Gravitation and Newton's Synthesis

AI Thread Summary
The discussion revolves around calculating the mean distance of the asteroid Icarus from the Sun using Kepler's Law. The user attempts to apply the formula but arrives at a distance of approximately 1.87 E 11 m, while the textbook states it should be 1.62 E 11 m. The user questions their approach, particularly regarding the period of the Earth, which they mistakenly consider as one day. Additionally, it is noted that converting periods into seconds is unnecessary for this calculation. The conversation highlights the importance of correctly applying Kepler's Law and understanding the units involved in orbital mechanics.
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Homework Statement


The asteroid Icarus, though only a few hundred meters across, orbits the Sun like the other planents. Its period is about 410 d. What is its mean distance from the Sun?


Homework Equations



Keplers Law
T_1 ^2 / T_2 ^2 = S_1 ^3 / S_2 ^3

The Attempt at a Solution



I chose my second reference point to be the earth
the distance from the Earth to the sun is about 1.5 E 11 m
the period of the Earht is one day or 8.64E4 s
410 d is equal to 3.542E7 s

from keplers law

S_1 = CUBEROOT( (T_1^2 S_2^3)/T_2^2

CUBEROOT( ((3.542 E 7 s)^2 (1.5 E 11 m)^3)/(8.64 E 4 s)^2
I'm getting about 1.87 E 11 m
the book says 1.62 E 11 m

what am I doing wrong
 
Physics news on Phys.org
What for the period of the Earth is one day ?
 
Also, it is not necessary to convert the periods into seconds in this problem.
 

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