DOC // NL-TN-2026-016VECTOR -Z1P / 1U · MATERIALS · ORBITAL

STATUS: PUBLISHED // REV 0.1

Tracking a 5 cm satellite

Rayleigh vs Mie radar cross-section, why the UHF wire antenna dominates radar return and post-deployment TLE lotteries

Author: nadir lab.
Published: 20 October 2026
Reading time: 2 min
Level: Basic
Tags: Radar cross-section
TLE
Space surveillance
Rideshare
UHF antenna
PocketQube

Abstract

A bare 50 mm cube sits deep in the Rayleigh scattering regime for UHF space-surveillance radars, yielding a radar cross-section near −43 dBsm. Once its 437 MHz tape-spring monopole or dipole deploys, resonant wire scattering boosts RCS by 25–30 dB. We examine radar cross-section across UHF, S-band and X-band and explain how Differential Doppler resolves rideshare TLE lotteries.

Contents

Rayleigh scattering of a 5 cm cube#

Space-surveillance radars operate primarily in UHF ( $440 MHz$ , $λ = 68 cm$ ), L/S-band ( $1.3 - 3.1 GHz$ , $λ = 23 - 9.7 cm$ ) and X-band ( $10 GHz$ , $λ = 3.0 cm$ )[1]. When the characteristic target radius $a$ is much smaller than the radar wavelength ( $k a = 2 π a / λ < 0.8$ ), scattering falls into the Rayleigh regime, where radar cross-section scales with the sixth power of size:

σ_{Rayleigh} \propto k^{4} V^{2} \propto \frac{a ^{6}}{λ ^{4}}

At UHF, a bare $50 mm$ $1 P$ cube has $σ \approx 5 \times 1 0^{- 5} m^{2}$ ( $- 43 dBsm$ )—often below the detection threshold for routine cataloguing. Once the spacecraft deploys its quarter-wave ( $171 mm$ ) or half-wave ( $342 mm$ ) $437 MHz$ tape-spring antenna, the thin wire acts as a resonant half-wave dipole in UHF/L-band and raises the effective RCS by more than $30 dB$ [1].

Approximate radar cross-section (RCS) across UHF (440 MHz), S-band (3.1 GHz), and X-band (10 GHz) space-surveillance regimes

Spacecraft configuration	UHF 440 MHz (dBsm)	S-band 3.1 GHz (dBsm)	X-band 10 GHz (dBsm)	S-band scattering regime
1P PocketQube (50 × 50 × 50 mm, bare bus)	−43.0	−24.5	−16.4	Mie
1P PocketQube + 34 cm UHF dipole	−11.1	−18.4	−8.3	Optical
3P PocketQube (50 × 50 × 178 mm)	−22.5	−13.8	−3.6	Optical
1U CubeSat (100 × 100 × 100 mm)	−25.0	−12.5	−2.3	Optical
1P PocketQube + mini X-band corner reflector	−38.3	−11.7	−3.6	Mie

Resolving the post-deployment "TLE lottery"#

On dedicated missions such as Falcon 9 Transporter-3, dozens of CubeSats and PocketQubes separate within seconds at relative velocities $Δ v \approx 0.3 - 1.5 m/s$ [2]. From the Clohessy–Wiltshire along-track drift equation[3]:

Δ s (t) \approx 3 Δ v t

a $Δ v = 0.5 m/s$ separation produces only $130 km$ of along-track spacing after $24 h$ ( $\approx 17 s$ of pass arrival difference), so radar tracks ("OBJECT A", "OBJECT B", …) cannot immediately be matched to individual spacecraft. Teams break the ambiguity within $3 - 7 days$ by fitting the zero-crossing time (TCA) and slope of the UHF curve recorded across globally distributed stations against each candidate [4].