Find mean distance from asteroid Icarus to the sun

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SUMMARY

The mean distance of the asteroid Icarus from the Sun is calculated using Kepler's Third Law, which relates the orbital period of a celestial body to its distance from the Sun. The period of Icarus is approximately 410 days, which converts to about 1.123 years. By applying the formula and converting the period to years, the mean distance is found to be 55.2 AU. Multiplying this by 1.5e8 km results in a mean distance of approximately 8.28e9 km.

PREREQUISITES
  • Understanding of Kepler's laws of planetary motion
  • Knowledge of astronomical units (AU)
  • Ability to convert time units (days to years)
  • Basic arithmetic operations for unit conversion
NEXT STEPS
  • Study Kepler's Third Law in detail
  • Learn about the conversion of time units in astronomical calculations
  • Explore the significance of astronomical units in space science
  • Investigate other celestial bodies' orbits and their mean distances from the Sun
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Astronomy students, astrophysicists, and anyone interested in understanding celestial mechanics and orbital dynamics.

SnowOwl18
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Ok, I keep trying to do the following problem:

----The asteroid Icarus orbits the Sun like the other planets. Its period is about 410 days. What is its mean distance from the Sun?
(Hint: You can derive the mean distance with the paramters known for the Earth: Period of the Earth = 365 days Mean distance from the sum = 1.5e8km)----------------


Ok, so, using Kepler's laws I took 410 days and put it to the (2/3) power...and I got 55.2 AU...one AU (astronomical unit) equals 1.5e8 km...so I multiplied 55.2 by 1.5e8 km and got 8278414420 km...or 8.28e9 km...but the computer program says I'm wrong. Does anyone know what I'm doing wrong? Thanks.
 
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Hint: Look at your units.
 
which units? if one AU=1.5e8 I can multiply 55.2 by that to get the answer, right?
 
What units are you supposed to use in kepler's third law?
 
oh do i have to convert 410 days to years? like 1.123 years?
 
oh that worked! Thanks for your help :D
 
Yup! That's exactly right.
 

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