Satellite Distance From Earth Calculator

Satellite Distance Formula:

\[ r = \left(\frac{T^2 G M}{4 \pi^2}\right)^{1/3} - R_{earth} \]

Satellite Distance (r):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Satellite Distance Calculation?

The satellite distance calculation determines how far a satellite is from Earth's surface based on its orbital period. This is derived from Kepler's third law of planetary motion.

2. How Does the Calculator Work?

The calculator uses the following equation:

\[ r = \left(\frac{T^2 G M}{4 \pi^2}\right)^{1/3} - R_{earth} \]

Where:

\( r \) — Satellite distance from Earth's surface (m)
\( T \) — Orbital period (s)
\( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
\( M \) — Earth's mass (5.972 × 10²⁴ kg)
\( R_{earth} \) — Earth's radius (6.371 × 10⁶ m)

Explanation: The equation calculates the semi-major axis of the orbit and subtracts Earth's radius to get the distance from the surface.

3. Importance of Satellite Distance

Details: Knowing a satellite's distance is crucial for orbital mechanics, communication satellite placement, and understanding orbital characteristics.

4. Using the Calculator

Tips: Enter the orbital period in seconds. The result will be the distance from Earth's surface in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is geostationary orbit distance?
A: For a period of 86400 seconds (24 hours), the distance is about 35,786 km above Earth's equator.

Q2: How does altitude affect orbital period?
A: Higher orbits have longer periods. The International Space Station at ~400 km has a period of about 90 minutes.

Q3: What's the lowest possible orbit?
A: About 160 km, below which atmospheric drag would quickly de-orbit a satellite.

Q4: Does this work for other planets?
A: Yes, but you'd need to substitute that planet's mass and radius.

Q5: Why subtract Earth's radius?
A: The equation gives distance from Earth's center, so we subtract the radius to get altitude above surface.