The rotation of the earth around the sun is 1.5 * 10 ^ 11 m. If the mass of the sun is 2 * 10 ^ 30 kg

The rotation of the earth around the sun is 1.5 * 10 ^ 11 m. If the mass of the sun is 2 * 10 ^ 30 kg, determine the speed of the earth.

According to the law of universal gravitation:
F = G * M * m / R², where F is the acting force (F = m * a, where m is the mass of the Earth, and is the acceleration of the Earth (a = V² / R, where V is the speed of the Earth, R is the distance to the Sun) (R = 1.5 * 10 ^ 11 m)), G – gravitational constant (G = 6.67 * 10 ^ -11 m³ / (kg * s²)), M – mass of the Sun (M = 2 * 10 ^ 30 kg).
m * V² / R = G * M * m / R².
V² = G * M / R.
V = √ (G * M / R) = √ (6.67 * 10 ^ -11 * 2 * 10 ^ 30 / (1.5 * 10 ^ 11)) = 29822 m / s.
Answer: The speed of the Earth is 29822 m / s.