In 1985 Braginsky and Thorne proposed the 'skyhook', an Earth-orbiting gravitational-wave detector for the 10–100 mHz band: two end masses joined by a roughly 25 km cable stretched radially by the Earth's tidal field, with a central spring transducing gravitational-wave-induced motion into a measurable displacement, thermal-noise-limited near h∼3×10−17h\sim3\times10^{-17} at 30 mHz. The letter itself left the concept's feasibility open because environmental noise sources were insufficiently characterized to be bounded below that floor: solar irradiance fluctuations (requiring ΔF/F≲3×10−6\Delta F/F\lesssim3\times10^{-6} at 30 mHz or on-board monitoring), electrodynamic coupling of a conducting tether to the magnetosphere, magnetospheric ULF micropulsations (Pc2–Pc4, Pi1–Pi2), gravity-gradient noise from the Earth's field and mass-density fluctuations (mitigated at altitudes above ~1,000 km), cable creep under repeated shadow-passage thermal cycling, and charged-particle/plasma drag interacting with cable charging. The objective of this task is to characterize the strain-equivalent noise of these environmental sources relative to the skyhook's thermal (Nyquist) noise floor, and to determine the design constraints (altitude, cable material, on-board monitoring) required for the detector to operate at thermal-noise-limited sensitivity.

Background

Gravitational waves — propagating ripples in spacetime curvature — are detected by measuring the fractional differential length change (the strain hh) they induce between free test masses. Below roughly 10 Hz, ground-based detectors are overwhelmed by seismic noise and by gravity-gradient noise (time-dependent Newtonian pulls from moving mass distributions), so the 10–100 mHz band — which contains compact binaries with minute-scale orbital periods — is inaccessible from the ground. In 1985 the most sensitive techniques in this band were Doppler tracking of interplanetary spacecraft, at strain sensitivities of order h∼3×10−13h\sim3\times10^{-13} (Hellings et al. 1981), and the excitation of seismic modes of the Earth itself (Dyson 1969). Space laser interferometers promised far better sensitivity, but at great complexity and cost.

In this context Braginsky and Thorne proposed the 'skyhook' (Nature 316, 610; 1985): a conceptually simple Earth-orbiting detector consisting of two masses at the ends of a long, thin cable, stretched radially by the Earth's tidal gravitational field as the system orbits — the same gravity-gradient stabilization proposed for earlier shuttle-borne tethered-satellite concepts, one of which was then planned for flight. A passing gravitational wave drives the two end masses apart and together; the cable transmits this motion to a spring at its centre, whose oscillating length is monitored by an on-board sensor. In the illustrative design of the letter (20 kg end masses, a roughly 25 km cable), the mechanical resonance lies near 35 mHz, and the band is bounded above by the requirement that the cable be shorter than a wavelength of sound in the cable so that tidal forces are transmitted rigidly. The authors estimated a thermal (Nyquist) noise floor of h∼3×10−17h\sim3\times10^{-17} near 30 mHz (rising toward lower frequencies as f−3/2f^{-3/2}) and argued that sources with strains near 10−1910^{-19}, such as compact binaries in minute-period orbits, could be detected by coherent integration over weeks.

