Pearson HW23, The Little Prince

[Enginearingmylimit]

Homework Statement

The Little Prince (a character in a book by Antoine de Saint-Exupery) lives on the spherically symmetric asteroid B-612. The density of B-612 is 5500 kg/m3.
For the first set of questions, assume that the asteroid does not rotate. The Little Prince notices that he feels lighter whenever he walks quickly around the asteroid. In fact, he finds that he starts to orbit the asteroid like a satellite if he speeds up to 2.20 m/s.

A. Find the radius of the asteroid. Also, find the magnitude of the acceleration of the Prince while he is in his circular orbit at the surface of asteroid B-612.

B. The Prince carries a small compressed-air rocket with him at all times; the rocket is a safety device in case he gets separated from his asteroid. If the Prince jumps straight Up from the asteroids surface, what is the maximum possible jumping speed which will allow the Prince to return to the surface without using his safety rocket? Note: "jumping speed" refers to the speed of the jumping Prince at the instant just after his feet leave the surface.

Relevant Equations

g=GM/r^2
G=GMm/r^2
V(escape)=sqrt(2Gm/r)

A. Correct answer is radius = 1770m, acceleration = 2.73*10^-3m/s.
B. I don't know how to approach this problem. I don't know if I should start with forces, energy, or basic kinematics.

 

[berkeman]

A: Do you know how to calculate those answers? Hint: use the Gravitational Attraction equation between two bodies (based on their masses, etc.), and then use a 2nd equation that involves the centripetal acceleration for uniform circular motion...

B: If you can assume that the asteroid is much more massive than the Prince, you can use the traditional calculation for escape velocity (like from the Earth -- try searching on that term).

 

[Enginearingmylimit]

A. Yes I solved those with some help from a tutor, but didn't get to the rest of this question because his office hours ended.
B. I used escape velocity=√(2GM/R) to get 3.26*10^-7. I used G=6.67*10^-11, M=1.277*10^14. I wasn't using this previously, because I miscalculated the mass. So, thank you for bringing me back to that. The answer I got was 3.1029m/s. Thank you for your help