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12.3 Amateur Satellites, Doppler Shift, and Earth-Moon-Earth (EME)

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ACMA Amateur Radio Advanced Recognition Certificate - Theory Exam

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1 Chapter 1: DC Theory, Circuit Laws & Passive Components

1.1 DC Circuit Analysis, Ohm's Law, and Kirchhoff's Laws 1.2 AC Fundamentals, Sine Waves, Peak, RMS, and Phase Relationships 1.3 Inductance, Capacitance, Reactance, and Time Constants

2 Chapter 2: Impedance, Resonance & Passive Filters

2.1 Complex Impedance, Phasors, and AC Circuit Analysis 2.2 Series and Parallel LC Resonance and Q Factor 2.3 Passive Filters, Cutoff Frequency, and Attenuator Pads

3 Chapter 3: Semiconductor Devices & Power Supplies

3.1 Semiconductor Diodes, Zener Regulators, and Rectifier Circuits 3.2 Bipolar Junction Transistors, FETs, and Operational Amplifiers 3.3 Thermionic Valves (Vacuum Tubes) and High-Power Linear Amplifiers 3.4 DC Power Supplies, Filter Networks, and Voltage Regulators

4 Chapter 4: Oscillators & Frequency Synthesis

4.1 RF Oscillators, LC Tank Topologies, and Frequency Stability 4.2 Phase-Locked Loops (PLLs) and Frequency Synthesisers 4.3 Direct Digital Synthesis (DDS), SDR Architectures, and Digital Filter Topologies

5 Chapter 5: RF Amplifiers & Linearity

5.1 Classes of Amplification, Conduction Angles, and Operating Efficiency 5.2 RF Power Amplifiers, Push-Pull Topologies, and Output Matching 5.3 Amplifier Stability, Neutralisation, and Intermodulation Distortion

6 Chapter 6: Modulation & Demodulation

6.1 Amplitude Modulation, Double Sideband, and Single Sideband (SSB) 6.2 Frequency Modulation, Phase Modulation, and FM Detectors 6.3 Digital Modulation Modes, Spectral Efficiency, and Weak-Signal Protocols

7 Chapter 7: Transmitters, Mixers & Receivers

7.1 RF Mixers, Frequency Translation, and Intermodulation 7.2 Transmitter Architectures, CW Keying, and Output Filtering 7.3 Superheterodyne Receiver Design, IF Selection, and Image Rejection 7.4 Receiver Performance Specifications, Dynamic Range, and Selectivity

8 Chapter 8: Transmission Lines & Waveguides

8.1 Transmission Line Characteristics, Impedance, and Velocity Factor 8.2 Standing Waves, Reflection Coefficient, SWR, and Return Loss 8.3 Resonant Line Sections, Quarter-Wave Transformers, and Stubs

9 Chapter 9: Impedance Matching & Baluns

9.1 Lumped-Element Matching Networks and Antenna Tuning Units 9.2 Baluns, Ununs, and Common-Mode Current Choking 9.3 Feedline Losses, High-SWR Stress, and Coaxial Installation Practice

10 Chapter 10: Practical Antennas & Arrays

10.1 Resonant Dipoles, Inverted-Vs, and Multiband Wire Antennas 10.2 Quarter-Wave Verticals, Ground Systems, and Radiation Efficiency 10.3 Parasitic Arrays, Yagi-Uda Antennas, and Quad Arrays 10.4 Antenna Gain, Aperture Antennas & Horns, ERP/EIRP, Radiation Patterns

11 Chapter 11: Radio Wave Propagation & Ionospheric Mechanics

11.1 Electromagnetic Wave Fundamentals, Polarisation, and Ground Waves 11.2 The Ionosphere, Solar Radiation, and Solar Cycles 11.3 Critical Frequency, Maximum Usable Frequency, and HF Propagation Paths

12 Chapter 12: VHF/UHF Propagation & Space Communications

12.1 Line-of-Sight, Tropospheric Ducting, and Diffraction 12.2 Sporadic-E, Auroral Scatter, and Trans-Equatorial Propagation 12.3 Amateur Satellites, Doppler Shift, and Earth-Moon-Earth (EME)

