What is the magnitude of the orbital velocity of the earth when the radius of the earth's orbit around the sun is 150000000?

To calculate the magnitude of the orbital velocity of the Earth, we need to use the formula for orbital velocity:

V = sqrt(G * M / R)

Where:
V is the orbital velocity,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2),
M is the mass of the Sun,
and R is the radius of the Earth's orbit around the Sun.

To find the mass of the Sun, we can use the known value: M = 1.989 × 10^30 kg.

Given that the radius of the Earth's orbit around the Sun is 150,000,000 km (which we need to convert to meters), we can now calculate the magnitude of the orbital velocity.

First, we convert kilometers to meters:
Radius (R) = 150,000,000 km * 1000 m/km = 150,000,000,000 m

Now, we can substitute the values into the formula:
V = sqrt((6.67430 × 10^-11 m^3 kg^-1 s^-2) * (1.989 × 10^30 kg) / (150,000,000,000 m))

By evaluating the expression, we can find the magnitude of the orbital velocity of the Earth around the Sun.