wheel off-loadings.

The spacecraft attitude and the direction of the thrust are chosen so that the manoeuvres help to control the orbit phasing.

The control is such that the signal elevation from the daily Cebreros passes rises to 10 ◦(when telecommanding may start) always close to 2 hours after periapsis passage.

The pass ends either 10 hours later, close to apoapsis, or at 10◦descending elevation, whichever is earlier.

Tracking data obtained in X-band up and downlink are thus almost never acquired during the descending leg of the orbit, nor around periapsis.

The combination of the unfavourable pattern of tracking data arcs, imperfect calibration of the wheel off-loadings and deficiencies in modeling forces due to solar radiation pressure, together with other factors depending on the nature of the orbit cause the accuracy of the orbit determination to be worse than that for MEX.

Typical values of the differences between range residuals derived from successive orbit solutions are a few metres but, occasionally, even away from solar conjunction periods, the differences can reach as high as 10 m.
4.3.

Spacecraft transponder group delay Subtracted from each range measurement is the nominal value of the group delay of the on-board transponder.

For MEX, the value corresponding to the normally used Xband up- and downlink signals is 2076 nanoseconds (about 622 m).

For VEX, that has a virtually identical transponder, the value is 2085 ns (about 625 m).

The nominal value is the average value measured at different occasions on ground before launch.

From the variations in measured values, ostensibly made under identical conditions, it is thought that the systematic error of the nominal value should not be larger than 30 ns (about 10 m).

In addition, it is known that the group delay is not perfectly stable and can fluctuate by a few ns, depending upon variations in a number of parameters such as temperature and signal
strength.

For MEX, these error estimates appear reasonable, and perhaps a little conservative, based upon the consistency with results determined from the NASA MGS and MO spacecraft range data during the spring of 2005.

For VEX, there is no independent means to verify the error estimates.
4.4.

Superior solar conjunction During the time that MEX and VEX range residuals have been generated and archived, both missions have experienced a superior solar conjunction.

The MEX Sun-Earthprobe (SEP) angle remained below 10◦for two months centred on 23rd October 2006, when the minimum SEP angle was 0.39◦(1.6 solar radii).

The VEX SEP angle was continuously less than 8◦over two months centred on 27th October 2006, when the minimum SEP angle was 0.95◦(3.8 solar radii).

The effects on spacecraft radiometric data at these conjunctions have been described by (Morley and Budnik, 2007).

The signals to and from the spacecraft pass through the solar corona surrounding the Sun.

The free electrons in the plasma cause a group delay on ranging measurements.

Since the electron density increases with decreasing distance from the Sun, following, at least approximately, an inverse square law, the delay increases as the SEP angle diminishes.

No solar corona model was applied when computing the range residuals, so the increased delay is the cause of the peak in figure 3 and gaps in figure 4.

The existing solar corona models that could be used to correct the range residuals are not very accurate.

They cannot take into account the quite large day-to-day variations in the signal delay caused by shortterm fluctuations in solar activity like sunspot formation, flares and coronal mass ejections, all of which can influence the surrounding electron density.

A secondary cause of increased errors in range residuals at solar conjunction is due to the main effect on Doppler measurements of a substantial increase in noise.

When the SEP angle falls to about 1◦, the measurement noise typically increases up to two orders of magnitude higher than is usual at large SEP angles.

The accuracy of range residuals is then indirectly and adversely affected by a degradation in the accuracy of the orbit determination solutions.

That is why the decision was taken to omit 30 days before and after the solar conjunction in range residuals.

To illustrate the impact of solar conjunction, peak in residuals is plotted in the case of VEX data on figure 3.

On figure 4, the gap in MEX data around October 2006 is induced by the solar conjunction.

Such solar conjunctions also occured during the MGS and MO missions and caused observation gaps such as about January 2000 and mid-2002.
5.

INPOP08 Fit For the fit of INPOP08, MEX and VEX observations provided by ESA and described previously were added to the INPOP06 data sets used for its adjustment.