Hello everyone,

I'm having a little trouble getting Maple to return a correct solution.  It's a simple equation, really, involving the relation of the period of an object around the sun and it's semi-major axis.  Specifically this involves Halleys comet.

Given that halleys comet takes 76 years to complete an orbit.

I set

restart;

eq1:=P^2=(4*Pi*a^3)/(G*M);

and convert P to seconds

P:=convert(76,units,year,second);

G:=6.672e-11;

M:=1.99e30;

solve(eq1,a);

The only answer I'm concerned about is the solution without any imaginary parts, the 3.931623589 10^12 part.  Sadly this answer maple gives is the wrong answer.  Why?  I don't know.  Can someone tell me what's wrong. 

However if I do it this way

restart;

P:=convert(76,units,year,second);

G:=6.672e-11;

M:=1.99e30;

evalf((P^2*G*M)/(4*Pi^2))^(1/3);

I get the right answer I'm supposed to get    2.684449929 10^12

Can someone tell me what I'm doing wrong in my first method?  Is it something to do with the cube root that maple doesn't like in my eq1?

Concerned about maple's ability to return the correct answers.