Final answer:
To determine Earth's mass using the given information, you can use Kepler's laws, the orbital period and distance formula, compare gravitational forces, or make lunar observations.
Step-by-step explanation:
There are several ways to determine the mass of Earth using the given information:
- Kepler's Laws: Kepler's third law can be used to calculate Earth's mass relative to the Sun. This law states that the square of the orbital period of a planet is proportional to the cube of its average distance from the Sun. However, this information alone does not provide enough data to calculate the mass of Earth relative to the Sun.
- Orbital Period and Distance: The orbital period and distance of the Moon can be used to find Earth's mass. Newton's version of Kepler's third law states that the square of the orbital period is proportional to the cube of the average distance from the center of mass. By plugging in the values of the Moon's orbital period (27.3 days) and distance from Earth (384,000 km), we can calculate Earth's mass.
- Gravitational Forces: We can compare the gravitational forces acting on the Moon and Earth. The force of gravity is given by the equation F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers. By equating the gravitational force on the Moon with the gravitational force on Earth, we can solve for Earth's mass.
- Lunar Observations: Based on lunar observations, we can determine the mass of Earth. This method involves measuring the period and distance of the Moon's orbit accurately and using these values to calculate Earth's mass.