1. What is the Planetary Mass Equation?

The planetary mass equation calculates the mass of a celestial body using its surface gravity, radius, and the gravitational constant. This fundamental physics equation helps astronomers determine the mass of planets when direct measurement isn't possible.

2. How Does the Calculator Work?

The calculator uses the planetary mass equation:

Where:

• \( M \) — Mass of the planet (kg)
• \( g \) — Surface gravity (m/s²)
• \( r \) — Radius of the planet (m)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)

Explanation: The equation derives from Newton's law of universal gravitation, relating a planet's gravitational pull to its mass and radius.

3. Importance of Planetary Mass Calculation

Details: Knowing a planet's mass is essential for understanding its composition, gravitational influence, and potential to retain an atmosphere. It's fundamental in astrophysics and planetary science.

4. Using the Calculator

Tips: Enter surface gravity in m/s² (Earth = 9.81 m/s²) and radius in meters (Earth = 6.371 × 10⁶ m). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How accurate is this calculation?
A: The calculation is mathematically precise if accurate inputs are provided, but real-world measurements may have uncertainties.

Q2: Can this be used for stars?
A: No, stellar mass requires different calculations accounting for nuclear fusion and other stellar processes.

Q3: What's the gravitational constant (G)?
A: G is 6.67430 × 10⁻¹¹ m³/kg·s², a fundamental physical constant measured experimentally.

Q4: Why does radius need to be squared?
A: Gravitational force follows an inverse-square law with distance from the mass center.

Q5: How does this relate to orbital mechanics?
A: A planet's mass determines the orbital periods of its moons and affects spacecraft trajectories.