conclusive analysis & cause of the yby anomaly

Introduction Theory Analysis Conclusion

Conclusive analysis & cause of the flyby anomalyRange proportional spectral shifts for general communication

V. Guruprasad

Inspired Research, New Yorkhttp://www.inspiredresearch.com

2019-07-17

c© 2019 V. Guruprasad IEEE NAECON 2019 1/20

http://www.inspiredresearch.com


Summary

• Popular context: Astrometric solar-system anomalies[1]

• Pioneer: ∆V ∼ r ≈ −H0r at r ≥ 5 AU (blueshift) – SOLVED[2]

• Flyby: ∆V trajectory discontinuity at satellite range• Lunar orbit eccentricity growth: also ∼ H0

[3]

• Earth orbit radius growth: also ∼ H0

• Present work: conclusive solution of the flyby anomaly

• All NASA-tracked flybys checked, fit to 1%, more issues found• Fit presence and absence, correlated to transponder

• Real motivation and result: wave theory+practice correction

• Rewrite communication and radar: source range in all signals• Rewrites physics and astrophysics since Kepler• Computation overlooked since Euler and d’Alembert• Needed extremely robust empirical validation

[1]Anderson and Nieto 2009.

[2]Turyshev et al. 2012.

[3]The terrestrial reference frame is uncertain to about same order..Altamimi et al. 2016



Faithful led by the blind• Fourier transform presumes clock rate stability

• Clock rate stability requires design and procedures• But even HST calibration cycles only correct cumulative errors

• No awareness of range proportional or scale drift rate errors• Best Allan deviations in any observations are o(H0)• What if drift rate errors ⇔ O(H0r) shifts – Hubble’s law!

• Translational invariance is selective• If only phase can change, dψ(t)/dt = iωψ, so ψ(t) = e iωt

• Sinusoidal waves historically preconceived• For vibrational modes under static boundaries

• Chirp transforms are known, what prevents their spectra?

• Chirps are translationally variant ⇔ Hubble-like shifts• We don’t need a contrived metric, any more than angels

• Translational invariance constrains analysis instead of physics• FM, Doppler rate = continuously varying frequency ω• Current analyses assume Fourier: ω = 0• The flyby anomaly is nature saying they are incomplete



Engineers need to pave the way

• Translational variance is fantastically useful[4]

• Spectrum no longer a limited, shared resource• Every receiver can be physically unjammable• Instant triangulation – no need for range codes, many radars

• d’Alembert equation notoriously factors unconditionally

• Wave equation admits (whole dimension of) expanding solutions• We just didn’t have a way to observe, access them• Optical diffraction gratings, prisms are rigid ∼ enforce invariance

• Spectral analysis and selection are macroscopic functions

• Correspondence Principle is a Zeno’s Paradox and a Red Herring• The kernel is always physical, macroscopic and continuously variable• Especially in radio receivers: local oscillator (LO)

• Chirp spectra are translationally variant

• Components exp(iω0eβ[t−∆t]/β) ⇔ shifts ∆ω = −ωβ∆t

• Don’t really depend on r ⇒ wave notions are irrelevant!

[4]Guruprasad 2005.



Spectra are computed representations 1

ωω

source receiver

T

eb

eg

ey

er

ωω

source receiver

T

e′ye′r

e′∗r

e′be′g

The representation defines component shifts,like an oblique coordinate grid.

Any FM in Fourier basis

- Discontinuous in ω

- Pieces violate d’Alembert!

- Velocity ω unrepresentablevanishes in ideal FT

Steady tone in chirp basis

- d’Alembert with ω 6= 0

- Zero Fourier amplitudes!

- Requires chirp basis– basis itself has velocity ω

- Inclined view with shifts

- A group under translations(so Fourier is degenerate)




ωω

source receiver

T

eb

eg

ey

erS

ωω

source receiver

T

S















ωω

source receiver

T

eb

eg

ey

er

S

ωω

source receiver

T

S















ωω

source receiver

T

eb

eg

ey

er

S

ωω

source receiver

T

e′y

e′∗y

S

The representation defines component shifts,like an oblique coordinate grid. Any wave, hencealso its components, are integrated only as theyarrive.














