Conclusive Analysis & Cause of the Flyby Anomaly

Introduction Theory Analysis Conclusion

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

V. Guruprasad

Inspired Research, New York http://www.inspiredresearch.com

2019-07-17

c 2019 V. Guruprasad IEEE NAECON 2019 1/20

Introduction Theory Analysis Conclusion Summary • Popular context: Astrometric solar-system anomalies[1] Pioneer: ∆V r˙ H r at r 5 AU (blueshift) – SOLVED[2] • 0 Flyby: ∆V trajectory∼ ≈ − discontinuity≥ at satellite range • [3] Lunar orbit eccentricity growth: also H0 • ∼ 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 c 2019 V. Guruprasad IEEE NAECON 2019 2/20

Introduction Theory Analysis Conclusion 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(H ) • 0 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) = eiωt • 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 frequencyω ˙ • Current analyses assume Fourier:ω ˙ = 0 • The ﬂyby anomaly is nature saying they are incomplete • c 2019 V. Guruprasad IEEE NAECON 2019 3/20

Introduction Theory Analysis Conclusion 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 β[t ∆t] Components exp(iω e − /β) shifts ∆ω = ωβ∆t • 0 Don’t really depend on r wave⇔ notions are irrelevant!− • ⇒ [4] Guruprasad 2005. c 2019 V. Guruprasad IEEE NAECON 2019 4/20

- Inclined view with shifts - A group under translations (so Fourier is degenerate)

Introduction Theory Analysis Conclusion

Spectra are computed representations 1

ω ω T Any FM in Fourier basis eb - Discontinuous in ω eg

ey - Pieces violate d’Alembert! er - Velocityω ˙ unrepresentable source receiver vanishes in ideal FT ω ω T eb0 eg0 Steady tone in chirp basis ey0

er0 - d’Alembert withω ˙ = 0 6 er0∗ - Zero Fourier amplitudes! source receiver - Requires chirp basis The representation deﬁnes component shifts, – basis itself has velocityω ˙ like an oblique coordinate grid.

c 2019 V. Guruprasad IEEE NAECON 2019 5/20

- Inclined view with shifts - A group under translations (so Fourier is degenerate)

Introduction Theory Analysis Conclusion

Spectra are computed representations 2

ω ω T Any FM in Fourier basis eb - Discontinuous in ω eg

ey - Pieces violate d’Alembert! S er - Velocityω ˙ unrepresentable source receiver vanishes in ideal FT ω ω T

S Steady tone in chirp basis

- d’Alembert withω ˙ = 0 6 - Zero Fourier amplitudes! source receiver - Requires chirp basis The representation deﬁnes component shifts, – basis itself has velocityω ˙ like an oblique coordinate grid.

c 2019 V. Guruprasad IEEE NAECON 2019 5/20

- Inclined view with shifts - A group under translations (so Fourier is degenerate)

Introduction Theory Analysis Conclusion

Spectra are computed representations 3

ω ω T Any FM in Fourier basis eb - Discontinuous in ω eg

S ey - Pieces violate d’Alembert! er - Velocityω ˙ unrepresentable source receiver vanishes in ideal FT ω ω T

S Steady tone in chirp basis

c 2019 V. Guruprasad IEEE NAECON 2019 5/20

- Inclined view with shifts - A group under translations (so Fourier is degenerate)

Introduction Theory Analysis Conclusion

Spectra are computed representations 4

ω ω T Any FM in Fourier basis eb - Discontinuous in ω S eg

ey - Pieces violate d’Alembert! er - Velocityω ˙ unrepresentable source receiver vanishes in ideal FT ω ω T

S Steady tone in chirp basis ey0

e0∗ - d’Alembert withω ˙ = 0 y 6 - Zero Fourier amplitudes! source receiver - Requires chirp basis The representation deﬁnes component shifts, – basis itself has velocityω ˙ like an oblique coordinate grid. Any wave, hence also its components, are integrated only as they arrive.

c 2019 V. Guruprasad IEEE NAECON 2019 5/20

- Inclined view with shifts - A group under translations (so Fourier is degenerate)

Introduction Theory Analysis Conclusion

Spectra are computed representations 5

ω ω T Any FM in Fourier basis S eb - Discontinuous in ω eg

ey - Pieces violate d’Alembert! er - Velocityω ˙ unrepresentable source receiver vanishes in ideal FT ω ω T eb0 S eg0 Steady tone in chirp basis ey0

c 2019 V. Guruprasad IEEE NAECON 2019 5/20

- A group under translations (so Fourier is degenerate)

