Local Gravitational Acceleration Calculator

Local Gravitational Acceleration Formula:

\[ g_{local} = g \times (1 - \frac{2h}{R}) \]

Local Gravitational Acceleration (g_local):

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1. What Is Local Gravitational Acceleration?

Local gravitational acceleration (g_local) refers to the acceleration due to gravity at a specific height above the Earth's surface. It decreases with increasing altitude due to the inverse square law of gravitation.

2. How Does The Calculator Work?

The calculator uses the local gravitational acceleration formula:

\[ g_{local} = g \times (1 - \frac{2h}{R}) \]

Where:

\( g \) — Standard surface gravity (9.81 m/s² on Earth)
\( h \) — Height above the Earth's surface (meters)
\( R \) — Radius of the Earth (approximately 6,371,000 meters)

Explanation: This formula provides an approximation of how gravity decreases with altitude, derived from the Taylor expansion of the full gravitational formula.

3. Importance Of Local Gravity Calculation

Details: Calculating local gravitational acceleration is important for precision engineering, satellite operations, geophysical surveys, and scientific experiments where gravitational variations matter.

4. Using The Calculator

Tips: Enter surface gravity (typically 9.81 m/s² for Earth), height above surface in meters, and planetary radius in meters. For other celestial bodies, use appropriate values for g and R.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this approximation?
A: This formula provides a good approximation for altitudes much smaller than Earth's radius. For higher precision or extreme altitudes, the full Newtonian gravitation formula should be used.

Q2: Does gravity change with latitude?
A: Yes, gravity is slightly stronger at the poles than at the equator due to Earth's rotation and oblate shape, but this formula focuses only on altitude effects.

Q3: Can I use this for other planets?
A: Yes, simply input the appropriate surface gravity and radius values for the celestial body you're calculating for.

Q4: How much does gravity decrease with altitude?
A: Gravity decreases by approximately 0.3086 mGal/m (0.0003086 m/s² per meter) of elevation gain near Earth's surface.

Q5: Why is the formula linear instead of inverse square?
A: This is a first-order approximation valid for h ≪ R. The full inverse square relationship is g_local = g × (R/(R+h))².