Find mean distance from asteroid Icarus to the sun

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Homework Help Overview

The problem involves calculating the mean distance of the asteroid Icarus from the Sun based on its orbital period using Kepler's laws. The context includes the relationship between the period of Icarus and that of Earth.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply Kepler's laws to derive the mean distance but encounters an issue with the calculation. Participants question the units used in the application of Kepler's third law and discuss the need to convert the orbital period from days to years.

Discussion Status

The discussion has progressed with participants providing hints regarding unit conversion, leading to a successful adjustment by the original poster. There is an acknowledgment of the correct approach, but no explicit consensus on the final outcome.

Contextual Notes

There is a hint provided in the problem statement regarding the parameters known for Earth, which may influence the calculations. The original poster's initial misunderstanding of units is a key point of discussion.

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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