Satellite Pass: Doppler Shift & Elevation Tracker (2D Orbital-Plane View)

Orbit & Link

Orbit altitude 550 km

Pass geometry — miss angle 8°

Downlink band

Time acceleration 120×

Pass Telemetry

BELOW HORIZON

Elevation

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Slant range

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Radial velocity

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Orbital speed

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Doppler shift Δf

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How it works

This is a top-down view of the satellite's own orbital plane. The satellite flies a circular orbit, so its angular rate follows Kepler's third law from Earth's gravitational parameter μ = GM_⊕:

orbital speed:  v = √(μ / r)
mean motion:    n = √(μ / r³)
where r = R⊕ + h  (Earth radius + altitude), μ = 398 600.4 km³/s²

The ground station is fixed on Earth's surface; because the pass isn't a perfect overhead crossing, the station sits slightly out of the orbital plane by the miss angle m. Writing the satellite's true anomaly as θ = n·t (t = 0 at closest approach), the central angle γ between station and satellite collapses to a clean closed form:

cos γ = cos θ · cos m
ρ = √(R⊕² + r² − 2·R⊕·r·cos γ)         (slant range)
sin ε = (r·cos γ − R⊕) / ρ              (elevation)

The received carrier frequency is shifted by the line-of-sight component of the satellite's velocity — the classical (non-relativistic) Doppler formula used for real satellite downlinks. Projecting the 3-D velocity vector onto the slant-range direction inside this orbital plane reduces to:

v_r   = v_sat · R⊕ · cos m · sin θ / ρ      (positive = receding)
Δf    = −f₀ · v_r / c
f_rx  = f₀ + Δf

Altitude sets orbital radius r, hence orbital speed v and period — higher orbits move slower, so the pass lasts longer and the Doppler swing is gentler.
Miss angle is how close the ground track comes to the station; 0° is a straight overhead pass (max Doppler swing, shortest visible window), larger values give a shallow, low-elevation pass.
Band scales the shift directly — Δf is proportional to f₀, which is why Ku-band trackers need far more aggressive frequency compensation than a 137 MHz beacon for the identical geometry.
The strip chart below the orbit view traces the classic Doppler S-curve: positive on approach, crossing zero exactly at closest approach, negative while receding — real ground stations run this same calculation continuously (Doppler tuning / AFC) to stay locked on.

RECEIVED CARRIER

437.000 MHz

Drag to pan · scroll/pinch to zoom

Orbit path Satellite Ground station Line of sight

Satellite Pass: Doppler Shift & Elevation Tracker — 2D Orbital-Plane View