representation of different contributions on the range (left panels) and range rate (right panels) between Juno and Earth over one year. The contributions represented are the corrections produced by the $J_2$ of Jupiter (top panels) and the contributions produced by the fact that the $J_2$ is moving (bottom panels).

Figure 4

Representation of different contributions on the range between Juno and Earth over one year. Top left panel: The 2PN contribution from the monopole of Jupiter (contribution proportional to ${\beta }_{\mathrm{Jup}}^2$). Bottom left panel: The contribution proportional to the acceleration of Jupiter. Right panels: The Sagnac contributions (proportional to the Sun mass and to Jupiter mass) due to the motion of Juno.