ωω

source receiver

T

eb

eg

ey

er

S

ωω

source receiver

T

e′ye′r

e′∗r

e′be′gS

The representation defines component shifts,like an oblique coordinate grid. Any wave, hencealso its components, are integrated only as theyarrive.














ω

source receiver

eb

eg

ey

er

S ψs

S

spectral view

dω/dt

ω

source receiver

e′ye′r

e′∗r

e′be′gS

spectral vie

w

ψc

S

−βω∆t

The representation defines component shifts,like an oblique coordinate grid. Any wave, hencealso its components, are integrated only as theyarrive. The views show 1:1 equivalence.




- Velocity ω unrepresentablevanishes in ideal FTthis is a power signal










ω

source receiver

eb

eg

ey

er

S ψs

S

spectral view

dω/dt

ω

source receiver

e′ye′r

e′∗r

e′be′gS

ψc

S

−βω∆te′g

e′ye′r

β

The representation defines component shifts,like an oblique coordinate grid. Any wave, hencealso its components, are integrated only as theyarrive. The views show 1:1 equivalence.




- Velocity ω unrepresentablevanishes in ideal FTthis is a power signal









The many challenges on the way

• Spectral connection to instrument scale variation was unclear

• Scale unit µ, target interval L, measure is L/µA drift rate µ must add −µ.L/µ2 ≡ −βL to velocitiesBut why would the virtual velocities have Doppler shifts?

• Time derivative of wavelength comb radar imaging[5]

• No fast continuously variable gratings for off-the-shelf optical test• Lacked “empirical authority” for confidence on chirp spectra• Made no sense to physics colleagues either (with Fourier view)

• Rigidity solvable in radio receivers, but

• Analogue is still rigid hardware & digital sampling rejects chirps• Basic questions, besides time and cost, against experimenting:

What β is critical, how long to ramp? (limits components)What signals to seek? Does it need “FM content”?

• Fortuitously answered by NASA, US STRATCOM, and ESA

[5]Guruprasad 2005.



Modern, non-phase lock receiver (after Cassini)[6]

Figure 5 Uplink Card Block Diagram

which is then forwarded to the CDU for data demodulation and command detection. For the New Horizons mission, this subcarrier is binary phase shift key (BPSK) modulated with commands at data rates of 2000, 500, 125, and 7.8125 bps. The CDU locks to and tracks the 16 KHz subcarrier and demodulates the command data, passing data and clock over to the CCD. In the CCD, designated critical relay commands are decoded, detected, and immediately sent to the power switching system. The CCD also forwards all commands to the C&DH system. The 2.5 MHz WBIF channel is buffered and routed to the Radiometrics Card for further processing. The 2.5 MHz WBIF is also demodulated in the quadrature demodulator built into the receiver IC. The resultant baseband channel (or ranging channel) is filtered through several filters designed to limit the noise power in this channel as well as reduce the level of various demodulation products, while at the same time allowing the desired ranging tones to pass through with minimal phase and amplitude distortion. The output of this ranging channel is buffered and routed to the downlink card for modulation onto the downlink X-band carrier. In addition, the ranging channel has the capability to route either the demodulated ranging tones or the regenerated pseudonoise (PN) ranging code produced by the regenerative ranging subsystem to the downlink card.

