Semi Major Axis of Jupiter's Orbit & Asteroid Period

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The semi-major axis of Jupiter's orbit is 7.8 x 10^8 km, and the question involves finding the semi-major axis of an asteroid with an orbital period half that of Jupiter. The user initially calculated the semi-major axis by simply halving Jupiter's value, resulting in 3.9 x 10^8 km, but questioned the validity of this approach. Kepler's third law states that the square of the orbital period is proportional to the square of the semi-major axis, which is essential for solving the problem correctly. The user recognizes the relevance of the formula T^2/a^3 = K but is unsure how to apply it without additional data. A proper application of Kepler's law is necessary to determine the accurate semi-major axis for the asteroid.
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my question is... the semimajor axis of the orbit of Jupiter is 7.8*108.
If an asteroid has an orbital period half of that of Jupiter what is the semi major axis?

All i did was times 7.8*108 by 1/2 and got 3.9*108.

Seems to simple!??

any comments much appreciated
 
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What does Kepler's third law say?
 
that the square of the orbital period is propotional to the square of the semi major axis.

im unsure of how to apply this though.

I believe T2/a3=K to be relivent but as i only know that the semi major of the sun and Jupiter is 7.8*108 I am confused what to do next
 
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