Pioneer Anomaly Test – Jonathan Fitt 1 System Design Assessment for a Mission to Explore the...

Pioneer Anomaly Test – Jonathan Fitt

1

System Design Assessment for a Mission to Explore the Pioneer

Anomaly

Jonathan FittTuesday, April 18, 2023

http://www.sr.bham.ac.uk/yr4pasr/project05/pioneer_anomaly/

Pioneer Anomaly Test - Jonathan Fitt2

Contents

• Pioneer Anomaly• Components of Project Work• Specific Details of Project Work• Project Summary


What is the Pioneer Anomaly?

The Pioneer Anomaly can be interpreted as a constant radial deceleration of Pioneer 10 and 11s’ velocity in the direction of the sun which was identified in Doppler tracking data.

210 )10168.8( msa p

f)( ResidualDoppler 20

mod

c

taf p

DSNobsff


Doppler Residuals – Doppler Velocity


Pioneer Orbits

20 A.U.

12.2 Km/s

’97

2006

67 A.U.90 A.U.

Modified from Anderson, J.D., et al., 2002, Phys. Rev. D 65


Project Components

1. Understanding the method behind discovering the Anomaly – updating to 21st century

2. An improved method to explore the Pioneer Anomaly

3. A potential use of new data


Design Requirements

• Explore the Anomaly to 10-12 ms-2 level of accuracy• Ability to distinguish between gravitational and non-

gravitational origin of the Anomaly• A craft on an escape hyperbolic trajectory• A velocity significantly different to the Pioneer craft• Communication in X-band• A passive retroreflector test mass• Radio ranging from the Earth to the primary craft• Laser ranging from the primary craft to the test

mass


1. Understanding and Updating

• Interpretation of Doppler residuals

• Doppler measurement errors• Solar corona phase scintillation• Random number generation +

Data analysis


2. An Improved Method

• Bounds on planetary orbits• New system architecture• Range measurement & error• Data rate• Laser range measurement• Radio communication link• Position Control System• Mass/power budget


3. Potential

• Behaviour of the primary/test mass system

How to use data from the new system to differentiate between a gravitational and a non-gravitational origin of the Pioneer Anomaly.


Understanding & Updating

Doppler Errors

Doppler Jitter:-

•Statistically inherent to the Doppler process•Dependent on the characteristics of the radio link•Constant

Allan Deviation:-

•Due to instability oscillator•Improves with extended observations

Solar Corona Phase scintillation:-

•Caused by radio wave passing through the solar corona•Randomly changes the phase of the carrier wave•Manifested as an error in Doppler velocity•Present for an SEP between 5 and 27 degrees•Below 5 degrees too large to make measurement

Doppler jitter: 0.0006 mm/sAllan deviation: 0.0001 mm/sSolar Corona: 0.6 mm/s (at its highest)


Doppler Residual Model

Anomaly Doppler Velocity (mm/s)

-30

-25

-20

-15

-10

-5

0

0 50 100 150 200 250 300 350 400

Time (days)

Do

pp

ler

velo

city

(m

m/s

)

Gradient (mm/s/day) -7.55E-02Error on graident 1.89E-07Acceleration (m/s/s) -8.74E-10Error on acceleration 2.19E-15

Summary


Possible Mechanism

• The Anomaly could be explained by heat radiating un-symmetrically from the craft

• Although 21st century offers better accuracy, it does eliminate this mechanism

• Need a new system


An Improved MethodPrimary/Test mass System

Earth

Primary

xP

xT

xxxxx TPdxTdxPr

)()(

dx dx

Test mass

Use a system that uses a primary craft with a test mass – similar to a drag free spacecraft but with the test mass outside of the craft.

By taking the vector addition of the Earth/primary range and the primary/test mass range any movement in primary position will not affect the overall result


Range Residual

Modelled Range Residual for 1 year

-500000

-450000

-400000

-350000

-300000

-250000

-200000

-150000

-100000

-50000

0

0 50 100 150 200 250 300 350 400

Time (days)

Ran

ge

resi

du

al (

m)


Range Residual

Velocity Residual for 1 year Observation

-3000

-2500

-2000

-1500

-1000

-500

0

0 50 100 150 200 250 300 350 400

Time (days)

Ran

ge

velo

city

(m

/day

)

