Calculate the escape velocity of a satellite launched from the earth surface if the radius of the earth is 6.4x10^6m
To calculate the escape velocity of a satellite launched from the Earth's surface, you can use the equation:
v = √(2GM/r)
Where:
- v: escape velocity
- G: gravitational constant (approximately 6.673 × 10^-11 Nm^2/kg^2)
- M: mass of the Earth (approximately 5.972 × 10^24 kg)
- r: radius of the Earth (6.4 × 10^6 m)
Plugging in the values, we have:
v = √(2 × 6.673 × 10^-11 Nm^2/kg^2 × 5.972 × 10^24 kg / 6.4 × 10^6 m)
Simplifying this equation gives:
v = √(1.3412 × 10^−13 Nm/kg)
Calculating the square root gives:
v ≈ 1.16 × 10^4 m/s
Therefore, the escape velocity from Earth's surface is approximately 1.16 × 10^4 m/s.
To calculate the escape velocity of a satellite launched from the Earth's surface, you can use the formula:
v = √ (2 * G * m / r)
Where:
v is the escape velocity
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
m is the mass of the Earth (approximately 5.972 × 10^24 kg)
r is the radius of the Earth (6.4 × 10^6 m)
Plugging in the values, we get:
v = √ (2 * 6.67430 × 10^-11 * 5.972 × 10^24 / 6.4 × 10^6)
Simplifying:
v = √ (8.98238 × 10^13)
Finally, we can find the exact value using a calculator:
v ≈ 2.994 × 10^4 m/s
So, the escape velocity of a satellite launched from the Earth's surface with a radius of 6.4x10^6 m is approximately 2.994 × 10^4 m/s.