International Gravity Formula Calculator

Gravitational Acceleration (\( g \)) in meters/second² (m/s²):

Gravitational Acceleration (\( g \)) in centimeters/second² (cm/s²):

Gravitational Acceleration (\( g \)) in feet/second² (ft/s²):

1. What is the International Gravity Formula Calculator?

Definition: This calculator computes the gravitational acceleration (\( g \)) at a specific latitude (\( \phi \)) using the International Gravity Formula, which accounts for the Earth's shape and rotation.

Purpose: It is used in geophysics and physics to determine the local gravitational acceleration, which varies with latitude due to the Earth's oblateness and rotational effects.

2. How Does the Calculator Work?

The calculator uses the relationship:

\[ g(\text{latitude}) = 9.7803267714 \cdot \frac{1 + 0.00193185138639 \cdot \sin^2(\phi)}{\sqrt{1 - 0.00669437999013 \cdot \sin^2(\phi)}} \]

Where:

\( g \) — Gravitational acceleration (in various units)
\( \phi \) — Latitude

Explanation: Enter the latitude in the chosen unit (degrees, radians, centiradians, gradians, minutes, seconds, or revolutions), and the calculator computes the gravitational acceleration. Results are displayed with 5 decimal places, using scientific notation if the value exceeds 100,000 or is less than 0.0001. For a default latitude of \( \phi = 45^\circ \), the calculated gravitational acceleration \( g \) is approximately 9.80620 m/s².

3. Importance of International Gravity Formula Calculation

Details: Calculating gravitational acceleration at different latitudes is essential for applications in geophysics, navigation, and engineering, as it affects measurements like pendulum periods, satellite orbits, and structural design.

FAQ

How do I find the gravitational acceleration at a specific latitude?

Measure the latitude in your chosen unit, convert it to radians if necessary, and compute the gravitational acceleration using the formula \( g = 9.7803267714 \cdot \frac{1 + 0.00193185138639 \cdot \sin^2(\phi)}{\sqrt{1 - 0.00669437999013 \cdot \sin^2(\phi)}} \). The result will be in meters/second².

Why does gravitational acceleration vary with latitude?

Gravitational acceleration varies with latitude due to the Earth's oblate shape (flattened at the poles) and its rotation. At the equator, the centrifugal force reduces the effective gravity, while at the poles, gravity is stronger.

What is the standard value of gravitational acceleration?

The standard value of gravitational acceleration at sea level and 45° latitude is approximately 9.80665 m/s², but it varies slightly with latitude, altitude, and local geology.

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