Mass of a Planet Calculator

Planetary Mass Formula:

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

Orbital Radius (r):

meters

Orbital Period (T):

seconds

Gravitational Constant (G):

m³ kg⁻¹ s⁻²

Planet Mass (M):

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1. What is the Planetary Mass Formula?

The planetary mass formula calculates the mass of a celestial body using orbital data of its satellite. This formula is derived from Newton's law of universal gravitation and Kepler's third law of planetary motion.

2. How Does the Calculator Work?

The calculator uses the planetary mass formula:

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

Where:

\( M \) — Mass of the planet (kg)
\( r \) — Orbital radius of the satellite (m)
\( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻²)
\( T \) — Orbital period of the satellite (s)

Explanation: The formula relates the mass of a planet to the orbital characteristics of its satellite, based on the balance between gravitational force and centripetal force.

3. Importance of Planetary Mass Calculation

Details: Calculating planetary mass is fundamental in astronomy for understanding celestial mechanics, gravitational interactions, and the composition of planetary systems.

4. Using the Calculator

Tips: Enter orbital radius in meters, orbital period in seconds, and gravitational constant. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for this calculation?
A: Use meters for orbital radius, seconds for orbital period, and m³ kg⁻¹ s⁻² for gravitational constant for consistent SI units.

Q2: Can this formula be used for any celestial body?
A: Yes, this formula can calculate the mass of any celestial body that has satellites with known orbital parameters.

Q3: Why is the gravitational constant important?
A: The gravitational constant is a fundamental physical constant that quantifies the strength of gravitational attraction between objects.

Q4: What if I have multiple satellites?
A: The formula works for each satellite individually. Multiple measurements can help verify accuracy through consistency.

Q5: Are there limitations to this calculation?
A: This assumes circular orbits and that the satellite's mass is negligible compared to the planet's mass. Elliptical orbits require more complex calculations.