The mass of Neptune, like that of other celestial objects, is determined through scientific observations and calculations based on the laws of physics. There are a few different methods used to determine the mass of Neptune, including:
Newton's law of universal gravitation: By observing the motion of Neptune's moons or other objects in its vicinity, scientists can apply Newton's laws of motion and gravitation to calculate the mass of Neptune. The gravitational pull exerted by Neptune on its moons can be measured, and by knowing the orbital parameters and applying the laws of gravitation, the mass of Neptune can be determined.
Perturbation of other planets: The presence of Neptune affects the orbits of other planets in our solar system, particularly Uranus. Astronomers observed deviations in Uranus's orbit that could not be explained solely by the gravitational pull of the known planets. The presence of an additional massive planet, later confirmed to be Neptune, was hypothesized to explain these perturbations. By studying the perturbations and the resulting changes in the orbits of other planets, scientists can calculate the mass of Neptune.
Spacecraft measurements: Space missions, such as NASA's Voyager 2, have conducted close flybys of Neptune. These missions collect valuable data about the planet's gravitational field and its effects on the spacecraft. By analyzing the trajectory and the gravitational interactions during the flyby, scientists can derive the mass of Neptune.
These methods, along with sophisticated mathematical modeling and analysis, allow scientists to estimate the mass of Neptune with a high degree of accuracy. The current accepted value for Neptune's mass is approximately 17 times that of Earth, or about 1.024 × 10^26 kilograms.