13 Chapter 13: Test Equipment & RF Measurements

13.1 Decibels, Power Ratios, and Cascaded Stage Calculations 13.2 RF Power Meters, Directional Couplers, and Dummy Loads 13.3 Multirange Meters, Waveform Diagnostics, Oscilloscopes, and Frequency Counters

14 Chapter 14: Advanced RF Analysis & Diagnostics

14.1 Spectrum Analyser Architecture, Operation, and Spectral Purity 14.2 Antenna Analysers, Vector Network Analysers, and Smith Charts 14.3 Calibrated Signal Generators, Grid Dip Meters, and Component Testing

15 Chapter 15: Electromagnetic Compatibility & Interference

15.1 Sources of Interference, Coupling Mechanisms, and Audio Rectification 15.2 Receiver Susceptibility, Desensitisation, and Front-End Intermodulation 15.3 Practical RFI Suppression, Filter Design, and Bonding Techniques

16 Chapter 16: Electrical, RF & Station Safety

16.1 Biological Effects of RF Energy and ARPANSA Exposure Standards 16.2 Safe Separation Distances, Power Density, and Duty Cycles 16.3 Station Electrical Safety, Battery Hazards, and Safe Headphone Use 16.4 Mast and Tower Construction, Power Line Clearance, and Lightning Protection

12.3 Amateur Satellites, Doppler Shift, and Earth-Moon-Earth (EME)

Key Takeaways Explain This Topic AI

Low Earth Orbit (LEO) amateur satellites orbit at altitudes of 400 to 1500 km 400\text{ to }1500\text{ km} 400 to 1500 km with 90 to 115 minute 90\text{ to }115\text{ minute} 90 to 115 minute periods, providing fleeting 10 to 15 minute 10\text{ to }15\text{ minute} 10 to 15 minute line-of-sight passes that require real-time azimuth/elevation antenna tracking and active Doppler compensation.

Linear inverting transponders use subtractive mixing to reverse frequency order and sidebands. Operators normally transmit LSB and receive USB; uplink and downlink Doppler shifts partially cancel when monitoring one's own downlink.

Rapid relative motion on LEO satellites introduces substantial Doppler shifts (up to ± 3.5 kHz \pm 3.5\text{ kHz} ± 3.5 kHz on 145 MHz 145\text{ MHz} 145 MHz and ± 10.5 kHz \pm 10.5\text{ kHz} ± 10.5 kHz on 435 MHz 435\text{ MHz} 435 MHz ), where downlink frequencies start high at Acquisition of Signal (AOS) and end low at Loss of Signal (LOS).

Faraday rotation rotates the polarization angle of linear radio waves traversing the ionosphere; utilizing circular polarization (RHCP/LHCP) via crossed-Yagi antennas with 90 ∘ 90^\circ 9 0 ∘ delay lines eliminates deep cross-polarization fading nulls.

EME uses the Moon as a passive radar reflector, with about 252 dB 252\text{ dB} 252 dB basic path loss at 144 MHz 144\text{ MHz} 144 MHz and 2.56 s 2.56\text{ s} 2.56 s propagation delay. Antenna gain, low receive-system noise and JT65/Q65 processing support weak-signal contacts. Australian class-licence power limits depend on band and emission; 400 W 400\text{ W} 400 W PEP is not a general CW or digital limit.

Last updated: November 2026

12.3 Amateur Satellites, Doppler Shift, and Earth-Moon-Earth (EME)

VHF, UHF, and microwave signals can pass through the ionosphere for space communications; penetration depends on frequency and ionospheric conditions. AMSAT organisations and other amateur groups design and support satellites, while the IARU Satellite Frequency Coordination Panel coordinates amateur satellite frequencies internationally. Amateur satellites have carried the OSCAR designation (Orbiting Satellite Carrying Amateur Radio) since OSCAR 1 in 1961. Radio amateurs also use the Moon as a passive reflector for Earth-Moon-Earth (EME) communication.

Operating in the space communications realm requires mastering orbital mechanics, transponder architectures, dynamic Doppler shifts, Faraday polarization rotation, and the link budgets needed to overcome astronomical path losses.

Amateur Radio Satellite Orbits and Keplerian Tracking

Amateur spacecraft operate across three primary orbital profiles, each presenting distinct operational trade-offs:

Low Earth Orbit (LEO):

Altitude: 400 to 1500 km 400\text{ to }1500\text{ km} 400 to 1500 km above Earth's surface.