Acceleration (m/s/s) Error (m/s/s)-8.74E-10 7.7118E-16


Uplink Link Budget

Ground to Space link

Parameter Value (linear) Value (dB) Parameter Value (linear) Value (dB)data rate (bps) 100 20 Noise powerrange (m) 1.50E+13 131.76 system noise temp (K) 220 23.42frequency up (Hz) 7.15E+09 98.54 specific thermal noise (W/Hz) 3.04E-21 -205.18frequency down (Hz) 8.45E+09 99.27 system noise (W) 1.82E-18 -177.40Bandwidth 6.00E+02 27.78 receiver amp noise (dB) 0.00SNR (dB) 2 receiver noise (dB) -1.50

total noise (dB) -178.90

Constants System requirementPI 3.1416 4.97 received S/N (dB) 1.29637574 1.13speed of light (m/s) 3.E+08 84.77 received Eb/N0 (dB) 7.778254438 8.91k (W/Hz/K) 1.38E-23 -228.60 required S/N (dB) 2.22

Transmitted link margin (dB) -1.09EIRP (dBW) 96.00ponting loss (dB) -0.20atmospheric loss (dB) -0.15Receivedspreading loss (m^-2) 4.44E-27 -263.52free space loss (m^2) 1.11485E-05 -49.53antenna gain (dB) 42.00amp gain (dB) 0.00antenna efficiency 0.6 -2.22

Received Power (dBW) 1.6718E-18 -177.77


Downlink Link Budget

Space to Ground link

Parameter Value (linear) Value (dB) Parameter Value (linear) Value (dB)data rate (bps) 500 27 Noise powerrange (m) 1.50E+13 131.76 system noise temp (K) 220 23.42frequency up (Hz) 7.15E+09 98.54 specific thermal noise (W/Hz) 3.04E-21 -205.18frequency down (Hz) 8.45E+09 99.27 system noise (W) 9.11E-16 -150.41Bandwidth 300000 54.77SNR (dB) -18 amp noise (dB) 0.00

receiver noise (dB) 0.00Constants total noise (dB) -150.41PI 3.1416 4.97speed of light (m/s) 3.E+08 84.77 System requirementk (W/Hz/K) 1.38E-23 -228.60 received S/N (dB) 13.00414893 11.14

received Eb/N0 (dB) 7802.489361 38.92Transmitted required S/N (dB) -17.77Antenna gain (dB) 15848.93 42.00antenna power (W) 2.00E+01 13.01 link margin (dB) 28.91antenna efficeincy 0.6 -2.22EIRP (w) 1.90E+05 52.79

Receivedspreading loss (m^-2) 4.44E-27 -263.52free space loss (m^2) 7.97E-06 -50.98amp gain (dB) 55.00

antenna gain (dB) 68pointing loss (dB) -0.40atmosphere loss (dB) -0.15

Received Power (dBW) 1.18442E-14 -139.26


Perturbations on Primary

Acceleration on craft due to bias forces

0.00E+00

2.00E-09

4.00E-09

6.00E-09

8.00E-09

1.00E-08

1.20E-08

1.40E-08

1.60E-08

1.80E-08

0 10 20 30 40 50 60 70 80 90 100

Radius (A.U.)

Acc

eler

atio

n (

m/s

/s)

Pioneer Anomaly Total Environmental Acceleration


Perturbations on Primary

Radio Beam Reaction Force Transmitted

Transmitted Power (W) 20Craft Mass (kg) 300Speed of light (m/s) 299792458

Force due to radio beam (N) 2.70E-07Acceleration (m/s/s) 9.00E-10

Orbital radius (A.U.) 20Solar Pressure Acceleration (m/s/s) 1.55E-10Total ENV Acceleration (m/s/s) 1.03E-09

dr after 0.5 days (m) 0.96Mission length (yr) 10

# position corrections 7300

Thruster type Specific Impulse (s) Thrust (N) Total Thruster mass (Kg) Mission fuel usage (kg)Power requirement (W)Hydrazine 215 0.9 4.29 79.0122Hydrazine type 2 230 4.45 5.33 164.2342Cold Gas Thruster 73 1 0.65 245.2950Ion Engine 2585 0.0178 71.8 0.9242 439Hall thruster 1300 0.03 0 2.3858 500FEEP 9000 0.00004 57 total upper limit 0.0126 5.28 + 100Colloid Thruster 575 0.0000076 6.5 0.0859 0.06688PPTs 1400 0.00086 39.2 0.3751 70


