To calculate the mass of the Earth, we can use the formula for gravitational force:
F = (G * M * m) / r^2,
where: F is the gravitational force between two objects, G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2), M is the mass of the Earth, m is the mass of the Moon, and r is the distance between the centers of the Earth and the Moon.
Since the Moon is in orbit around the Earth, the gravitational force provides the centripetal force necessary to keep the Moon in its orbit. The centripetal force can be calculated using the formula:
F = (m * v^2) / r,
where: v is the velocity of the Moon in its orbit.
Since both forces are equal, we can equate the formulas:
(G * M * m) / r^2 = (m * v^2) / r.
Now, we can solve for the mass of the Earth, M:
M = (v^2 * r) / (G).
Let's plug in the given values: v = 3,683 km/h = (3,683 * 1000) m/h = (3,683 * 1000) / 3600 m/s, r = 384,400 km = 384,400,000 m, G = 6.67430 × 10^-11 N(m/kg)^2.
M = ((3,683 * 1000 / 3600)^2 * 384,400,000) / (6.67430 × 10^-11).
Evaluating this expression will give us the mass of the Earth in kilograms.