5

Carrier acquisition and tracking is provided via a type-II phase locked loop and noncoherent AGC system. Both the

RF and IF synthesized LOs are tuned through the use of a common 30.1 MHz carrier tracking reference clock; this clock is generated by mixing the 30 MHz spacecraft frequency reference with a 100 KHz DDS. The DDS phase and frequency is dynamically tuned by the DPLL carrier tracking system to in-turn tune the RF and IF LOs. An open loop, fixed downconversion mode is required for REX; in this mode, the DDS frequency is set at a fixed value that is reprogrammable during the mission. All clocks and frequency sources in the digital receiver system are referenced to the 30 MHz spacecraft reference oscillator. Features

Performance highlights include the following: total secondary power consumption of 2.5 W (including the integrated on-board command detector unit (CDU) and critical command decoder (CCD)), built-in support for regenerative ranging and REX, carrier acquisition threshold of -157 dBm, high RF carrier acquisition and tracking rate capability for near-Earth operations (2800 Hz/s down to -100 dBm, 1800 Hz/s down to -120 dBm, 650 Hz/s down to -130 dBm), ability to digitally tune to any X-band RF channel assignment (preprogrammed on Earth for this mission) without the need for analog tuning and tailoring, use of an even 30.0 MHz ultrastable oscillator (USO) as a frequency reference, a noncoherent AGC system, and best lock frequency (BLF) telemetry accuracy to 0.5 Hz at X-band and BLF settability plus stability error < +/- 0.1 ppm

∫T exp(iω0e

β[t−r/c]/β) × exp(−iωx0eβ′t/β′) dt

[6]Chen et al. 2000; DeBoy et al. 2003.



Modern, non-phase lock receiver (after Cassini)[6]

Figure 5 Uplink Card Block Diagram

which is then forwarded to the CDU for data demodulation and command detection. For the New Horizons mission, this subcarrier is binary phase shift key (BPSK) modulated with commands at data rates of 2000, 500, 125, and 7.8125 bps. The CDU locks to and tracks the 16 KHz subcarrier and demodulates the command data, passing data and clock over to the CCD. In the CCD, designated critical relay commands are decoded, detected, and immediately sent to the power switching system. The CCD also forwards all commands to the C&DH system. The 2.5 MHz WBIF channel is buffered and routed to the Radiometrics Card for further processing. The 2.5 MHz WBIF is also demodulated in the quadrature demodulator built into the receiver IC. The resultant baseband channel (or ranging channel) is filtered through several filters designed to limit the noise power in this channel as well as reduce the level of various demodulation products, while at the same time allowing the desired ranging tones to pass through with minimal phase and amplitude distortion. The output of this ranging channel is buffered and routed to the downlink card for modulation onto the downlink X-band carrier. In addition, the ranging channel has the capability to route either the demodulated ranging tones or the regenerated pseudonoise (PN) ranging code produced by the regenerative ranging subsystem to the downlink card.

5

Carrier acquisition and tracking is provided via a type-II phase locked loop and noncoherent AGC system. Both the

RF and IF synthesized LOs are tuned through the use of a common 30.1 MHz carrier tracking reference clock; this clock is generated by mixing the 30 MHz spacecraft frequency reference with a 100 KHz DDS. The DDS phase and frequency is dynamically tuned by the DPLL carrier tracking system to in-turn tune the RF and IF LOs. An open loop, fixed downconversion mode is required for REX; in this mode, the DDS frequency is set at a fixed value that is reprogrammable during the mission. All clocks and frequency sources in the digital receiver system are referenced to the 30 MHz spacecraft reference oscillator. Features

Performance highlights include the following: total secondary power consumption of 2.5 W (including the integrated on-board command detector unit (CDU) and critical command decoder (CCD)), built-in support for regenerative ranging and REX, carrier acquisition threshold of -157 dBm, high RF carrier acquisition and tracking rate capability for near-Earth operations (2800 Hz/s down to -100 dBm, 1800 Hz/s down to -120 dBm, 650 Hz/s down to -130 dBm), ability to digitally tune to any X-band RF channel assignment (preprogrammed on Earth for this mission) without the need for analog tuning and tailoring, use of an even 30.0 MHz ultrastable oscillator (USO) as a frequency reference, a noncoherent AGC system, and best lock frequency (BLF) telemetry accuracy to 0.5 Hz at X-band and BLF settability plus stability error < +/- 0.1 ppm

∫T exp(iω0e


β′ = 0(sinusoid)

digital loop: updatesat IF samples only

RFDopplerrateβ

(chirp)

[6]Chen et al. 2000; DeBoy et al. 2003.