Orbital Velocity: Approximately 7.5 km/s 7.5\text{ km/s} 7.5 km/s ( 27 , 000 km/h 27,000\text{ km/h} 27 , 000 km/h ).

Orbital Period: 90 to 115 minutes 90\text{ to }115\text{ minutes} 90 to 115 minutes per orbit.

Pass Characteristics: Useful passes commonly last 10 to 15 minutes 10\text{ to }15\text{ minutes} 10 to 15 minutes between Acquisition of Signal (AOS) and Loss of Signal (LOS) . For altitudes of 400 to 1500 km 400\text{ to }1500\text{ km} 400 to 1500 km , the satellite's geometric footprint radius is about 2200 to 4000 km 2200\text{ to }4000\text{ km} 2200 to 4000 km ; a minimum usable elevation reduces this coverage.

Examples: The International Space Station (ISS, about 400 km 400\text{ km} 400 km altitude), SO-50, AO-91, and AO-7. AO-7 launched in 1974, fell silent after battery failure in 1981, and resumed solar-powered operation in 2002.

Geostationary Orbit (GEO):

Altitude: Exactly 35 , 786 km 35,786\text{ km} 35 , 786 km above the equator.

Orbital Velocity: 3.07 km/s 3.07\text{ km/s} 3.07 km/s , matching the Earth's sidereal rotation period ( 23 h 56 m 04 s 23\text{h }56\text{m }04\text{s} 23 h 56 m 04 s ).

Characteristics: The satellite appears stationary in the sky. It provides continuous, 24/7 coverage over roughly 42 % 42\% 42% of the Earth's surface with zero Doppler shift and fixed dish antennas.

Example: QO-100 (Qatar-OSCAR 100 / Es'hail-2) , launched in 2018, carries an amateur linear transponder with an uplink at 2.4 GHz 2.4\text{ GHz} 2.4 GHz and a downlink at 10.49 GHz 10.49\text{ GHz} 10.49 GHz . While its footprint encompasses Europe, Africa, the Middle East, India, and parts of Brazil, it sits below the horizon for mainland Australia.

Highly Elliptical Orbit (HEO):

Geometry: A large difference between perigee and apogee produces a strongly elongated orbit. A Molniya orbit is a particular HEO with a roughly 12 hour 12\text{ hour} 12 hour period and 63.4 ∘ 63.4^\circ 63. 4 ∘ inclination, chosen to limit rotation of the line of apsides.

Characteristics: By Kepler's second law, the satellite moves slowly near apogee, giving hours of visibility over the favoured hemisphere. Amateur HEOs need not use Molniya geometry: AO-10 had about 4000 km 4000\text{ km} 4000 km perigee, 35 , 440 km 35,440\text{ km} 35 , 440 km apogee and 26.5 ∘ 26.5^\circ 26. 5 ∘ inclination. AO-40 was another historical amateur HEO.

Keplerian Elements (Two-Line Element Sets - TLE)

To predict precisely when a LEO satellite will rise above the local horizon and where to aim directional antennas, tracking software processes Keplerian elements . These are distributed by space agencies in standard Two-Line Element (TLE) sets: Illustrative TLE Format (not tracking data)

  • OSCAR 7 (AO-7)
  • 1 07530U 74089B 26282.45182935 -.00000012 00000-0 10000-3 0 9998
  • 2 07530 101.9834 234.1205 0012140 321.4589 38.5412 12.53612845341255

The fundamental classical parameters defined within a TLE are:

Epoch: The UTC reference time to which the element set applies, expressed as a year and fractional day of year.

Inclination ( i i i ): The angle between the orbital plane and Earth's equatorial plane ( 101.98 ∘ 101.98^\circ 101.9 8 ∘ in the sample). Values above 90 ∘ 90^\circ 9 0 ∘ indicate retrograde motion; polar orbits have inclination near 90 ∘ 90^\circ 9 0 ∘ .

Right Ascension of the Ascending Node ( Ω \Omega Ω / RAAN): The celestial longitude at which the satellite crosses the equator from south to north.

Eccentricity ( e e e ): The shape of the ellipse ( 0.0012140 0.0012140 0.0012140 , where 0 0 0 is a circle and values approaching 1 1 1 become elongated).

