Final answer:
The force required to keep the Earth in orbit around the Sun is calculated using the centripetal force formula, yielding a result of 4 x 10^22 N.
Step-by-step explanation:
To calculate the force required to keep the Earth in orbit, we can use Newton's law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The formula for gravitational force is F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.To calculate the force required to keep the Earth in orbit around the Sun, we use the formula for centripetal force, which is F = m·v^2/r, where m is the mass of the Earth, v is the orbital velocity, and r is the radius of the orbit. From the information given in the question, we know the mass of the Earth (m) is approximately 6 x 10^24 kg, the velocity (v) is 3 x 10^4 m/s, and the orbital radius (r) is 1.5 x 10^11 m. Plugging these values into the equation, we get:
F = (6 x 10^24 kg) x (3 x 10^4 m/s)^2 / (1.5 x 10^11 m)
After calculating, the force F comes out to be:
F = 4 x 10^22 N
This is the centripetal force that keeps the Earth in its circular orbit around the Sun.