Radio occultation

Radio Occultation, also referred to as Okkultationsmethode, is a measurement technique for probing planetary atmospheres using phase faithful radio signals propagating through the atmosphere from a transmitter to a receiver. Both the transmitter and receiver are located during the measurement phase outside the atmosphere to be probed.

Carrying out the measurement requires a special geometry of the spacecraft to the receiving station, wherein the spacecraft disappears during the measurement from the viewpoint of the receiver behind the planet and therefore enters occultation.

During the radio beam from outer space runs above the atmosphere at a point in the atmosphere, there will be a continuous record of the observation data. The probed medium acts in a characteristic way on the radio signal and changes its phase, amplitude and polarization.

The signal being influenced by the medium produces a time-dependent data record that corresponds to the height profile of the refractive index. This profile of the neutral atmosphere is proportional to the density of gas mixtures, from which can be calculated with the hydrostatic core equation and the ideal gas law height profiles of pressure and temperature of the neutral atmosphere. From the proportionality of the electron density at the height profile of the refractive index of statements about the electron density of the ionosphere are also possible.

History

The idea of ​​stellar occultation to the study of planetary atmospheres, as it had been published in 1904 by Anton Pannekoek in the " Astronomische Nachrichten ", served 1962 VR Eshleman of Stanford University in California as a template for the Radio Okkultationsexperiment.

At the same time developed DL Cain and colleagues at the JPL error analysis for satellite navigation with the then new maser array antenna systems. Main focus of the analysis were error contributions of the atmosphere and ionosphere on - the locating signal. Cain and his colleagues noticed that the atmosphere of another planet represents a non-negligible source of error, from which, however, in turn, statements can be obtained through the planet's atmosphere. The difference consisted in the Eshleman based on the total time of flight methods of observation. While the Stanford team to Eshleman emanated from a one-way mode, wherein a transmitter should generate the reference signal on board the spacecraft, beat Cain and his team at the JPL before a Zweiwegverfahren, where with the help of the then-new Burl technology of precision not to be striking reference signal to the ground station should be generated, which should then be received from the spacecraft and easily returned to modified phase faithful again.

Since the disposable Ever Driving with the technology at that time was not accurate enough, NASA decided to use the two-way process during the Mariner 4 mission for the first time.

The importance of the new measurement method was developed in the early 1960s at the Mariner project, in which a Mars landing was provided clearly. Such landing places high demands on the design and the landing strategy of the spacecraft. Precise knowledge of the Martian atmosphere were essential, and although information was available from ground-based spectroscopy, there was doubt as to the time measured values ​​from the year 1950 by de Vaucouleurs. What should be shown later, was Vaucouleurs ' acceptance of the atmospheric pressure at 100 hPa too high. Mariner 4 was launched in 1964 to Mars, where the question of the surface pressure was still unresolved. With the help of the new measurement technique, a pressure on the surface of Mars could be measured, which was about two orders of magnitude below the then benchmark.

Measurement process

When radio Okkultationsexperiment a highly stable continuous wave shines through the planetary atmosphere to be examined in the micrometer range. Is sent in the so-called X-band at 8.4 GHz and in the S-band at 2.3 GHz. With detailed knowledge of all velocity components involved the refractive index profile of the atmosphere can be assigned based on the phase stability of the reference signals frequency shifts. From this it can be a first step corresponding diffraction angle and beam parameters are calculated. Denotes the diffraction angle, the deflection, the beam is subject to a radio in the atmosphere. Are available for each diffraction angle exactly one beam parameters, which is perpendicular to the Strahlasymptoten ( Figure 2). In a further step can be by means of an Abel transform of the corresponding refractive index determined.

Is measured with high precision, the signal sent from the space vehicle, namely, the shift of the received frequency with respect to the transmitting frequency at each time point. The shifts in the measured frequencies stir from the velocities of the transmitter and the receiver. This classical Doppler effect is an additional shift by the illumined medium impressed. To extract this portion of the frequency offset from the measured frequency data is subtracted from the measured data, the design frequency, which can be determined from the known speed of the emitter and receiver, and does not contain any atmospheric components. This portion of the frequency shift is called Residuenfrequenz and contains ideally only shares of the probed medium. The model takes into account speed frequency components from the rotation, nutation and precession of the Earth, ideally, from the tidal effects as well as shares of special and general relativity. Furthermore, to be considered for the separation of the frequency change of the carrier wave by the planetary atmosphere of which the atmosphere, the effects of the Earth's atmosphere and Erdionosphäre by models and empirically determined values ​​such as temperature, pressure and humidity.

It is known that an electromagnetic wave is refracted and shifted in phase in a medium. Compared to the vacuum signal it travels a longer path. This can be expressed by the following formula:

Is the corresponding phase shift at the signal wavelength and the corresponding (theoretical) way of the vacuum line of sight.

Atmospheric frequency shift corresponding to the time derivative of, so that the time dependent implicit exploratory experiment atmospheric frequency shift occurs:

With

F is the transmission frequency, and c is the vacuum velocity of light.