Argument of Perigee ( ω \omega ω ): The angular distance along the orbit from the ascending node to the point of closest approach ( 321.46 ∘ 321.46^\circ 321.4 6 ∘ ).

Mean Motion ( n n n ): The number of revolutions the satellite completes around Earth per solar day ( 12.536 revs/day 12.536\text{ revs/day} 12.536 revs/day ). From this, the semi-major axis and orbital altitude are calculated.

Mean Anomaly ( M M M ): An angle that increases uniformly in the ideal Keplerian orbit, from 0 ∘ 0^\circ 0 ∘ at perigee to 360 ∘ 360^\circ 36 0 ∘ after one revolution ( 38.54 ∘ 38.54^\circ 38.5 4 ∘ at the sample epoch). The actual position angle is the true anomaly.

Ground tracking software (e.g., Gpredict, SatPC32) utilizes the SGP4 (Simplified General Perturbations) mathematical model to propagate these elements forward in time. The software outputs real-time Azimuth ( 0 ∘ to 360 ∘ 0^\circ\text{ to }360^\circ 0 ∘ to 36 0 ∘ ) and Elevation ( 0 ∘ to 90 ∘ 0^\circ\text{ to }90^\circ 0 ∘ to 9 0 ∘ ) angles, controlling computer-automated antenna rotators.

Doppler Shift in Space Communications

Because a LEO satellite travels at an orbital velocity of roughly v orb ≈ 7.5 km/s v_{\text{orb}} \approx 7.5\text{ km/s} v orb ​ ≈ 7.5 km/s relative to a ground observer, electromagnetic waves experience a substantial Doppler frequency shift . Δ f = f 0 v rel c \Delta f = f_0 \frac{v_{\text{rel}}}{c} Δ f = f 0 ​ c v rel ​ ​

where:

f 0 f_0 f 0 ​ is the nominal transmitted frequency,

v rel v_{\text{rel}} v rel ​ is the relative radial velocity between the satellite and ground station along the line of sight (defined as positive when the spacecraft is approaching and negative when receding),

c ≈ 3.00 × 10 8 m/s c \approx 3.00 \times 10^8\text{ m/s} c ≈ 3.00 × 1 0 8 m/s is the speed of light. Received downlink frequency during an overhead LEO pass

  • f0 + Δf o AOS: approaching
  • |\
  • | \
  • | \
  • f0 +------o TCA: radial velocity zero
  • | \
  • | \
  • f0 - Δf | o LOS: receding
  • +------------+------------> Time
  • AOS TCA LOS

Schematic: frequency decreases through nominal f0.

Magnitude of Doppler Shift Across Bands

At low elevation angles near AOS or LOS, the line-of-sight radial velocity approaches the spacecraft's orbital velocity ( v rel ≈ 7.0 to 7.5 km/s v_{\text{rel}} \approx 7.0\text{ to }7.5\text{ km/s} v rel ​ ≈ 7.0 to 7.5 km/s ):

2-Meter Band ( 145 MHz 145\text{ MHz} 145 MHz ): Δ f max ≈ 145 × 10 6 × ± 7.2 × 10 3 3.00 × 10 8 ≈ ± 3.48 kHz \Delta f_{\text{max}} \approx 145 \times 10^6 \times \frac{\pm 7.2 \times 10^3}{3.00 \times 10^8} \approx \pm 3.48\text{ kHz} Δ f max ​ ≈ 145 × 1 0 6 × 3.00 × 1 0 8 ± 7.2 × 1 0 3 ​ ≈ ± 3.48 kHz The total frequency excursion from AOS to LOS is approximately 7 kHz 7\text{ kHz} 7 kHz .

70-Centimeter Band ( 435 MHz 435\text{ MHz} 435 MHz ): Δ f max ≈ 435 × 10 6 × ± 7.2 × 10 3 3.00 × 10 8 ≈ ± 10.44 kHz \Delta f_{\text{max}} \approx 435 \times 10^6 \times \frac{\pm 7.2 \times 10^3}{3.00 \times 10^8} \approx \pm 10.44\text{ kHz} Δ f max ​ ≈ 435 × 1 0 6 × 3.00 × 1 0 8 ± 7.2 × 1 0 3 ​ ≈ ± 10.44 kHz The total frequency excursion from AOS to LOS is approximately 21 kHz 21\text{ kHz} 21 kHz .

