Local Acceleration Due To Gravity Calculator

Gravity Acceleration Formula:

\[ g = g_0 \times \left(1 - \frac{2h}{R}\right) \times \left(1 + \frac{\lambda^2 R}{g_0}\right) \]

Local Gravity Acceleration:

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1. What Is Local Gravity Acceleration?

Local gravity acceleration (g) varies with latitude and altitude due to Earth's shape, rotation, and mass distribution. The standard gravity value of 9.80665 m/s² is an average that changes based on geographic location.

2. How Does The Calculator Work?

The calculator uses the international gravity formula:

\[ g = g_0 \times \left(1 + 0.0053024\sin^2\lambda - 0.0000058\sin^2 2\lambda\right) \times \left(1 - \frac{2h}{R}\right) \]

Where:

\( g \) — Local gravity acceleration (m/s²)
\( g_0 \) — Standard gravity (9.80665 m/s²)
\( \lambda \) — Latitude in radians
\( h \) — Altitude above sea level (meters)
\( R \) — Earth's radius (6,378,137 meters)

Explanation: The formula accounts for Earth's ellipsoidal shape (latitude effect) and the decrease in gravity with altitude.

3. Importance Of Local Gravity Calculation

Details: Accurate local gravity values are essential for precision measurements in geophysics, engineering, metrology, and scientific research where gravitational effects are significant.

4. Using The Calculator

Tips: Enter latitude in degrees (-90° to 90°, negative for Southern Hemisphere) and altitude in meters above sea level. Values must be within valid ranges.

5. Frequently Asked Questions (FAQ)

Q1: Why does gravity vary with latitude?
A: Earth's rotation creates centrifugal force that reduces effective gravity, and the equatorial bulge means you're farther from Earth's center at the equator.

Q2: How much does gravity change with altitude?
A: Gravity decreases by approximately 0.000003086 m/s² per meter of altitude increase.

Q3: What is the range of gravity on Earth's surface?
A: Gravity ranges from about 9.7639 m/s² at Mount Nevado Huascarán (Peru) to 9.8337 m/s² at the Arctic Ocean surface.

Q4: Does local geology affect gravity?
A: Yes, dense rock formations can increase local gravity by 0.0001-0.0005 m/s², while less dense areas show slightly lower values.

Q5: How accurate is this calculation?
A: This provides theoretical values accurate to about ±0.001 m/s² for most locations, but precise measurements require gravimeter instruments.