The Little Prince ( a character in a book by Antoine de Saint-Exupery) lives on

Question

The Little Prince ( a character in a book by Antoine de Saint-Exupery) lives on the sphereically symmetric asteroid B-612. The denisty of B-612 is 5200 kg/cubic meter. Assume that the asteroid does not rotate. The Little prince noticed that he felt lighter whenever he walked quickly around the asteroid. In fact, he found that he became weightless and started to orbit the asteroid like a sattelite whenever he speeded up to 2 m/s. a) estimate the radius of the asteroid from these data. b) what was the escape speed for the asteroid? c) suppose that B-612 does rotate about an axis such that the length of the day there is 12 h. Can the Little Prince take advantage of this rotation when he wants to orbit the asteroid? What is his minimum ground speed for orbit in this case?
a)1.66km b)2.83m/s c)1.76m/s
These are the correct answers but i dont know how to solve this The Little Prince ( a character in a book by Antoine de Saint-Exupery) lives on the sphereically symmetric asteroid B-612. The denisty of B-612 is 5200 kg/cubic meter. Assume that the asteroid does not rotate. The Little prince noticed that he felt lighter whenever he walked quickly around the asteroid. In fact, he found that he became weightless and started to orbit the asteroid like a sattelite whenever he speeded up to 2 m/s. a) estimate the radius of the asteroid from these data. b) what was the escape speed for the asteroid? c) suppose that B-612 does rotate about an axis such that the length of the day there is 12 h. Can the Little Prince take advantage of this rotation when he wants to orbit the asteroid? What is his minimum ground speed for orbit in this case?
a)1.66km b)2.83m/s c)1.76m/s
These are the correct answers but i dont know how to solve this
a)1.66km b)2.83m/s c)1.76m/s
These are the correct answers but i dont know how to solve this

Explanation / Answer

a)   Here, GM/R = v2

=>   G * (d * 4/3 *piR3)/R = v2

=>     G * (d * 4/3 *piR2) = v2

=>    6.67 * 10-11 * (5200 * 4/3 *piR2) = 22

=> R =    1.66   km           --------------------------->   radius of the asteroid

b)    escape speed for the asteroid = sqrt(2GM/R)

                                                    = 2.83 m/s

where, M = density * 4/3 *piR3

R = 1.66 km

c)     minimum ground speed for orbit = v

=>    mv2/R = GMm/R2

Also, v =   2piR/t

where, t = 12 hours

=> v =    1.76 m/s

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