23-Centimeter Band ( 1.296 GHz 1.296\text{ GHz} 1.296 GHz ): Δ f max ≈ ± 31.1 kHz ( Total excursion ≈ 62 kHz ) \Delta f_{\text{max}} \approx \pm 31.1\text{ kHz} \quad (\text{Total excursion } \approx 62\text{ kHz}) Δ f max ​ ≈ ± 31.1 kHz ( Total excursion ≈ 62 kHz )

Important

Doppler shift is directly proportional to the operating frequency . The 70 cm 70\text{ cm} 70 cm band experiences three times as much frequency shift as the 2 m 2\text{ m} 2 m band. Consequently, during a pass, tuning adjustments must occur far more rapidly and across a wider range on 435 MHz 435\text{ MHz} 435 MHz than on 145 MHz 145\text{ MHz} 145 MHz .

Operational Doppler Tuning Rules

Acquisition of Signal (AOS): The satellite is rapidly approaching the ground station ( v rel > 0 v_{\text{rel}} > 0 v rel ​ > 0 ). The received downlink signal is shifted higher than nominal ( f nominal + Δ f f_{\text{nominal}} + \Delta f f nominal ​ + Δ f ). The receiver must be tuned high.

Time of Closest Approach (TCA): As the satellite reaches its maximum elevation angle, the radial velocity passes through zero ( v rel = 0 v_{\text{rel}} = 0 v rel ​ = 0 ). The received frequency equals the exact nominal frequency ( f nominal f_{\text{nominal}} f nominal ​ ). The rate of change of frequency ( d f / d t df/dt df / d t ) is at its maximum slope.

Loss of Signal (LOS): The satellite is rapidly receding ( v rel < 0 v_{\text{rel}} < 0 v rel ​ < 0 ). The received downlink signal is shifted lower than nominal ( f nominal − Δ f f_{\text{nominal}} - \Delta f f nominal ​ − Δ f ). The receiver must be tuned low.

Satellite Transponder Architectures

Amateur satellites carry two distinct types of communication transponders: channelized FM repeaters and linear transponders.

1. Channelized FM Voice Repeaters

FM satellites operate as orbiting cross-band repeaters (e.g., VHF uplink and UHF downlink, termed Mode V/u). They are popular because they can be operated using inexpensive handheld dual-band transceivers and portable handheld Yagi antennas (such as an Arrow or Elk antenna).

The FM Capture Effect Bottleneck: Frequency Modulation exhibits the capture effect: an FM discriminator demodulates only the single strongest received carrier, suppressing weaker signals. If multiple stations transmit simultaneously, the signals collide, creating a loud heterodyne squeal and mutually destructive blocking. Only one QSO can occur at any instant across the satellite's entire continental footprint.

CTCSS Tones: Accessing an FM satellite transponder almost always requires transmitting a continuous sub-audible CTCSS tone (e.g., 67.0 Hz 67.0\text{ Hz} 67.0 Hz ) to un-mute the uplink receiver.

2. Linear Inverting Transponders

A linear transponder does not demodulate incoming signals. Instead, it acts as a wideband RF translator, receiving a whole slice of spectrum (typically 30 to 100 kHz 30\text{ to }100\text{ kHz} 30 to 100 kHz wide), translating it to a different frequency band, amplifying it linearly, and retransmitting it. Linear transponders permit dozens of stations to conduct simultaneous independent contacts using Single Sideband (SSB) and Morse code (CW). Linear Inverting Transponder Architecture

  • Uplink Passband (145.900 - 145.950 MHz) Downlink Passband (435.200 - 435.250 MHz)
  • Low Freq High Freq Low Freq High Freq
  • [---------------------------------] [----------------------------------]
  • Station A Station B Station B Station A
  • (145.910) (145.940) (435.210) (435.240)
  • (LSB) (LSB) (USB) (USB)
  • =======================================================================
  • Transponder Mixing: f_down = f_LO - f_up

Frequency & Sideband Inversion!

Almost all modern amateur linear transponders are inverting transponders :

Mathematical Inversion: The internal mixer subtracts the incoming uplink frequency from a fixed local oscillator ( f down = f LO − f up f_{\text{down}} = f_{\text{LO}} - f_{\text{up}} f down ​ = f LO ​ − f up ​ ). Consequently, an uplink signal transmitted at the lower end of the uplink passband appears at the higher end of the downlink passband.

