1. What is the Planetary Mass Equation?

The planetary mass equation calculates the mass of a celestial body based on the orbital velocity of its satellite, the orbital radius, and the gravitational constant. This is derived from Newton's law of universal gravitation and centripetal force.

2. How Does the Calculator Work?

The calculator uses the planetary mass equation:

Where:

• \( M \) — Planetary mass (kg)
• \( v \) — Orbital velocity of satellite (m/s)
• \( r \) — Orbital radius (meters)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)

Explanation: The equation balances the gravitational force between two bodies with the centripetal force required to keep the satellite in orbit.

3. Importance of Planetary Mass Calculation

Details: Calculating planetary mass is fundamental in astrophysics for understanding celestial mechanics, gravitational effects, and the composition of planets and stars.

4. Using the Calculator

Tips: Enter orbital velocity in m/s, orbital radius in meters, and gravitational constant (default is 6.67430 × 10⁻¹¹). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for accurate results?
A: For consistent results, use meters for distance, meters/second for velocity, and m³/kg·s² for the gravitational constant.

Q2: Can this be used for stars as well as planets?
A: Yes, this equation works for any celestial body that has satellites orbiting it, including stars, planets, and moons.

Q3: How precise is this calculation?
A: The precision depends on the accuracy of your input values. For real astronomical applications, relativistic effects may need to be considered.

Q4: What if the orbit isn't circular?
A: For elliptical orbits, use the average orbital velocity and semi-major axis for the radius.

Q5: Why is the gravitational constant important?
A: G is a fundamental constant that determines the strength of gravitational attraction in the equation.