Transponder phase lock loop (Galileo, NEAR, Cassini)[7]

∫T exp(iω0e


[7]Mysoor, Perret, and Kermode 1991; Bokulic et al. 1998; Chen et al. 2000.



Transponder phase lock loop (Galileo, NEAR, Cassini)[7]

∫T exp(iω0e


RFDopplerrateβ

analogue loop β′continuous update

• Red path: carrier phase-locked loop, teal path: signal

• Phase error value is typically digital – using logic gates• Analogue in time ⇒ phase error is detected continuously⇒ resonators track each RF cycle⇒ carrier Doppler, demodulated signal from chirp spectrum

[7]Mysoor, Perret, and Kermode 1991; Bokulic et al. 1998; Chen et al. 2000.



Opportunity in the flyby data

• The distinct circumstances in Earth flybys (and NASA)

• Sustained Doppler rate β > 0 in approach, β < 0 in retreat• Tracked by 2-way Doppler of telemetry carrier

Requires dedicated DSN (or ESTRACK) antennasEven geostationary satellites do not merit this

• Non-repeating and used for subsequent mission calibrationso any lag or advance in Doppler stands out

• NASA started with phase lock transponder, and published dataESA only due to NASA role, no data for JAXA, other countries

• Signature of the chirp mode in the flyby data

• SSN residuals fit range lags: ∆r = −v∆t, ∆t = r/c• Anomaly fits velocity lags: ∆v = −a∆t, a ≡ v• Velocity lags ∆v ⇔ Doppler lags ∆ω = ω∆t• Identical in sign, magnitude to CWFM but in excess



The tracking and the anomaly

• Deep space tracking using telemetry• PN codes (initial range) + Doppler integration (fine range)[8]

• Precise enough for general relativity tests[9]

• Velocity discrepancies ∆V across gap in tracking[10]

• Galileo 1990: 4.3 mm/s• NEAR 1998: 13.46 mm/s• Rosetta 2005: 3.6 mm/s[11]

Reported as 1.82, tracking resumed before perigee[12]

• Limitations of the JPL definition

- If there is no gap, ∆V cannot manifest (Cassini)- Trajectory can be dynamically wrong even with ∆V = 0- ∆V is a computed error 6⇒ real force/energy at orbit range

[8]Anderson, Laing, et al. 2002.

[9]Bender and Vincent 1989.

[10]Antreasian and Guinn 1998; Anderson, Campbell, et al. 2008.

[11]Morley and Budnik 2006.

[12]T Morley (2017). Pvt comm.



Other symptoms

• Perigee shift relative to target at last control manoeuvre

• NEAR: +6.8 km change in altitude (NASA press releases)• Rosetta 2005: −340 ms (advance, ∼ 10.2 km)

Compare: Juno: +0.26 ms[13][14]

• Large residual swings

• Around perigee (Galileo[15], Rosetta[16])• Large diurnal oscillations post-perigee (NEAR[11][17])

• Large range errors against SSN radars (NEAR[11], Galileo[18])

• Up to 1 km ∼ 100×precision, � 5σ[19]

• Yet JPL thought it was “noise”[14], buried in AIAA 1998![13]

Thompson et al. 2014.[14]

P F Thompson (2019). Pvt comm.[15]

Antreasian and Guinn 1998.[16]

Morley and Budnik 2006.[17]

Anderson, Campbell, et al. 2008.[18]

J K Campbell (2015-). Pvt comm.[19]

P G Antreasian (2017). Pvt comm.c© 2019 V. Guruprasad IEEE NAECON 2019 11/20


NEAR’s SSN radar range residuals: errors ∆r

A - AltairM - Millstone

Pre-fit Data

06:14 06:22 06:29 06:36 06:43 06:50

−1,000 m

−800 m

−600 m

−400 m

∆r-25 for ALTAIR (m)

∆r for Millstone (m)

±25 m bounds for ALTAIR

±5 m bounds for Millstone

06:14 06:22 06:29 06:36 06:43 06:5015,000 km

20,000 km

25,000 km

30,000 km

35,000 km

r for ALTAIR (km)

r for Millstone (km)

