Local Acceleration Due To Gravity Calculator

Local Gravity Equation:

\[ g_{local} = g - \omega^2 r \cos^2(\phi) \]

Standard Gravity (g):

m/s²

Angular Velocity (ω):

rad/s

Radius (r):

Latitude (φ):

degrees

Local Gravity (g_local):

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1. What is Local Acceleration Due To Gravity?

Local acceleration due to gravity (g_local) accounts for the Earth's rotation effect on gravitational acceleration. It varies with latitude due to the centrifugal force from Earth's rotation, making gravity slightly weaker at the equator than at the poles.

2. How Does the Calculator Work?

The calculator uses the local gravity equation:

\[ g_{local} = g - \omega^2 r \cos^2(\phi) \]

Where:

\( g \) — Standard gravity (typically 9.81 m/s²)
\( \omega \) — Angular velocity of Earth's rotation (7.292 × 10⁻⁵ rad/s)
\( r \) — Distance from Earth's center (radius at location)
\( \phi \) — Latitude in degrees

Explanation: The equation subtracts the centrifugal acceleration component (which is maximum at the equator and zero at the poles) from the standard gravitational acceleration.

3. Importance of Local Gravity Calculation

Details: Accurate local gravity values are essential for precise scientific measurements, geophysical studies, engineering applications, and calibration of sensitive instruments that measure gravitational forces.

4. Using the Calculator

Tips: Enter standard gravity (typically 9.81 m/s²), Earth's angular velocity (typically 7.292e-5 rad/s), radius at your location (in meters), and latitude (in degrees between -90 and 90). All values must be valid and positive (except latitude which can be negative for southern hemisphere).

5. Frequently Asked Questions (FAQ)

Q1: Why does gravity vary with latitude?
A: Gravity is weaker at the equator due to the centrifugal force from Earth's rotation and because the Earth is slightly oblate (wider at the equator).

Q2: What is the typical range of g_local on Earth?
A: Local gravity typically ranges from about 9.78 m/s² at the equator to 9.83 m/s² at the poles.

Q3: How significant is the rotation effect on gravity?
A: The rotation effect reduces gravity by about 0.3% at the equator compared to the poles.

Q4: Does altitude affect local gravity?
A: Yes, gravity decreases with altitude following the inverse square law, though this calculator focuses on the rotational effect at a given radius.

Q5: When is this calculation most important?
A: This calculation is crucial for precision measurements in geophysics, metrology, and any application requiring exact gravitational values.