Calculate the mass of the Earth, if it had a radius of 3000 km and a gravity of 6 m/s^2.
To calculate the mass of the Earth, we can use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2), m1 and m2 are the masses of the two objects, and r is the distance between them.
In this case, we are given the radius of the Earth (3000 km = 3,000,000 m) and the gravitational acceleration (6 m/s^2). We can use these values to find the mass of the Earth.
Since the Earth's gravity is caused by its own mass, m1 and m2 in the equation can be considered the same, which we will denote as m (the mass of the Earth).
Using the equation for the gravitational acceleration:
g = (G * m) / r^2
We can rearrange this equation to solve for mass:
m = (g * r^2) / G
Plugging in the given values, we get:
m = (6 * (3,000,000)^2) / (6.67430 × 10^-11)
Calculating this expression will give us the mass of the Earth.