Jupiter-Sun Mass Comparison
Using Io's orbit to calculate Jupiter's mass relative to the Sun
Celestial Body Parameters
Io's Orbital Period:
1.769 days
Io's Orbital Radius:
4.22 × 10⁸ m
Earth's Orbital Period:
365.25 days
Earth's Orbital Radius:
1.496 × 10¹¹ m
Physics Explanation
Using Kepler's Third Law to calculate masses:
M = 4π²R³/GT²
Where:
- M = mass of the central body
- R = orbital radius of the satellite
- T = orbital period of the satellite
- G = gravitational constant
Calculating Jupiter's mass from Io's orbit:
Mⱼ = 4π²(4.22×10⁸)³ / G(1.769×24×3600)² ≈ 1.90×10²⁷ kg
Calculating Sun's mass from Earth's orbit:
Mₛ = 4π²(1.496×10¹¹)³ / G(365.25×24×3600)² ≈ 1.99×10³⁰ kg
The ratio shows Jupiter's mass is about 1/1000th of the Sun's mass:
Mⱼ/Mₛ ≈ (1.90×10²⁷)/(1.99×10³⁰) ≈ 0.00095 ≈ 1/1000
