I'm having trouble with the following formula:
$$\frac{4\pi^2}{GP^2}r_1(r_1+r_2)^2$$
Where:
$G = 9.8$
$P = 10$ years (orbital period) $(3.154 \times 10^8$ seconds$)$
$r_1 = 4.5 \times 10^{12}$
Where according to the task it can be plugged with the numbers as following:
$2.6 \times 10^7 (r_1 + r_2)^2$
But I can't figure out how to solve for the value of $2.6 \times 10^7$ to begin with.
I'm terribly sorry for the poor formatting, I know it's expected to be formatted correctly but I struggled as much with that as with the formula it self.
$G$ is supposed to be the gravitational constant, which is $6.674\times 10^{-11}$m$^3$kg$^{-1}$s$^{-2}$, not the acceleration of gravity at the earth's surface, which is usually denoted $9.8$m/s$^2$ If you plug this value in and use the seconds value of the period you will come out right. You also have a problem that the original problem has an extra factor of $r_1$ compared to the expected result. Please check.