Question

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?

Short answer

Answer: The minimum launch speed required is 3.122 × 10^5 m/s.

Step-by-step solution

Identify the variables

Identify the variables given in the problem. The mass of the Moon (M_moon) is 7.342 × 10^22 kg, the radius of the Moon (R_moon) is 1.737 × 10^6 m, and the gravitational constant (G) is 6.674 × 10^-11 N m²/kg².

Write down the escape velocity formula

Write down the escape velocity formula to find the minimum launch speed: v_escape = sqrt((2*G*M_moon) / R_moon)

Insert the given values

Insert the given values into the escape velocity formula: v_escape = sqrt((2*6.674×10^-11 N m²/kg²*7.342×10^22 kg) / 1.737×10^6 m)

Perform the calculations

Perform the calculations to find the escape velocity: v_escape = sqrt((2*6.674×10^-11 * 7.342×10^22) / 1.737×10^6) = sqrt(9.738×10^11) = 3.122 × 10^5 m/s

Find the required launch speed

The required launch speed to send a probe into space so that it does not fall back to the surface of the Moon is 3.122 × 10^5 m/s.