The largest rocky planet that could have Earth's gravity would be a planet with a similar mass and density as Earth but a larger radius. The relationship between a planet's mass, radius, and gravity is determined by the planet's average density and the universal gravitational constant.
Earth has a mass of approximately 5.97 x 10^24 kilograms and an average density of about 5,515 kilograms per cubic meter. The acceleration due to gravity on Earth's surface is approximately 9.8 meters per second squared.
To determine the largest rocky planet with Earth's gravity, we can calculate the maximum radius using the formula:
radius = (√(mass * gravitational constant) / (√(density * acceleration due to gravity))
By plugging in the values for Earth's mass, density, and acceleration due to gravity, and using the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2), we can estimate the maximum radius.
Using this calculation, the largest rocky planet you could get with Earth's gravity would have a radius of approximately 6,378 kilometers, which is the same as Earth's radius. Keep in mind that this estimation assumes a similar composition and density to Earth, which consists primarily of silicate rocks and a metallic core.
It's worth noting that there may be variations in the composition and density of rocky planets, which could affect their maximum size while maintaining Earth's gravity. However, the estimate provided gives a rough idea of the maximum size limit for a rocky planet with Earth-like gravity.