Determine the escape velocity from the Sun's gravitational field, considering the Sun's mass and radius. Express the result in kilometers per second.
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To determine the escape velocity from the Sun's gravitational field, we can use the formula:
v = sqrt((2 * G * M) / R)
where:
- v is the escape velocity
- G is the gravitational constant (6.67430 x 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the Sun (1.989 x 10^30 kg)
- R is the radius of the Sun (6.9634 x 10^8 m)
First, let's convert the mass and radius of the Sun to meters:
M = 1.989 x 10^30 kg
R = 6.9634 x 10^8 m
Now, we can substitute these values into the formula:
v = sqrt((2 * G * (1.989 x 10^30 kg)) / (6.9634 x 10^8 m))
Calculating this expression gives:
v = sqrt((2 * (6.67430 x 10^-11 m^3 kg^-1 s^-2) * (1.989 x 10^30 kg)) / (6.9634 x 10^8 m))
v = 617.5 m/s
Therefore, the escape velocity from the Sun's gravitational field is approximately 617.5 m/s. To express this result in kilometers per second, we can convert it by dividing by 1000 (1 km = 1000 m):
v = 617.5 m/s / 1000
v ≈ 0.6175 km/s
So, the escape velocity from the Sun's gravitational field is approximately 0.6175 km/s.
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