1. The text uses the relation v_rms > v_esc/6 for the velocity needed to lose a component of the atmosphere, and from that obtains equation 19.6. Using a different criterion, the relation v_rms > v_esc/10, how would equation 19.6 be modified? Give the new equation.

2. The Moon cannot hold on to water vapor (H₂O) or oxygen molecules (O₂) because it is too small. Referring to the example calculation for the Moon done in the lecture, how much more massive would the Moon have to be to retain O₂? How much more massive would it have to be to retain H₂O? Express your answer in units of the Moon's mass.