In connection with the geometry of radio probing measurement and the speed variables involved can get in touch above equation for the frequency shift with the relevant kinematic variables from Figure 2:

Atmospheric frequency shift is therefore, the contribution by the projection of the speed on the Strahlasymptoten minus the kinematic Doppler contribution along the line of sight. Having obtained from a measurement, so the above equation for the component to be solved. The assumption of spherical symmetry provides with the law of refraction Snell on spherical surfaces ( Benndorff rate or Bouguer - set) a second equation. With the two equations can be the unknown or Strahlasymptoten and determine what leads to the diffraction angle and beam parameters.

Coordinate transformation

Assuming spherical symmetry it can be shown that the radio beam always moves in a plane in the direction of increasing refractive index. This level is referred to below as Okkultationsebene is the reference for the calculation of the diffraction angle. Such a plane at a given time is defined by the three points of the ground station, the center planetary and satellite position, as shown in Figure 3. In general, each time a new measurement of the Okkultationsebene that must be calculated at each measurement time point.

All the orbit data of the spacecraft, as well as the ephemeris are available in a particular coordinate system ( KS). Usually, these are at the level of the average Earth's equator, with respect to the dynamic equinox of epoch J2000. To change the coordinate system of Okkultationsebene are two coordinate transformations necessary. Firstly the planetozentrische coordinate system which is analogous to the above the earth's equator system and then into the Okkultationsebene. Figure 4 gives an overview of this. Other approaches are possible.

With the Ephemeridenbibliothek SPICE, the calculations can easily perform. The Spice library is provided by the NAIF group ( NASA) freely available and is present in the source code. The NAIF Group also provides the corresponding orbit data in Spice format.

Diffraction angle and beam parameters

The Okkultationsebene, as shown in Figure 5, is defined by the two axes Z and R. The components of the individual velocity vectors can be specified in terms of these axes. The unknowns directions of the unit vectors and the Strahlasymptoten specified by the angle shown between Strahlasymptote at the ground station and line of sight, and by the angle between Strahlasymptote at the Rausmsonde and line of sight. Are further shown the angle between the coordinate axes and the line of sight; is the angle between the z axis and the line of sight of, the angle between r and the axis line of sight.

The two unknown angles and can be solved iteratively by a system of equations. The system of equations is presented in detail in. Summation of the two unknown angle is just the angle of diffraction. The beam parameters is then obtained also from one of the unknown angle and the Snell's law at spherical surfaces:

The diffraction angle and beam parameters were determined for each beam, as can be calculated by means of a Abel transform of the diffraction angle corresponding to each index.

Abel transform and refractivity

Under an Abel transform is defined as the solution of an Abelian integral equation. Integral Equations are characterized in that the unknown function occurs as the integrand in a definite integral. Integral Equations known are, for example, the Fourier transform and the Hankel transform. In the theory of integral equations of the Abelian integral equation is assigned to the weakly singular Volterra integral equations of the first kind to the Niels Henrik Abel 1826 a solution was found.

In general cause problems, in which the reconstruction of two-dimensional radially symmetric distributions f (r ) from its projections g ( y) is required for the Abel transform. It finds application, for example in plasma physics, astrophysics or medical computed tomography. The relationship between the radial distribution f (r) and their projections g (y) leads to the equation:

The Abel transform called. A common form of the inverse transform is given by Abel:

The measured diffraction angle corresponds to the Abel transform of a radially symmetric refractive index. An inverse Abel transform of the angle thus yields the refractive index can be specified. Fjelbo et al. could show that an atmosphere with the refractive index profile bends a beam with beam parameters by the following percentage:

At Strahlperiapsis, the point of closest approach of the beam at the planet is the product of refractive index and radius equal, Abel transform is determined by the inverse of:

The refractive index for air is a number close to 1 in order to make dealing with this number handy, you subtract a 1, multiplied by, this is the refractivity N

Wherein the refractive index is a function of the height h. The refractivity of the neutral atmosphere is to respond to the assets of the medium on the dynamic effect of the electromagnetic wave, which is referred to in the electromagnetic theory as dielectric polarization. The polarization is defined as averaging over many particles. This results in a proportionality of the refractivity to the particle density. The particle is subject to the barometric height distribution, such that the refractivity is also a function of the height. The change in refractivity, which is established at a certain height, depends on the thermodynamic variables pressure and temperature at this altitude, further ionized particles act directly on the signal.

The corresponding radius of the Strahlperiapsis is. It marks the point of closest approach of the beam at the planet, this is shown in Figure 6. Thus occur after the Abel transform of the diffraction angle profiles of refractivity as a function of height in front. With this information, the height profiles of the characteristic features of the planet's atmosphere can be determined very accurately.

Temperature, pressure and density profiles

With the results from the previous section can now be the fundamental state variables of the neutral atmosphere calculated. The proportionality of the refractivity of the number density, the ideal gas law and the hydrostatic equation, basic pressure, temperature and density can be calculated. Furthermore, can the electron density profile of the ionosphere calculated.

• Number density:

• Hydrostatic basic equation:

• Ideal gas law:

• Electron density:

Examples