Introduction Theory Analysis Conclusion

Spectra are computed representations 6

ω Any FM in Fourier basis S ψs eb - Discontinuous in

dt ω eg ω/ d spectral view ey - Pieces violate d’Alembert! S er - Velocityω ˙ unrepresentable source receiver vanishes in ideal FT ω this is a power signal e ψ b0 S c e0 βω∆t g Steady tone in chirp basis − ey0

er0 - d’Alembert withω ˙ = 0 spectral view 6 S er0∗ - Zero Fourier amplitudes! source receiver - Requires chirp basis The representation deﬁnes component shifts, – basis itself has velocityω ˙ like an oblique coordinate grid. Any wave, hence - Inclined view with shifts also its components, are integrated only as they arrive. The views show 1:1 equivalence.

c 2019 V. Guruprasad IEEE NAECON 2019 5/20

Introduction Theory Analysis Conclusion

Spectra are computed representations 7

ω Any FM in Fourier basis S ψs eb - Discontinuous in

dt ω eg ω/ d spectral view ey - Pieces violate d’Alembert! S er - Velocityω ˙ unrepresentable source receiver vanishes in ideal FT ω this is a power signal e ψ b0 S c e g0 β e0 βω∆t g Steady tone in chirp basis e0 − ey0 y er0 er0 - d’Alembert withω ˙ = 0 6 S er0∗ - Zero Fourier amplitudes! source receiver - Requires chirp basis The representation deﬁnes component shifts, – basis itself has velocityω ˙ like an oblique coordinate grid. Any wave, hence - Inclined view with shifts also its components, are integrated only as they arrive. The views show 1:1 equivalence. - A group under translations (so Fourier is degenerate)

c 2019 V. Guruprasad IEEE NAECON 2019 5/20

Introduction Theory Analysis Conclusion The many challenges on the way

• Spectral connection to instrument scale variation was unclear Scale unit µ, target interval L, measure is L/µ • A drift rateµ ˙ must add µ.˙ L/µ2 βL to velocities But 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. c 2019 V. Guruprasad IEEE NAECON 2019 6/20

Introduction Theory Analysis Conclusion Modern, non-phase lock receiver (after Cassini)[6]

exp(iω eβ[t r/c]/β) exp( iω eβ0t /β ) dt T 0 − × − x0 0 R

Figure 5 Uplink Card Block Diagram

[6] whiChench is th eten al. forwarded 2000; DeBoy to the C etDU al. for 2003 data. demodulation RF and IF synthesized LOs are tuned through the use of a c 2019 V. Guruprasad IEEE NAECON 2019 7/20 and command detection. For the New Horizons mission, common 30.1 MHz carrier tracking reference clock; this this subcarrier is binary phase shift key (BPSK) modulated clock is generated by mixing the 30 MHz spacecraft with commands at data rates of 2000, 500, 125, and 7.8125 frequency reference with a 100 KHz DDS. The DDS phase bps. The CDU locks to and tracks the 16 KHz subcarrier and frequency is dynamically tuned by the DPLL carrier and demodulates the command data, passing data and clock tracking system to in-turn tune the RF and IF LOs. An open over to the CCD. In the CCD, designated critical relay loop, fixed downconversion mode is required for REX; in commands are decoded, detected, and immediately sent to this mode, the DDS frequency is set at a fixed value that is the power switching system. The CCD also forwards all reprogrammable during the mission. All clocks and commands to the C&DH system. frequency sources in the digital receiver system are referenced to the 30 MHz spacecraft reference oscillator. The 2.5 MHz WBIF channel is buffered and routed to the Radiometrics Card for further processing. The 2.5 MHz Features WBIF is also demodulated in the quadrature demodulator Performance highlights include the following: total built into the receiver IC. The resultant baseband channel secondary power consumption of 2.5 W (including the (or ranging channel) is filtered through several filters integrated on-board command detector unit (CDU) and designed to limit the noise power in this channel as well as critical command decoder (CCD)), built-in support for reduce the level of various demodulation products, while at regenerative ranging and REX, carrier acquisition threshold the same time allowing the desired ranging tones to pass of -157 dBm, high RF carrier acquisition and tracking rate through with minimal phase and amplitude distortion. The capability for near-Earth operations (2800 Hz/s down to - output of this ranging channel is buffered and routed to the 100 dBm, 1800 Hz/s down to -120 dBm, 650 Hz/s down to downlink card for modulation onto the downlink X-band -130 dBm), ability to digitally tune to any X-band RF carrier. In addition, the ranging channel has the capability channel assignment (preprogrammed on Earth for this to route either the demodulated ranging tones or the mission) without the need for analog tuning and tailoring, regenerated pseudonoise (PN) ranging code produced by use of an even 30.0 MHz ultrastable oscillator (USO) as a the regenerative ranging subsystem to the downlink card. frequency reference, a noncoherent AGC system, and best