Sideband Inversion: Frequency inversion reverses the sidebands: a USB uplink becomes LSB on the downlink, and an LSB uplink becomes USB. The usual amateur operating convention for an inverting transponder is LSB uplink and USB downlink .

Doppler Self-Correction Advantage: Inverting transponders provide an invaluable physical benefit: as Doppler shift drives the uplink frequency upward, the inverted downlink is transmitted at a lower frequency. For an operator listening to their own downlink signal, the uplink Doppler shift and downlink Doppler shift oppose each other, substantially reducing the net frequency drift heard on their own voice.

Power-Sharing and Transponder Discipline

A linear transponder has a strictly limited total RF output power (typically 1 to 5 Watts 1\text{ to }5\text{ Watts} 1 to 5 Watts ) shared among all active stations in the passband. The satellite utilizes an Automatic Gain Control (AGC) loop referenced to total composite received power.

Caution

If an operator transmits with excessive uplink power, the satellite AGC triggers on that single massive signal and immediately reduces the gain of the entire transponder. This robs power from all other active signals in the passband, squelching weaker stations. Operating Rule: Amateurs must run the minimum necessary power (typically 5 to 20 W 5\text{ to }20\text{ W} 5 to 20 W ERP), ensuring their downlink signal never exceeds the signal strength of the satellite's telemetry beacon.

Wave Polarization and Faraday Rotation

When a linearly polarized electromagnetic wave (horizontal or vertical) propagates through the ionosphere, it interacts with free electrons in the presence of the Earth's geomagnetic field. This interaction causes the wave's plane of polarization to continuously rotate as it travels—a phenomenon known as Faraday rotation .

The total angle of polarization rotation ( Ω rot \Omega_{\text{rot}} Ω rot ​ ) is: Ω rot ∝ B ⋅ TEC f 2 \Omega_{\text{rot}} \propto \frac{B \cdot \text{TEC}}{f^2} Ω rot ​ ∝ f 2 B ⋅ TEC ​

where B B B is the geomagnetic field component along the path, TEC \text{TEC} TEC is the Total Electron Content of the ionosphere, and f f f is frequency.

Because the ionosphere's electron density varies continuously, the polarization of a wave reaching the ground station will rotate dynamically. If the receiving station uses a fixed linearly polarized antenna, the incoming wave will periodically arrive cross-polarized ( 90 ∘ 90^\circ 9 0 ∘ out of alignment) with the antenna, causing polarization fading nulls exceeding 20 to 30 dB 20\text{ to }30\text{ dB} 20 to 30 dB .

The Circular Polarization Solution

To eliminate Faraday fading nulls, space communications systems employ Circular Polarization :

Right-Hand Circular Polarization (RHCP) or Left-Hand Circular Polarization (LHCP) , where the electric field vector rotates continuously in a helical spiral as the wave travels.

A circularly polarized antenna responds equally to any linear polarization angle (with a fixed, constant 3 dB 3\text{ dB} 3 dB penalty compared to perfectly matched linear polarization), completely eliminating the deep 20 − 30 dB 20 - 30\text{ dB} 20 − 30 dB nulls caused by Faraday rotation.

Antenna Implementation: Ground stations use crossed-Yagi antennas consisting of two orthogonal sets of dipole elements mounted on the same boom. The two driven elements are fed in quadrature—differing in phase by exactly 90 ∘ 90^\circ 9 0 ∘ —achieved using a quarter-wavelength ( λ / 4 \lambda/4 λ /4 ) coaxial phasing harness or an RF hybrid coupler.

Earth-Moon-Earth (EME / Moonbounce)

Earth-Moon-Earth (EME) communication represents one of the most extreme technical challenges in radio engineering: using the Moon as a passive bistatic radar reflector to establish intercontinental VHF, UHF, and microwave links. Earth-Moon-Earth (EME) Link Geometry

  • Total distance: 2d ≈ 768,800 km
  • Propagation delay: τ ≈ 2.56 seconds
  • Ground transmitter --------------------------> Moon
  • Ground receiver <-------------------------- radar echo
  • Nominal lunar radar cross-section: σ ≈ 0.07 × πR_Moon²
  • Basic path loss at 144 MHz: approximately 252 dB

Antenna gains and equipment losses complete the link budget.

