1. What is Gravity at Altitude?

The gravity at altitude equation calculates how gravitational acceleration decreases with increasing height above the Earth's surface. This approximation accounts for the inverse square law of gravitation at moderate altitudes.

2. How Does the Calculator Work?

The calculator uses the gravity at altitude equation:

Where:

• \( g_{alt} \) — Gravity at altitude (m/s²)
• \( g_0 \) — Standard gravity at sea level (9.81 m/s²)
• \( h \) — Altitude above Earth's surface (meters)
• \( R_{earth} \) — Earth's radius (6,371,000 meters)

Explanation: This linear approximation is valid for altitudes where h << R_earth, derived from the binomial expansion of the full gravitational formula.

3. Importance of Gravity Calculation

Details: Accurate gravity calculations are essential for aerospace engineering, satellite operations, geophysical surveys, and understanding how weight changes with elevation.

4. Using the Calculator

Tips: Enter altitude in meters, standard gravity (default 9.81 m/s²), and Earth's radius (default 6,371,000 m). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this approximation?
A: Very accurate for altitudes up to about 100 km. For higher altitudes, use the full inverse square law: g_alt = g_0 × (R_earth/(R_earth + h))²

Q2: Does gravity really decrease with altitude?
A: Yes, gravitational acceleration decreases by approximately 0.0031 m/s² for every kilometer of altitude gained.

Q3: What is standard gravity at sea level?
A: Approximately 9.80665 m/s², though it varies slightly with latitude due to Earth's rotation and shape.

Q4: How does this affect weight?
A: Weight = mass × gravity, so at higher altitudes where gravity is lower, objects weigh slightly less.

Q5: What about gravity inside the Earth?
A: This equation only works for altitudes above the surface. Inside Earth, gravity decreases linearly toward the center.