lock frequency (BLF) telemetry accuracy to 0.5 Hz at X- Carrier acquisition and tracking is provided via a type-II band and BLF settability plus stability error < +/- 0.1 ppm phase locked loop and noncoherent AGC system. Both the

5 Introduction Theory Analysis Conclusion Modern, non-phase lock receiver (after Cassini)[6]

exp(iω eβ[t r/c]/β) exp( iω eβ0t /β ) dt T 0 − × − x0 0 R (chirp)

β RF Doppler rate

β0 = 0 (sinusoid) digital loop: updates at IF samples only

Figure 5 Uplink Card Block Diagram

5 Introduction Theory Analysis Conclusion Transponder phase lock loop (Galileo, NEAR, Cassini)[7]

exp(iω eβ[t r/c]/β) exp( iω eβ0t /β ) dt T 0 − × − x0 0 R

[7] Mysoor, Perret, and Kermode 1991; Bokulic et al. 1998; Chen et al. 2000. c 2019 V. Guruprasad IEEE NAECON 2019 8/20

Introduction Theory Analysis Conclusion Transponder phase lock loop (Galileo, NEAR, Cassini)[7]

exp(iω eβ[t r/c]/β) exp( iω eβ0t /β ) dt T 0 − × − x0 0

β R RF Doppler rate

analogue loop β0 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. c 2019 V. Guruprasad IEEE NAECON 2019 8/20

Introduction Theory Analysis Conclusion 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) antennas Even geostationary satellites do not merit this Non-repeating and used for subsequent mission calibration • so any lag or advance in Doppler stands out NASA started with phase lock transponder, and published data • ESA 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 •

c 2019 V. Guruprasad IEEE NAECON 2019 9/20

Introduction Theory Analysis Conclusion 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 real force/energy at orbit range 6⇒ [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. c 2019 V. Guruprasad IEEE NAECON 2019 10/20

Introduction Theory Analysis Conclusion 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

Introduction Theory Analysis Conclusion NEAR’s SSN radar range residuals: errors ∆r

35,000 km 400 m Pre-fit Data − r for ALTAIR (km) r for Millstone (km) 30,000 km

600 m −

25,000 km

800 m −

∆r-25 for ALTAIR (m) 20,000 km ∆r for Millstone (m) A - Altair M - Millstone 25 m bounds for ALTAIR 1,000 m ± − 5 m bounds for Millstone ± 15,000 km 06:14 06:22 06:29 06:36 06:43 06:50

• Against integrated telemetry Doppler range Too systematic for circuit ﬂuctuations: R/S > 5σ • Too large for random error: 40 Altair, 140 Millstone • Too large for transponder latency: error ∆t = 60-140 ms • • ∆t = one-way “light times”a r/c, whence ∆v = −ar/c

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

Introduction Theory Analysis Conclusion NEAR’s SSN radar range residuals: the choices

35,000 km 400 m Pre-fit Data − r for ALTAIR (km) r for Millstone (km) 30,000 km

600 m −

25,000 km

800 m −

∆r-25 for ALTAIR (m) 20,000 km ∆r for Millstone (m) A - Altair M - Millstone 25 m bounds for ALTAIR 1,000 m ± − 5 m bounds for Millstone ± 15,000 km 06:14 06:22 06:29 06:36 06:43 06:50

• 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 • a Since ∆t is the full one-way light time

c 2019 V. Guruprasad IEEE NAECON 2019 12/20

Introduction Theory Analysis Conclusion NEAR perfect ﬁt: ∆v ' ∆V – post-encounter (Canberra)