Lunar Geometry, Albedo, and Path Delay

Distance and Path Delay: The mean distance to the Moon is d ≈ 384 , 400 km d \approx 384,400\text{ km} d ≈ 384 , 400 km , giving a total round-trip travel distance of 2 d ≈ 768 , 800 km 2d \approx 768,800\text{ km} 2 d ≈ 768 , 800 km . The round-trip propagation latency ( τ \tau τ ) is: τ = 2 d c = 768 , 800 km 300 , 000 km/s ≈ 2.56 seconds \tau = \frac{2d}{c} = \frac{768,800\text{ km}}{300,000\text{ km/s}} \approx 2.56\text{ seconds} τ = c 2 d ​ = 300 , 000 km/s 768 , 800 km ​ ≈ 2.56 seconds An operator transmitting a CW call hears their own echo return through their headphones roughly 2.5 seconds 2.5\text{ seconds} 2.5 seconds after releasing the key.

Angular Diameter: Viewed from Earth, the Moon subtends an angular diameter of only 0.5 ∘ 0.5^\circ 0. 5 ∘ .

Lunar Radar Albedo: A nominal value is ρ ≈ 0.065 to 0.07 \rho \approx 0.065\text{ to }0.07 ρ ≈ 0.065 to 0.07 . This is the Moon's backscatter radar cross-section divided by its projected disc area: σ = ρ π R Moon 2 \sigma = \rho\pi R_{\text{Moon}}^2 σ = ρ π R Moon 2 ​ . It describes the echo returned toward Earth; it is not the fraction of all incident RF energy reflected. The rough surface spreads the echo in delay and Doppler frequency.

EME Path Loss Calculation

Unlike two-way satellite transponders where path loss increases with the square of distance ( d 2 d^2 d 2 ), EME is governed by the bistatic radar range equation , where received power ( P r P_r P r ​ ) decreases with the fourth power of distance ( d 4 d^4 d 4 ) : P r = P t G t G r λ 2 σ ( 4 π ) 3 d 4 P_r = \frac{P_t G_t G_r\lambda^2\sigma}{(4\pi)^3 d^4} P r ​ = ( 4 π ) 3 d 4 P t ​ G t ​ G r ​ λ 2 σ ​

Here both Earth–Moon legs are approximated by distance d d d , λ \lambda λ is wavelength, and σ \sigma σ is lunar radar cross-section. With unity antenna gains and nominal lunar albedo, the basic path losses are approximately:

  • 144 MHz 144\text{ MHz} 144 MHz (2m): ≈ 252 dB \approx 252\text{ dB} ≈ 252 dB
  • 432 MHz 432\text{ MHz} 432 MHz (70cm): ≈ 262 dB \approx 262\text{ dB} ≈ 262 dB
  • 1296 MHz 1296\text{ MHz} 1296 MHz (23cm): ≈ 271 dB \approx 271\text{ dB} ≈ 271 dB
  • 10 GHz 10\text{ GHz} 10 GHz (3cm): ≈ 289 dB \approx 289\text{ dB} ≈ 289 dB
  • Libration Fading

The Moon exhibits slight rocking motions known as libration (apparent orbital wobble caused by lunar orbital eccentricity and inclination). Different craters, mountains, and surface features move with slight relative velocity toward or away from Earth, causing microscopic Doppler shifts between different scattering facets. These multiple reflections interfere constructively and destructively, producing libration fading —rapid signal fluctuations of 10 to 20 dB 10\text{ to }20\text{ dB} 10 to 20 dB occurring at rates of several hertz.

Technical Requirements for EME Station Design

To bridge a 252 + dB 252+\text{ dB} 252 + dB path loss, an amateur EME station must optimize every component of the RF chain:

Transmitter Power: Use enough power for the link while observing the applicable band and emission limits. Under Australia's amateur class licence, ordinary Advanced Table C bands allow 400 W 400\text{ W} 400 W PEP for C3F, J3E and R3E , and 120 W 120\text{ W} 120 W mean power for other emissions , including CW and common digital EME modes.

High-Gain Directional Antennas:

On 144 MHz 144\text{ MHz} 144 MHz : Arrays of four, eight, or sixteen long-boom Yagis stacked horizontally and vertically ( > 20 dBi > 20\text{ dBi} > 20 dBi gain).

