Einstein's theory of gravity, also known as general relativity, describes gravity as the curvature of spacetime caused by mass and energy. It does not directly provide a formula to calculate the weight of an object or the volume of a planet. However, we can still determine the weight of the Earth given its mass and the acceleration due to gravity.
The weight of an object can be calculated using the formula:
Weight = Mass x Acceleration due to gravity
The mass of the Earth is approximately 5.972 × 10^24 kilograms, and the acceleration due to gravity at the Earth's surface is approximately 9.8 meters per second squared (m/s^2).
To determine the weight of the Earth, we multiply its mass by the acceleration due to gravity:
Weight = 5.972 × 10^24 kg x 9.8 m/s^2
Calculating this gives us the weight of the Earth in Newtons, which is the unit for force. The result is approximately:
Weight of the Earth = 5.868 × 10^25 Newtons
However, you mentioned the "volume of the Earth measured in square meters." Volume is typically measured in cubic meters (m^3), not square meters (m^2). Square meters measure area, not volume. If you meant to ask for the weight of the Earth per unit volume, please clarify the question, specifying the desired units for volume (cubic meters, cubic kilometers, etc.).