• Against integrated telemetry Doppler range

• Too systematic for circuit fluctuations: R/S > 5σ• Too large for random error: 40ε Altair, 140ε Millstone• Too large for transponder latency: error ∆t = 60-140 ms

• ∆t = one-way “light times”a r/c , whence ∆v = −ar/ca

Guruprasad 2015a.c© 2019 V. Guruprasad IEEE NAECON 2019 12/20


NEAR’s SSN radar range residuals: the choices

A - AltairM - Millstone

Pre-fit Data

06:14 06:22 06:29 06:36 06:43 06:50

−1,000 m

−800 m

−600 m

−400 m

∆r-25 for ALTAIR (m)

∆r for Millstone (m)

±25 m bounds for ALTAIR

±5 m bounds for Millstone

06:14 06:22 06:29 06:36 06:43 06:5015,000 km

20,000 km

25,000 km

30,000 km

35,000 km

r for ALTAIR (km)

r for Millstone (km)

• Physicists’ interpretations

• Blame radar (JPL physics) ⇒ DoD’s SSN superluminal at 2ca

• Source-dependent c (EPL comment) ∼ telemetry at c/2

• Concede JPL’s graph already shows ∆ω = −ωHr in Doppler• Hubble’s law with H = β/c , β: fractional Doppler rate ∼ 10−6/s

aSince ∆t is the full one-way light time



NEAR perfect fit: ∆v ' ∆V – post-encounter (Canberra)

00:0001-23

12:0001-23

00:0001-24

12:0001-24

00:0001-25

12:0001-25

00:0001-26

12:0001-26

00:0001-27

0

500

1,000

1,500

2,000

2,500

Ran

ge[100

0km

]

range r

5.5

6

6.5

7

7.5

Ran

gerate

[km/s]

range rate vacceleration a

−300

−200

−100

0

100

AOSCanberra

11.13 mm/s

Velocity

lag[m

m/s]

∆v = −ar/c

• ∆v ≡ −ar/c = 11.13 mm/s at AOS ∼ 20% of anomalya

• Correlation with ∆v ⇒ JPL’s direction prediction issueb

• Impossible growth in v (range rate from JPL Horizons)

aGuruprasad 2015a.

bAnderson, Campbell, et al. 2008.



NEAR perfect fit: ∆v ' ∆V – pre-encounter (Goldstone)

00:0001-23

02:2401-23

04:4801-23

07:1201-23

09:3601-23

12:0001-23

0

50

100

150

200Ran

ge[100

0km

]

range r

−15

−10

−5

0

5

10

15

Ran

gerate

[km/s]

range rate v−300

−200

−100

0

LOSGoldstone

2.51 mm/s7.0 mm/s

Velocity

lag[m

m/s]

∆v = −ar/c

• Balance of ∆v found at LOS

• Total ∆v = 11.13 + 2.51 = 13.64 mm/s

• Result is 1.3% of ∆V = 13.46 mm/sa

aAnderson, Campbell, et al. 2008.



Explaining Rosetta 2005 residuals

Range rate v

02/28 03/02 03/04 03/06 03/08 03/10

Acceleration a

• Large residuals ⇒ Doppler not following range rate

• Consistency with velocity lags ⇐ residuals follow acceleration

• Broken residual tracks: fresh acquisition every day

• New Norcia track consistently follows acceleration



Explaining Rosetta 2005 residuals

Range rate v

02/28 03/02 03/04 03/06 03/08 03/10

Acceleration a

• Large residuals ⇒ Doppler not following range rate

• Consistency with velocity lags ⇐ residuals follow acceleration

• Broken residual tracks: fresh acquisition every day

• Goldstone tracks acceleration till 05, even “outgassing” on 01



Explaining Rosetta’s later flybys (2009)

