You are on the Moon and would like to send a probe into space so that it does not fall back to the surface of the Moon. What launch speed do you need?
Vescape = sqrt (2 G M/R)
G = 6.67 * 10^-11
M = mass of moon = 7.35*10^22 kg
R = moon radius = 1.74 * 10^6 meters
2373.815494
To calculate the launch speed required for a probe to escape the gravitational pull of the Moon and not fall back to its surface, you need to understand the concept of escape velocity.
Escape velocity is the minimum speed an object needs to reach in order to break free from the gravitational pull of a celestial body. It allows an object to overcome gravity and continue moving away indefinitely.
To calculate the escape velocity, you can use the equation:
v = √(2 * G * M / R)
Where:
- v is the escape velocity.
- G is the gravitational constant (approximately 6.67430 x 10^-11 m^3/kg/s^2).
- M is the mass of the Moon (approximately 7.348 x 10^22 kg).
- R is the radius of the Moon (approximately 1,737.5 km or 1,079.6 miles).
To solve this equation, substitute the given values into the formula and calculate the result:
v = √(2 * 6.67430 x 10^-11 * 7.348 x 10^22 / 1,737,500)
v ≈ √(9.9329 x 10^11 m^3/kg/s^2)
v ≈ 10,000 m/s (approximately)
Therefore, to ensure that the probe does not fall back to the surface of the Moon, it needs to be launched with a speed of approximately 10,000 meters per second (m/s).