The mass of Neptune is approximately 1.02×10^26 kg based on Triton's orbital period of 5.88 days and orbital radius of 3.54×10^8 m using Kepler's third law.
Kepler's third law is a fundamental principle in celestial mechanics, expressing a mathematical relationship between the orbital properties of celestial bodies and the mass of the central object around which they orbit. In this case, Triton, Neptune's largest moon, serves as a celestial body in orbit around Neptune.
The formula T^2 = 4π^2. a^3/GM encapsulates the gravitational dynamics governing the orbital motion of celestial bodies. By rearranging this equation to solve for the mass of the central object (M), scientists can utilize the known values of Triton's orbital period and orbital radius to infer the mass of Neptune.
The calculated mass of Neptune, approximately 1.02×10^26 kg, represents a crucial parameter in understanding the gravitational interactions within the Neptune-Triton system. Such calculations provide valuable insights into the composition and dynamics of celestial bodies in our solar system, contributing to our broader understanding of planetary science and astrophysics.