How to Calculate Planet Mass

Kepler's Third Law Formula:

\[ M = \frac{4 \pi^2 r^3}{G T^2} \]

Planet Mass (M):

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1. What is Kepler's Third Law?

Kepler's Third Law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This law allows us to calculate the mass of a central body (like a planet) when we know the orbital characteristics of its satellite.

2. How Does the Calculator Work?

The calculator uses Kepler's Third Law formula:

\[ M = \frac{4 \pi^2 r^3}{G T^2} \]

Where:

\( M \) — Mass of the planet (kg)
\( r \) — Orbit radius (meters)
\( T \) — Orbital period (seconds)
\( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula derives from Newton's law of universal gravitation and describes the relationship between orbital parameters and the mass of the central body.

3. Importance of Planet Mass Calculation

Details: Calculating planetary mass is fundamental to understanding gravitational forces, orbital mechanics, and the composition of celestial bodies. It helps astronomers determine if a planet is terrestrial or gaseous and predict its gravitational influence on other objects.

4. Using the Calculator

Tips: Enter orbit radius in meters, orbital period in seconds, and gravitational constant. The default value for G is 6.67430 × 10⁻¹¹ m³/kg·s². All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the inputs?
A: Use meters for orbit radius, seconds for orbital period, and m³/kg·s² for gravitational constant. Ensure consistent units for accurate results.

Q2: Can this formula calculate the mass of any celestial body?
A: Yes, this formula can calculate the mass of any central body (planet, star, etc.) when you know the orbital parameters of an object orbiting it.

Q3: What is the typical range of planetary masses?
A: Planetary masses range from about 3.3 × 10²³ kg (Mercury) to 1.9 × 10²⁷ kg (Jupiter). Earth's mass is approximately 5.97 × 10²⁴ kg.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact based on the inputs. Accuracy depends on the precision of your orbital measurements and the gravitational constant value used.

Q5: Can I use this for elliptical orbits?
A: For elliptical orbits, use the semi-major axis (average distance) for 'r' in the formula. The law applies to elliptical orbits when using the semi-major axis.