On 1296 MHz 1296\text{ MHz} 1296 MHz and 10 GHz 10\text{ GHz} 10 GHz : Parabolic dish reflectors of 3 to 6 metres 3\text{ to }6\text{ metres} 3 to 6 metres in diameter ( > 30 to 45 dBi > 30\text{ to }45\text{ dBi} > 30 to 45 dBi gain) with precision computer-controlled Azimuth and Elevation rotators capable of 0.1 ∘ 0.1^\circ 0. 1 ∘ tracking accuracy.

Ultra-Low-Noise Preamplifiers (LNAs): Because incoming echo power is measured in fractions of a femtowatt ( − 140 dBm -140\text{ dBm} − 140 dBm ), masthead preamplifiers using Gallium Arsenide (GaAs) or pseudomorphic High Electron Mobility Transistors (pHEMT) are mandatory. The preamp is mounted directly at the antenna feed point to bypass feedline loss, achieving noise figures under 0.5 dB 0.5\text{ dB} 0.5 dB ( N F < 0.5 dB NF < 0.5\text{ dB} NF < 0.5 dB , equivalent noise temperature T e < 35 K T_e < 35\text{ K} T e ​ < 35 K ).

Digital Weak-Signal Protocols: Historically, EME required multi-kilowatt transmitters and ears trained to extract sub-audible CW tones. In modern amateur radio, Nobel laureate Joe Taylor (K1JT) revolutionized EME by introducing digital protocols utilizing forward error correction (FEC):

JT65 and Q65: Both use MFSK, forward error correction and synchronized transmit/receive sequences. JT65 normally uses one-minute sequences. Q65 offers 15, 30, 60, 120 and 300 second sequences, with several tone spacings. Decoding sensitivity depends on the submode and signal conditions; quoted WSJT-X SNR values use a 2500 Hz 2500\text{ Hz} 2500 Hz reference bandwidth . These techniques allow contacts with much weaker signals than ordinary voice reception.

Space Communications Mode Comparison

System Orbit / Path Distance to Target Round-Trip Latency Typical Bands Doppler Excursion Antenna & Tracking Requirements

LEO Satellites (e.g., ISS, SO-50, AO-7) Low Earth Orbit ( 400 − 1500 km 400 - 1500\text{ km} 400 − 1500 km ) 500 − 2500 km 500 - 2500\text{ km} 500 − 2500 km 5 − 20 ms 5 - 20\text{ ms} 5 − 20 ms 145 MHz , 435 MHz 145\text{ MHz}, 435\text{ MHz} 145 MHz , 435 MHz ± 3.5 kHz \pm 3.5\text{ kHz} ± 3.5 kHz (VHF), ± 10.5 kHz \pm 10.5\text{ kHz} ± 10.5 kHz (UHF) Dual-axis Az/El rotators or handheld crossed-Yagi; dynamic frequency tracking

Geostationary Satellites (e.g., QO-100) Geostationary ( 35 , 786 km 35,786\text{ km} 35 , 786 km ) ≈ 38 , 000 km \approx 38,000\text{ km} ≈ 38 , 000 km ≈ 250 ms \approx 250\text{ ms} ≈ 250 ms 2.4 GHz 2.4\text{ GHz} 2.4 GHz uplink, 10.49 GHz 10.49\text{ GHz} 10.49 GHz downlink 0 Hz 0\text{ Hz} 0 Hz (stationary relative to ground) Fixed parabolic dish ( 60 − 120 cm 60 - 120\text{ cm} 60 − 120 cm ); zero rotator tracking required

Earth-Moon-Earth (EME) Lunar reflection ( 384 , 400 km 384,400\text{ km} 384 , 400 km ) ≈ 768 , 800 km \approx 768,800\text{ km} ≈ 768 , 800 km (round-trip) ≈ 2.56 s \approx 2.56\text{ s} ≈ 2.56 s 144 MHz , 432 MHz , 1.296 GHz , 10 GHz 144\text{ MHz}, 432\text{ MHz}, 1.296\text{ GHz}, 10\text{ GHz} 144 MHz , 432 MHz , 1.296 GHz , 10 GHz Frequency- and geometry-dependent; compensate the predicted lunar Doppler shift High-gain multi-Yagi array or large parabolic dish; high-accuracy Az/El tracking