Phyrsics question for my Astronomy Class

Question

1.) The orbital period of Mars is 2.095 years. Mars is 1.5 au. (distance) Combine the two?
2.) Graph the period in years squared against the distance from the Sun (in au) cubed?

Answer 1

The data in the problem statement is incorrect.  The mean orbital radius (a) of Mars is 1.52 AU and the period (P) is 1.88 years.  You can look these up in an astronomy book.  You can also test them, for by Kepler's 3rd law, 

 

(P²/a³)_Mars = (P²/a³)_Earth = (1 year)²/(1 AU)³ = 1 year²/AU³

 

(P²/a³)_Mars = (1.88²/1.52³) ≅ 1.01 year²/AU³

 

This forum is not set up for graphing.

 

The intent of the problem may be to compute P²/a³ for several planets, and show they are the same, as predicted by Kepler's 3rd law.