Gal (Galileo): CGS Unit of Acceleration

Introduction

The gal, symbol Gal, is a unit of acceleration in the centimetre-gram-second (CGS) system named after Galileo Galilei. One gal equals one centimetre per second squared (1 cm·s⁻²). Although the SI unit of acceleration is the metre per second squared (m·s⁻²), the gal remains prevalent in geophysics, seismology, and gravimetry because it conveniently expresses small variations in Earth’s gravitational field. Microgal (µGal) and milligal (mGal) submultiples quantify subtle gravity anomalies associated with mineral exploration, groundwater changes, and volcanic activity.

Understanding the gal bridges historical CGS measurements with modern SI-based instrumentation, ensuring continuity in long-term geophysical datasets.

Definition and Conversions

Because 1 gal = 0.01 m·s⁻², standard gravity (g₀ ≈ 9.80665 m·s⁻²) corresponds to 980.665 gal. Milligal (1 mGal) equals 10^-3 gal or 10^-5 m·s⁻², while microgal (1 µGal) equals 10^-6 gal or 10^-8 m·s⁻². Gravimeters often report readings in mGal or µGal to capture small deviations from standard gravity caused by local geology, tides, or temporal mass redistribution. When converting between gal and SI units, multiply by 0.01 to obtain m·s⁻² or by 100 to return to gal.

In some contexts, engineers use gals to describe vibration acceleration in structural monitoring. To ensure clarity, specify units explicitly (e.g., “peak ground acceleration of 350 gal”) and provide SI equivalents for international stakeholders. ISO 80000-4 recognizes the gal as a non-SI unit accepted for use with the SI, provided its relationship to m·s⁻² is clearly stated.

Adopt consistent notation when forming compound units, such as mGal·km for gravity gradients or gal·s for impulse responses in seismology.

Historical Background

The gal emerged in the early twentieth century as physicists formalized the CGS system for electromagnetism and mechanics. Gravimetrists required a convenient unit to express small departures from standard gravity during surveys conducted with pendulum apparatuses and later with spring-based instruments. Naming the unit after Galileo recognized his foundational work on acceleration and free fall. International geophysical conventions adopted the gal and its submultiples, creating continuity across surveys conducted by different nations and research programs.

With the SI’s introduction in 1960, many CGS units faded from common use, yet the gal persisted due to its practicality in gravimetry. The International Association of Geodesy (IAG) and other scientific bodies continue to publish standards referencing mGal or µGal, and modern satellite missions like GRACE and GRACE-FO report gravity field variations effectively in these units. The gal thus represents a successful compromise between historical measurement traditions and contemporary SI-based science.

Comparing the gal’s longevity with other legacy units, such as the gauss in magnetism, highlights how niche scientific communities maintain specialized units for practicality.

Core Concepts and Equations

Measurement Techniques

Early gravimeters used reversible pendulums and mechanical balances to measure gravity with precisions of a few mGal. Modern instruments include spring-based relative gravimeters, superconducting gravimeters, and absolute gravimeters employing laser interferometry to track free-fall trajectories. Superconducting gravimeters achieve sensitivities better than 1 µGal, capturing Earth tides, seismic signals, and groundwater fluctuations.

Satellite missions such as GRACE map global gravity variations by measuring changes in distance between twin satellites, translating observations into spherical harmonic coefficients expressed effectively in µGal. Airborne and marine gravimetry integrate inertial sensors with GPS to survey large areas quickly, correcting for motion-induced accelerations to obtain accurate gal-level gravity data. Calibration procedures compare instrument readings against reference sites with well-characterized gravity values tied to the International Gravity Reference System.

Consult the second and metre entries to appreciate how precise timing and length measurements enable gal-level accuracy in interferometric gravimeters.

Applications

Importance and Future Directions

The gal endures because it offers an intuitive scale for gravity variations that would otherwise appear as cumbersome decimals in SI units. Future gravimetry missions, quantum sensors, and distributed sensor networks will achieve sub-microgal sensitivity, enabling real-time monitoring of hydrology, seismic activity, and infrastructure health. Integrating gal-based datasets with other geophysical measurements—magnetics, seismics, and remote sensing—will enhance Earth system models and support climate resilience strategies. Maintaining conversion discipline with SI units ensures that specialized communities can collaborate effectively across scientific and engineering domains.

Explore complementary units such as the sievert and watt articles to see how precise measurements across disciplines inform safety and energy management in gravity-sensitive projects.

Key Takeaways

• One gal equals 0.01 m·s⁻², making it a convenient unit for expressing small gravity variations.
• Milligal and microgal measurements reveal subtle subsurface and temporal mass changes.
• Gravimetry, seismology, and structural monitoring rely on gal-based data for decision-making.
• Modern instruments—from superconducting gravimeters to satellites—achieve microgal sensitivity.
• Maintaining clear conversions between gal and SI units enables collaboration across geoscience and engineering disciplines.