Final answer:
The Moon's orbit and phases are influenced by its sidereal and synodic periods, providing a way to calculate Earth’s mass using astronomical data. Lunar eclipses occur due to the tilt in the Moon's orbit and bring variation to moonrise times.
Step-by-step explanation:
Earth's satellite, the Moon, has a significant presence in our night sky and plays a crucial role in astronomy and physics. A remarkable feature of the Moon is its sidereal period, which is the time it takes to complete one orbit around Earth relative to the stars, measuring approximately 27.3217 days. However, when considering the Sun's position, we track the synodic period, which is longer, at about 29.5306 days, because the Earth moves in its orbit around the Sun during the Moon's cycle.
To calculate the mass of Earth relative to the Sun using Kepler's third law as modified by Newton, we can use the Moon's orbital distance and period as a reference. The Moon's average distance from Earth is about 384,000 kilometers. Using these data and the knowledge that the orbital period of an artificial satellite in closer proximity to Earth differs, we can make calculations on Earth's gravitational effects and, by extension, its mass.
Lunar Eclipses and Moon's Orbit
The Moon's orbit is tilted relative to Earth's orbital plane, resulting in lunar eclipses only when Earth's shadow falls on the Moon, an event that does not occur every month. This tilt also accounts for the regular occurrence of a full moon and variations in moonrise times.