Whether such sensitivity survives the low-Earth-orbit environment is the open issue the letter itself identified. The contemporaneous restatement of the letter (Paik 1989) enumerates four serious noise sources — Nyquist noise from internal dissipation, fluctuations in cable length produced by fluctuations in solar and Earth heating, fluctuating forces due to the gravity gradients of the high harmonics of the Earth, and fluctuating electric and magnetic forces including micropulsations. Of these, Nyquist noise is the thermal floor rather than an environmental source, and the combined electric and magnetic forces comprise two distinct environmental sources, so this restatement contributes four environmental sources — radiative heating, electrodynamic coupling, ULF micropulsations, and gravity-gradient noise — to which two further sources, cable creep and plasma drag, are added; these six environmental sources are enumerated below. (1) Radiative heating: solar irradiance fluctuations must satisfy ΔF/F≲3×10−6\Delta F/F\lesssim3\times10^{-6} at 30 mHz in the illustrative design, or else be continuously monitored on board; the irradiance-oscillation data available at the time — from the Active Cavity Radiometer Irradiance Monitor (ACRIM) on the Solar Maximum Mission satellite, and contemporary detections of solar oscillations in total irradiance at milli-hertz frequencies (Woodard & Hudson 1983) — did not cover 10–100 mHz, and extrapolations were uncertain. (2) A conducting cable electro-dynamically couples to the ambient magnetosphere; the magnetospheric impedance and the resulting cable charging currents and electromagnetic noise were poorly known, leaving open whether the cable must be nonconducting and what on-board electric-field sensing would be required. (3) Magnetospheric ultra-low-frequency (ULF) geomagnetic pulsations — the standard continuous (Pc) and irregular (Pi) classes, here Pc2–Pc4 and Pi1–Pi2, with periods of seconds to minutes — drive electromagnetic noise at the detector, with poorly characterized time/frequency/space statistics, especially during magnetically disturbed periods; during some micropulsations the disturbance is expected to greatly exceed the Nyquist level, and the required orbit selection (per the contemporaneous restatement, altitudes below ~6,000 km to maximize time in quiet E-field regions, with on-board electric-field probes) was undetermined. (4) Gravity-gradient noise from terrestrial and atmospheric mass-density fluctuations was insufficiently mapped globally; the authors' calculation makes the effect negligible at altitudes above ~1,000 km, and lower-altitude operation would require the gravity-gradient field to be known orders of magnitude better than then modelled. (5) Repeated thermal cycling through the Earth's shadow leaves cable creep and long-term strain stability unquantified, possibly requiring multiple detectors and cross-correlation. (6) Charged-particle and plasma drag, and its interplay with cable charging, remained difficult to analyze and might impose stricter altitude or design limits. Items (5) and (6) are attributed to the letter's open issues rather than separately enumerated as noise sources in the contemporaneous restatement (Paik 1989), though the 1989 conference discussion records the plasma processes as not fully analyzed.

Problem Statement

Determine the environmental noise budget of the proposed Earth-orbiting 'skyhook' gravitational-wave detector in the 10–100 mHz band — that is, characterize the strain-equivalent noise of the environmental noise sources identified in connection with Braginsky and Thorne (1985) relative to the skyhook's thermal (Nyquist) noise floor (h∼3×10−17(f/30 mHz)−3/2h\sim3\times10^{-17}(f/30\ \mathrm{mHz})^{-3/2} in the illustrative design: 20 kg end masses, ~25 km cable, ~35 mHz resonance, Q∼105Q\sim10^{5}), and determine which practical design constraints (altitude, cable material, on-board monitoring) are required for a skyhook to operate at thermal-noise-limited sensitivity. The sources and their associated open requirements are: (1) solar irradiance fluctuations in the 10–100 mHz band (does ΔF/F≲3×10−6\Delta F/F\lesssim3\times10^{-6} at 30 mHz hold, or is continuous on-board irradiance monitoring and mitigation mandatory?); (2) electrodynamic coupling of a conducting tether to the magnetosphere (magnetospheric impedance, cable charging currents, and electromagnetic noise amplitude; a nonconducting cable is proposed to minimize electric and magnetic force effects — must the cable be nonconducting, and what on-board electric-field sensing is needed?); (3) magnetospheric ULF micropulsations (Pc2–Pc4, Pi1–Pi2) and their time/frequency/space statistics, especially during disturbed times, during some of which the disturbance is expected to greatly exceed the Nyquist level (what orbit selection and on-board electric-field sensing do the micropulsation statistics require?); (4) gravity-gradient noise from terrestrial mass-density fluctuations (negligible above ~1,000 km altitude per the authors' calculation; is lower-altitude operation possible without prior high-resolution gravity-gradient mapping, given that the field would need to be known orders of magnitude better than then modelled?); (5) cable creep and long-term strain stability under repeated shadow-passage thermal cycling (are multiple detectors and cross-correlation necessary?); (6) charged-particle and plasma drag and its interplay with cable charging (what altitude or design constraints follow?). The task is to bound the strain-equivalent noise of sources (1)–(4) relative to the thermal floor, together with the altitude, cable-material and on-board-monitoring design constraints they imply; sources (5) and (6) are attributed open issues.

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