07:0511-13

07:1211-13

07:1911-13

07:2611-13

07:3411-13

07:4111-13

07:4811-13

07:5511-13

5

10

15

20

25

30

Range[1000km]

range r

−15

−10

−5

0

5

10

15

Rangerate

[km/s]

range rate v

−1,200

−1,000

−800

−600

−400

−200

0

200

AOSNew

Norcia

LOSNew

Norcia

0.0395 mm/s

−530 mm/s

Velocity

lag[m

m/s]

∆v = −2ar/c

2009 : both LOS, AOS at New Norcia

• ∆vAOS ≈ −530 mm/s ∼ 15 Hz – way outside loop filter band

• ∆vLOS = 0.0395 mm/s ∼ 1 mHz – indistinguishably small

• Consistent with no anomaly



Explaining Rosetta’s later flybys (2007)

16:48

11-13

18:00

11-13

19:12

11-13

20:24

11-13

21:36

11-13

0

50

100

150

Range[1000km]

range r

−10

−5

0

5

10

Rangerate

[km/s]

range rate v

−800

−600

−400

−200

0 −41.76 mm/s

LOSNew

Norcia

Velocity

lag[m

m/s]

∆v = −2ar/c

2007 : LOS at New Norcia, AOS at Goldstone

• ∆vAOS ≈ −514 mm/s ∼ 14 Hz – way outside loop filter band

• ∆vLOS = −41.76 mm/s ∼ 1.2 Hz – also outside loop band

• New Norcia likely acquired Fourier mode much earlier



The cold case of Galileo 1990[20][21]

G - GoldstoneC - CanberraM - Madrid

Close Approach23-Jan-1998 07:22:55 UTC08-Dec-1990 20:34:34 UTC

12-07/12 12-08/00 12-08/12 12-09/00 12-09/12 12-10/00

Canberra velocity

Madrid velocity

Goldstone velocity

G - GoldstoneC - CanberraM - Madrid

Close Approach23-Jan-1998 07:22:55 UTC08-Dec-1990 20:34:34 UTC

12-07/12 12-08/00 12-08/12 12-09/00 12-09/12 12-10/00

Canberra acceleration

Madrid acceleration

Goldstone acceleration

• Goldstone residuals follow velocity late on the 9th⇒ unlikely to have caused anomaly

• Canberra residuals follow acceleration around C/A⇒ most likely cause of anomaly

• Start/end times too imprecise this close to C/A for ∆v -∆V fit

[20]Antreasian and Guinn 1998.

[21]P G Antreasian (2017). Pvt comm.



Continuously tracked: Cassini[22]

06/23 07/03 07/13 07/23 08/02 08/12 08/22 09/01

DSS 15 (Goldstone)

DSS 45 (Canberra)

• Continuously tracked by multiple stations (watched pot!)⇒ dragging even by large ∆v gets averaged out⇒ spikes could be chirp lock at AOS, but too small

• No tracking gap ⇒ no possibility of ∆V discontinuity

[22]Guman et al. 2000.



Non-phase lock: Juno[23], MESSENGER[24]

• Juno residuals (above) comparable to Rosetta’s• But entirely consistent with multi-path reflections under spin• “Deleted data” – tracks excluded for very large spin issues• No anomaly consistent with non-phase locking:

• Tracks not overlapping but agree on trajectory: no ∆v• Perigee shift: +0.26 ms, versus −340 ms for Rosetta

• MESSENGER residuals ∼ Cassini’s: 0.15 mHz – no anomaly

[23]Thompson et al. 2014.

[24]J K Campbell (2015-). Pvt comm.



Onward and outward• We are truly done with the flyby anomaly

• All flybys analyzed where anomaly details and data available• Only exclusions – all non-NASA and

Galileo 1992 (uncertain anomaly, no AOS/LOS details)Stardust, DI/EPOXI[25], OSIRIS-REx (no anomaly, details)

• Requested and overseen by J K Campbell of “JPL anomaly team”Team noted consistent absence of anomaly since CassiniCampbell noticed correlation with transponder change

• Chirp mode evidence is most robust observations of mankind• Trajectory fits verify consistency – ∆V fit meaningless beyond 1%• Direct evidence is NEAR’s SSN residuals

• Millstone data is 100σ : overall 5σ ignoring independence• Astrophysics, particle physics less robust on Allan deviations

• Chirp mode receivers would be simple, immensely significant

• Sawtooth FM of LO[26] – POC challenge is LO signal conditioning

[25]Bhaskaran et al. 2011.

