Pearson HW23, The Little Prince

In summary, "The Little Prince" tells the story of a young prince who travels from his home asteroid to various planets, meeting different inhabitants and learning valuable life lessons. Through his encounters, he reflects on themes of love, friendship, and the nature of human relationships. The narrative emphasizes the importance of seeing beyond appearances and cherishing what truly matters in life, ultimately revealing the wisdom of childlike perspective.
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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.
 
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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).
 
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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
 
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FAQ: Pearson HW23, The Little Prince

What is the main theme of "The Little Prince"?

The main theme of "The Little Prince" is the exploration of human nature, love, and the importance of seeing with the heart rather than just with the eyes. It emphasizes the value of relationships, the innocence of childhood, and the critique of the superficial aspects of adult life.

Who is the author of "The Little Prince"?

"The Little Prince" was written by Antoine de Saint-Exupéry, a French writer and aviator. The book was first published in 1943 and has since become one of the most translated and best-selling books in the world.

What is the significance of the fox in "The Little Prince"?

The fox in "The Little Prince" teaches the prince about the nature of love and relationships. The fox's lesson that "one sees clearly only with the heart" and that "what is essential is invisible to the eye" is a central message of the story, highlighting the importance of emotional bonds and understanding.

Why does the little prince leave his asteroid?

The little prince leaves his asteroid because he is curious about the universe and wants to explore other planets. His journey is also motivated by his feelings of loneliness and his desire to understand more about love and relationships, particularly his feelings towards the rose he left behind.

What does the rose symbolize in "The Little Prince"?

The rose in "The Little Prince" symbolizes love, beauty, and the complexity of relationships. Although the rose is vain and demanding, the little prince learns to love her and realizes that his feelings make her unique and special to him, illustrating the theme that true love comes with responsibility and care.

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