Prepared by: M. Marabucci, L. Iess M. Di Benedetto, S. Finocchiaro, A.Genova, R. Meriggiola, P....

Prepared by:

M. Marabucci, L. Iess

M. Di Benedetto, S. Finocchiaro, A.Genova, R. Meriggiola, P. Racioppa, G.Rapino

Progress Meeting 15 October 2009

Simulations of the impact of the RW maneuvers on MORE experiment

MORE Progress Meeting – October 2009

Summary

• SECTION 1: Comparison between settings with different value of residual DeltaVs

• SECTION 2: Comparison between a Ka configuration and a putative X-Ka configuration

• SECTION 3: Preliminary analysis of the impact of the accelerometer noise in the estimation of the gravity field


SECTION 1 - Configurations

BOT EOT BOT EOT

0h 24hKa Ka

DSM 1 DSM 2

0h 24h

BOT EOT BOT EOTKa Ka

DSM 1 DSM 2

General setup:- 88 arcs each lasting 24 hours

-Gravitational field up to the degree 30- The onboard accelerometer allows a complete knowledge of non-

gravitational accelerations, therefore they are not included in the

model

- WGN Allan deviation = 10-14 @ 1000s


SECTION 1 - Cases

Solve-for parameters (all cases):

State vector A priori covariance matrix by propagation from previous arc

Coefficients of gravity field

A priori uncertainties following Kaula’s rule

Case A

Residual DeltaVs 1mm/s

Solved-for YES

Case B


Solved-for NO

Case C

Residual DeltaVs 0.15mm/s

Solved-for YES

Case D


Solved-for NO


SECTION 1 - Multiarc estimate

Case A Case B

Case C Case D


SECTION 2 - Configurations

BOT EOT BOT EOT

0h 24hKa Ka

DSM 1 DSM 2

BOT EOT BOT EOT

0h 24hKa Ka

DSM 1 DSM 2

X X

General setup:

- 88 arcs each lasting 24 hours

-Gravitational field up to the degree 30

- The onboard accelerometer allows a complete knowledge of non-

gravitational accelerations, therefore they are not included in the model

- WGN Allan deviation = 10-14 @ 1000s


SECTION 2 - Cases

Solve-for parameters (all cases):

State vector A priori covariance matrix by propagation from previous arc

Coefficients of gravity field

A priori uncertainties following Kaula’s rule

Residual DeltaVs A priori uncertainties proportional to the value

Case A


Tracking Ka

Case B


Tracking X-Ka

Case C


Tracking Ka

Case D


Tracking X-Ka


SECTION 2 - Multiarc estimate

Case A Case B

Case C Case D


Case A – Ellipsoid and Geoid


Case A – Second iteration

Multiarc estimate

Corrected value of coefficients of gravity field

Associatedformal uncertainties

Nominal value of coefficients of gravity field

A priori formal uncertainties

Multiarc estimateSecond iteration


Case A – Second iteration - Results

km (log) km/s

(log)


SECTION 3 - Accelerometer noise

From “Gravity field and rotation state of Mercury from the BepiColombo Radio Science Experiments”, Milani et al., 2001


Periodic acceleration (ODP model)

Let r and v denote the spacecraft position and velocityθ denote the angle from the ascending node of the spacecraft orbit

on the planet equatorial plane to the spacecraft:

1 2 1 2

1 2 1 2

1 2 1 2

ˆcos cos 2 sin sin 2



p R R R R R

T T T T T

N N N N N

r P C C S S R

P C C S S T

P C C S S N

where:

ˆ ˆ ˆ ˆ ˆ, ,r r v

R N T N Rr r v


Periodic acceleration - Settings


Multiarc estimate

Estimated parameters: A priori uncertainties:

State vector Propagation of previous arc covariance matrix

Constant coefficients of periodic accelerations 1.000E-11 km/s2

Cosine coefficients of periodic accelerations 1.000E-11 km/s2

Impulsive burns (1mm/s) 5.000E-06 km/s

Gravity field coefficients up to degree 29 ≈ Kaula’s rule

Love number 6.000E-02


Conclusions

- In a Ka configuration, the gravity field is correctly recovered if residual DeltaVs of 0.15mm/s are considered. On the other hand, if the residual DeltaVs of 1mm/s are considered, it is necessary to include the impulsive burns in the solve-for parameters, but estimation errors larger than 3 sigma occur for degree higher than 18. Impulsive maneuvers of 1mm/s, not included in the solve-for parameter, jeopardize the recovering of the gravity field.

- If an additional X band ground station is available, the gravity field can be correctly estimated also if residual DeltaVs of 1mm/s are considered.

- The current Ka configuration with residual DeltaVs of 1mm/s (case A) shows error of few centimeters in the geoid radius (considering a gravity field up to degree 10) and will allow, at the end of the mission, to reconstruct the trajectory with accuracies compliant with altimeter requirements.

- The preliminary analysis of the accelerometer noise provide information about a possible worsening of the estimation of the gravity field and make necessary an in-depth study of the impact of accelerometer noise and residual DeltaVs.


Case A – Ellipsoid and Geoid

Prepared by: M. Marabucci, L. Iess M. Di Benedetto, S. Finocchiaro, A.Genova, R. Meriggiola, P....

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