Gravitational Acceleration Calculator Altitude

Gravitational Acceleration Formula:

\[ g_h = g \left( \frac{R}{R + h} \right)^2 \]

Gravitational Acceleration at Altitude (gₕ):

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1. What is Gravitational Acceleration at Altitude?

Gravitational acceleration decreases with altitude above the Earth's surface. This calculator determines the gravitational acceleration at a specific altitude using the standard formula that accounts for the inverse square relationship with distance from the Earth's center.

2. How Does the Calculator Work?

The calculator uses the gravitational acceleration formula:

\[ g_h = g \left( \frac{R}{R + h} \right)^2 \]

Where:

\( g \) — Standard gravitational acceleration (9.81 m/s² at Earth's surface)
\( R \) — Earth's radius (approximately 6371 km)
\( h \) — Altitude above Earth's surface (km)
\( g_h \) — Gravitational acceleration at altitude h

Explanation: The formula shows that gravitational acceleration decreases with the square of the distance from Earth's center, following Newton's law of universal gravitation.

3. Importance of Gravitational Acceleration Calculation

Details: Calculating gravitational acceleration at different altitudes is crucial for aerospace engineering, satellite orbit calculations, atmospheric studies, and understanding how gravity varies with elevation for precise scientific measurements.

4. Using the Calculator

Tips: Enter gravitational acceleration at surface (typically 9.81 m/s²), Earth's radius (typically 6371 km), and altitude in kilometers. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why does gravitational acceleration decrease with altitude?
A: Gravitational force follows an inverse square law with distance. As you move farther from Earth's center, the gravitational pull weakens.

Q2: How accurate is this calculation?
A: This provides a good approximation, but actual values may vary slightly due to Earth's non-spherical shape and density variations.

Q3: Does this formula work for other celestial bodies?
A: Yes, but you would need to use the appropriate values for g and R for that specific planet or moon.

Q4: How much does gravity change with altitude?
A: The change is relatively small. At 10 km altitude, gravity is about 99.7% of its surface value.

Q5: Why is the Earth's radius used in the calculation?
A: Gravitational acceleration depends on distance from the center of mass, so we measure altitude from Earth's center, not its surface.