100 7.5 2,500 11.13 mm/s

2,000 O Canberra AOS 0 7 s] / 1,500

s] 6.5

/ 100 −

1,000 6 Range [1000 km] Range rate [km 200 − 500 range r acceleration a Velocity lag [mm range rate v ∆v = ar/c − 5.5

0 300 −

00:00 12:00 00:00 12:00 00:00 12:00 00:00 12:00 00:00 01-23 01-23 01-24 01-24 01-25 01-25 01-26 01-26 01-27

• ∆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)

a Guruprasad 2015a. b Anderson, Campbell, et al. 2008.

c 2019 V. Guruprasad IEEE NAECON 2019 13/20

Introduction Theory Analysis Conclusion NEAR perfect ﬁt: ∆v ' ∆V – pre-encounter (Goldstone)

15 7.0 mm/s 2.51 mm/s 200 0 10

150 5 100 s] /

− s] /

100 0

200 − LOS Goldstone Range [1000 km] 5 Range rate [km − 50 Velocity lag [mm range r 300 range rate v 10 − − ∆v = ar/c − 0 15 00:00 02:24 04:48 07:12 09:36 12:00− 01-23 01-23 01-23 01-23 01-23 01-23 • 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

a Anderson, Campbell, et al. 2008.

c 2019 V. Guruprasad IEEE NAECON 2019 13/20

Introduction Theory Analysis Conclusion Explaining Rosetta 2005 residuals

Range rate v Acceleration a

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

• 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

c 2019 V. Guruprasad IEEE NAECON 2019 14/20

Introduction Theory Analysis Conclusion Explaining Rosetta 2005 residuals

Range rate v Acceleration a

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

• 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 c 2019 V. Guruprasad IEEE NAECON 2019 14/20

Introduction Theory Analysis Conclusion Explaining Rosetta’s later ﬂybys (2009) 200 15

0.0395 mm/s 30 0 10

200 Norcia New LOS − 5 s] / s]

20 400 / − 0 600 15 − 530 mm/s − Range [1000 km] AOS New Norcia 5 Range rate [km 800 range r − 10 − Velocity lag [mm range rate v 1,000 ∆v = 2ar/c − − 10 5 − 1,200 − 15 07:05 07:12 07:19 07:26 07:34 07:41 07:48 07:55 − 11-13 11-13 11-13 11-13 11-13 11-13 11-13 11-13 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 c 2019 V. Guruprasad IEEE NAECON 2019 15/20

Introduction Theory Analysis Conclusion Explaining Rosetta’s later ﬂybys (2007) 10 41.76 mm/s 0 −

150 range r range rate v 5 200 ∆v = 2ar/c − − s] / s] / 100 400 0 − Range [1000 km] Range rate [km LOS New Norcia

600 Velocity lag [mm 5 50 − −

800 − 10 − 0 16:48 18:00 19:12 20:24 21:36 11-13 11-13 11-13 11-13 11-13

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 c 2019 V. Guruprasad IEEE NAECON 2019 15/20

Introduction Theory Analysis Conclusion The cold case of Galileo 1990[20][21]

Canberra velocity Canberra acceleration Madrid velocity Madrid acceleration Goldstone velocity Goldstone acceleration

Close Approach G - Goldstone Close Approach G - Goldstone C - Canberra C - Canberra 08-Dec-199023-Jan-1998 07:22:55 20:34:34 UTC UTC 08-Dec-199023-Jan-1998 07:22:55 20:34:34 UTC UTC M - Madrid M - Madrid 12-07/12 12-08/00 12-08/12 12-09/00 12-09/12 12-10/00 12-07/12 12-08/00 12-08/12 12-09/00 12-09/12 12-10/00

• 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. c 2019 V. Guruprasad IEEE NAECON 2019 16/20

Introduction Theory Analysis Conclusion Continuously tracked: Cassini[22]

DSS 15 (Goldstone) DSS 45 (Canberra)

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

• 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. c 2019 V. Guruprasad IEEE NAECON 2019 17/20

Introduction Theory Analysis Conclusion 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. c 2019 V. Guruprasad IEEE NAECON 2019 18/20

Introduction Theory Analysis Conclusion 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 Cassini Campbell 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. c 2019 V. Guruprasad IEEE NAECON 2019 19/20

Introduction Theory Analysis Conclusion References Anderson, 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 (7162 MHx/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. c 2019 V. Guruprasad IEEE NAECON 2019 20/20