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.