[26]Guruprasad 2015b.



ReferencesAnderson, J D and Nieto, M M (2009). “Astrometric Solar-System Anomalies”. In: Proc IAU Symp No. 261.

arXiv: 0907.2469v2.Turyshev, S G et al. (2012). “Support for the thermal origin of the Pioneer anomaly”. In: Phys Rev Lett 108 (24).

arXiv: 1204.2507v1.Altamimi, Z et al. (2016). “ITRF2014: A new release of the International Terrestrial Reference Frame modeling

nonlinear station motions”. In: J Geophy Res: Solid Earth 121.8, pp. 6109–6131.Guruprasad, V (2005). “A wave effect enabling universal frequency scaling, monostatic passive radar, incoherent

aperture synthesis, and general immunity to jamming and interference”. In: MILCOM (classified session).arXiv: physics/0812.2652v1.

Mysoor, N R, Perret, J D, and Kermode, A W (1991). Design concepts and performance of NASA X-Band (7162MHx/8415 MHz) Transponder for Deep-space Spacecraft Applications. Tech. rep. 42-104. Descanso NASA.

Bokulic, R S et al. (1998). “The NEAR spacecraft RF telecommunication system”. In: JHU APL Tech Digest 19.2.Chen, C-C et al. (2000). Small Deep Space Transponder (SDST) DS1 Technological Validation Report. Tech. rep.

Descanso NASA.DeBoy, C C et al. (2003). “The RF Telecommunications System for the New Horizons Mission to Pluto”. In:

IEEEAC. paper 1369.Anderson, J D, Laing, P A, et al. (2002). “Study of the anomalous acceleration of Pioneer 10 and 11”. In: Phys

Rev D 65, pp. 082004/1–50. arXiv: gr-qc/0104064.Bender, P L and Vincent, M A (1989). Small Mercury Relativity Orbiter. Tech. rep. N90-19940 12-90. NASA.Antreasian, P G and Guinn, J R (1998). “Investigations into the unexpected Delta-V increases during the earth

gravity assists of Galileo and NEAR”. In: AIAA. 98-4287.Anderson, J D, Campbell, J K, et al. (2008). “Anomalous Orbital-Energy Changes Observed during Spacecraft

Flybys of Earth”. In: PRL 100.9, p. 091102.Morley, T and Budnik, F (2006). “Rosetta Navigation at its First Earth-Swingby”. In: 19th Intl Symp Space Flight

Dynamics. ISTS 2006-d-52.Thompson, P F et al. (2014). “Reconstruction of the Earth flyby by the Juno spacecraft”. In: AAS. 14-435.Guruprasad, V (2015a). “Observational evidence for travelling wave modes bearing distance proportional shifts”.

In: EPL 110.5, p. 54001. arXiv: 1507.08222. url: http://stacks.iop.org/0295-5075/110/i=5/a=54001.Guman, M D et al. (2000). “Cassini orbit determination from first Venus flyby to Earth flyby”. In: AAS. 00-168.Bhaskaran, S et al. (2011). “Navigation of the EPOXI spacecraft to comet Hartley 2”. In: AAS. 11-486.Guruprasad, V (2015b). “Chirp travelling waves and spectra”. In: PCT/US2015/015857.

Pub. No. WO/2016/099590 published 2016-06-23.


http://arxiv.org/abs/0907.2469v2

http://arxiv.org/abs/1204.2507v1

http://arxiv.org/abs/physics/0812.2652v1

http://arxiv.org/abs/gr-qc/0104064

http://arxiv.org/abs/1507.08222

http://stacks.iop.org/0295-5075/110/i=5/a=54001

conclusive analysis & cause of the yby anomaly

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