Positioning Control System

Fuel usage of different thruster types for the whole mission (kg)

0

50

100

150

200

250

Hydrazine Hydrazine type 2 Cold Gas Thruster Ion Engine Hall thruster FEEP Colloid Thruster PPTs

Thruster Type

Fu

el m

asss

(kg

)


Positioning Control System

Fuel usage of different thruster types for the whole mission (kg)

0

0.5

1

1.5

2

2.5

Ion Engine Hall thruster FEEP Colloid Thruster PPTs

Thruster Type

Fu

el m

asss

(kg

)


Mass/Power Budget

Mass/Power Budget

Power (w) Power (w)Subsystem Component Mass (kg) Operation Total (W) Subsystem Component Mass (kg) OperationTotal (W)TT&C Thermal 0Science Transponder 3 -12.9 -12.9 0

Antenna 10 0 0TWTA 2.6 -51.6 -51.6 0Laser 4.7 -16.8 -16.8 0Laser reciever 2 -10.8 -10.8 0Laser range unit 2 -10.8 -10.8 Structure 0

0 Test mass 20.6 0Power 0 0

GPHS-RTG 55 290 290 Propulsion 00 0

Command/Data Handling 0 0Solid State Memory 1.64 -6.8 -6.8 Fuel 0Solid State Memory 1.64 -6.8 -6.8 0

Attitude Complete FEEP system 57 -110 -110 00

Total Mass (Kg) 160.18Total Power (W) 63.5


A Potential Use of New Data

1. Both primary and test mass feel a force acting towards the sun due to solar gravity

2. Both craft can potentially experience any unknown forces (Pioneer Anomaly)

3. The primary craft will experience forces acting on it due to the local space environment (solar radiation pressure)

4. Any onboard systematic forces such as heat radiation will affect the primary

5. The test mass will not be affected by onboard systematic forces as it is passive

6. The test mass will not experience environmental forces because it is in an environmentally quiet position relative to the primary


Equation of Motion of Primary Craft

pENVpSYSpUNKpppp FFFgmamF ,,,

(N)primary on the acting forces talenvironmenAny

(N)primary on the acting forces systematicAny

(N)primary on the acting forcesunknown Any

)(msgravity solar todueon Accelerati

)(mssun thewardsprimary to ofon Accelerati

(kg)craft primary theof Mass

(N)sun the towardsForce

,

,

,

2-

2-

pENV

pSYS

pUNK

p

p

p

F

F

F

g

a

m

F


Equation of Motion of Test Mass

tUNKtttt FgmamF ,

(N) mass test on the acting forcesunknown Any

)(msgravity solar todueon Accelerati

)(mssun the towardsmass test ofon Accelerati

(kg) mass test theof Mass

(N)sun the towardsForce

,

2-

2-

tUNK

t

t

t

F

g

a

m

F


Test Mass Motion Relative to the Primary

p

pENV

p

pSYS

t

tUNK

p

pUNKtprelative m

F

m

F

m

F

m

Faaa ,,,,

The bracketed term describes the motion of the test mass relative to the primary craft due to any unknown forces acting on both the primary and the test mass, positive in the sun direction.


The Origin of the Pioneer Anomaly

p

pENV

t

tUNK

p

pUNKrelative m

F

m

F

m

Fa ,,,

•These unknown forces could be the Pioneer Anomaly

•If the Pioneer Anomaly is gravitational in nature then there will be no relative motion

•If the Anomaly is due to a drag force or a radiation force then the primary will experience a smaller force than the test mass

Observed as a change in primary/test mass distance over time.


A Potential Use of Data

Earth/Test Mass Range Residual, including Environmental Effects and the PCS

-25000.00

-20000.00

-15000.00

-10000.00

-5000.00

0.00

0 10 20 30 40 50 60 70 80 90

Time (days)

Ra

ng

e r

es

idu

al

(m)

Range Residual (non-gravitational) Range Residual (gravitational)


System Behaviour

Gravitational behaviour

Non-gravitational behaviour


Possible Results

Comparison of Test Mass Observable Between Grav and Non-Grav

880.00

900.00

920.00

940.00

960.00

980.00

1000.00

0 1 2 3 4 5

Time (days)

Ra

ng

e

(m)

NON-grav grav


Summary

• Studied the Pioneer Anomaly – how it was discovered

• A model created• Updates were explored• A new system architecture was adopted• System design requirements built up• A potential of the new system

highlighted


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