feat(sat): Doppler tracking on the radio

The hard part of satellite tuning is not the arithmetic, it is deciding
who owns the dial. A tracker that forces both frequencies fights the
operator every time they turn the knob to follow a station across a
linear transponder; one that never touches the receiver leaves them
chasing a signal that slides nine kilohertz across a 70 cm pass.

So the operator owns the receiver and the tracker follows them. Every
second it asks the radio where the receiver actually is. Where it put it,
nothing has changed. Further than a dial-turn's tolerance, and the
operator has chosen a station: what they landed on is converted back into
a nominal frequency, and the transmitter is derived from that. Which is
the division of labour on a linear bird — the operator listens, the radio
does the sums.

Three ways to reach the radio, because a satellite pair is a shape of
operating rather than a manufacturer's feature. An IC-9700 or IC-9100 is
asked for its OWN satellite mode: it pairs main and sub, gives full
duplex, and keeps the dials linked the way its designers meant, which is
always better than an imitation built out of split. A Flex gets two
slices, A the downlink and B the uplink, created when missing, because
"slice B does not exist" is not something to make an operator fix at the
start of a ten-minute pass. Everything else gets the downlink, and is
told so — half the job announced beats half the job hidden.

What goes in the log is the NOMINAL pair. Two stations working each other
through a transponder read different numbers off their dials at the same
instant; the only figure they can both agree on is the transponder's own.
FREQ is the uplink and FREQ_RX the downlink — the one place a satellite
QSO differs from every other kind, and the reason FREQ alone cannot
describe one.

app_sat_track_test.go

@@ -0,0 +1,47 @@
+package main
+
+import (
+	"testing"
+
+	"hamlog/internal/sat"
+)
+
+// The dial arithmetic has to be the exact inverse of the correction, or every
+// touch of the knob would nudge the nominal frequency a little further off and
+// the uplink would walk across the passband over a pass.
+func TestSatNominalFromDialRoundTrip(t *testing.T) {
+	// A range of range rates: hard approach, drifting, hard recession. ±8 km/s
+	// covers a low orbit overhead.
+	for _, rate := range []float64{-8, -3.2, -0.4, 0, 0.4, 3.2, 8} {
+		p := sat.Position{RangeRate: rate}
+		for _, nominal := range []int64{29_450_000, 145_900_000, 435_850_000, 10_489_675_000} {
+			sh := sat.Doppler(p, nominal, 0)
+			factor := -rate / satLightKmS
+			got := satNominalFromDial(sh.DownHz, factor)
+			if diff := got - nominal; diff > 1 || diff < -1 {
+				t.Errorf("rate %.1f km/s, %d Hz: heard %d, came back as %d (%+d)",
+					rate, nominal, sh.DownHz, got, diff)
+			}
+		}
+	}
+}
+
+// SAT_MODE is what goes on a QSL card, and the letters are the uplink's then
+// the downlink's — the order operators write and the order ADIF wants.
+func TestSatModeLetters(t *testing.T) {
+	for _, tc := range []struct {
+		name     string
+		up, down int64
+		want     string
+	}{
+		{"FO-29: 2 m up, 70 cm down", 145_950_000, 435_850_000, "V/U"},
+		{"AO-91: 70 cm up, 2 m down", 435_250_000, 145_960_000, "U/V"},
+		{"AO-7 mode A: 2 m up, 10 m down", 145_900_000, 29_450_000, "V/A"},
+		{"QO-100: 13 cm up, 3 cm down", 2_400_175_000, 10_489_675_000, "S/X"},
+		{"receive only", 0, 145_800_000, ""},
+	} {
+		if got := satModeLetters(tc.up, tc.down); got != tc.want {
+			t.Errorf("%s: got %q, wanted %q", tc.name, got, tc.want)
+		}
+	}
+}