Gravitation and Newton's Synthesis

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SUMMARY

The discussion focuses on calculating the mean distance of the asteroid Icarus from the Sun using Kepler's Law. The user applied the formula T_1^2 / T_2^2 = S_1^3 / S_2^3, selecting Earth as the reference point with a distance of approximately 1.5 x 1011 m and a period of 1 day (8.64 x 104 s). The user calculated a mean distance of about 1.87 x 1011 m, while the expected value is 1.62 x 1011 m. The discrepancy arises from unnecessary conversion of periods into seconds, which is not required for this problem.

PREREQUISITES
  • Understanding of Kepler's Laws of planetary motion
  • Familiarity with basic algebra and cube root calculations
  • Knowledge of astronomical units and distances (e.g., distance from Earth to the Sun)
  • Ability to convert time units (days to seconds) for calculations
NEXT STEPS
  • Review Kepler's Laws, specifically their application in orbital mechanics
  • Practice calculations involving orbital periods and distances using Kepler's Law
  • Explore the significance of astronomical units in space science
  • Investigate common errors in unit conversion in physics problems
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Astronomy students, physics enthusiasts, and educators seeking to understand orbital mechanics and the application of Kepler's Laws in real-world scenarios.

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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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