← INDEX — FIG. 00 — 4 OCTOBER 1957, 19:28 UTC 20.005 MHz · 40.002 MHz

BEEP
SPUTNIK, EXPLORER AND THE FIRST SATELLITES

In six months, five small objects went into orbit and changed what people thought was possible.

CH.01 / 10 — A YEAR OF GEOPHYSICS, A MISSILE AND A BALL

The simplest satellite anyone could build

Both superpowers promised a scientific satellite for the International Geophysical Year.

PS-1 was a polished aluminium sphere with four antennas and two transmitters.

Satellite	Launched (UTC)	Mass	Initial orbit	What it did

Masses from NASA's chronology; orbits from Gunter's Space Page and NASA.

CH.02 / 10 — FALLING AROUND THE EARTH

An ellipse, a period and two speeds

The orbit follows from perigee, apogee and Earth's gravity.

Pick a satellite or set your own perigee and apogee.

KEPLER'S THIRD LAW AND VIS-VIVA

T = 2π √(a³/μ) · v² = μ (2/r − 1/a) · a = R + (h_p + h_a)/2

μ = 398,600 km³/s² for the Earth.

PERIGEE HEIGHT—

APOGEE HEIGHT—

Two-body Kepler orbit, no drag.

CH.03 / 10 — HEARING AN ORBIT

The beep that became satellite navigation

Guier and Weiffenbach recorded the Doppler shift of Sputnik's 20 MHz signal.

The shape of the Doppler curve carries the geometry; reversed, it became Transit.

DOPPLER SHIFT OF A PASSING SATELLITE

Δf = −f₀ ṙ / c · ṙ = v² t / √(r²_min + v²t²) · dΔf/dt|_t=0 = −f₀ v² / (c r_min)

Straight-line pass at constant speed.

SATELLITE HEIGHT—

YOUR DISTANCE FROM THE GROUND TRACK—

Beat note against the receiver's oscillator, 1 kHz offset; pass compressed 60×.

CH.04 / 10 — LAIKA

The first animal in orbit, and a truth told 45 years later

Sputnik 2 was built in about four weeks and carried the dog Laika.

Laika died from overheating within hours; the truth came out in 2002.

CH.05 / 10 — AMERICA'S ANSWER IN 84 DAYS

A missile, a pencil-thin satellite and a Geiger counter

After Vanguard exploded, the Army's Jupiter-C launched Explorer 1.

Explorer 1 spun at 750 rpm and climbed to 2,535 km.

CH.06 / 10 — THE COUNTER THAT READ ZERO

Too much radiation looks like none at all

A Geiger tube saturated by too much radiation reads zero.

The silence meant a radiation intensity a thousand times the cosmic-ray level.

PARALYSABLE DEAD-TIME MODEL

m = N · e^{−N τ} · m_max = 1 / (e τ) at N = 1/τ

N true rate, m recorded rate, τ dead time.

ALTITUDE—

The counting formula is exact; the altitude profile is illustrative.

CH.07 / 10 — WHY EXPLORER 1 FLIPPED OVER

A long, thin spinner is stable only if nothing inside it flexes

Explorer 1 spun about its minor axis; flexing antennas dissipated energy.

Energy dissipation drives a body to spin about its major axis.

ENERGY AT FIXED ANGULAR MOMENTUM

E(θ) = H²/2 · [ cos²θ / I_s + sin²θ / I_t ]

θ: angle between symmetry axis and H.

ENERGY LOSS (ANTENNA FLEX)—

Motion from E(θ); time compressed.

CH.08 / 10 — THE GRAPEFRUIT THAT IS STILL UP THERE

1.47 kg, the first solar cells, and a pear-shaped Earth

Vanguard 1 was the first solar-powered satellite and is still in orbit.

Tracking Vanguard 1 revealed the Earth's pear shape.

CH.09 / 10 — LEGACY: EIGHTEEN MONTHS THAT STARTED EVERYTHING

From a ball with antennas to NASA, navigation and geodesy

None of them was built to discover anything big.

CH.10 / 10 — REFERENCES

BEEPSPUTNIK, EXPLORER AND THE FIRST SATELLITES