Question

Suppose a comet has an orbital period of 309.1 years around the sun. What is it’s average distance from the sun?

Answer 1

As we know from kepler's law that

$\frac{T_1^2}{T_2^2} = \frac{r_1^3}{r_2^3}$

here we know that for earth we have time period T = 1 year and its average distance from Sun is 1 AU

so here from above equation we have

$\frac{1^2}{309.1^2} = \frac{1^3}{r^3}$

from above equation we have

$r = 45.7 AU$

as we also know that

$1 AU = 1.5 \times 10^{11} km$

so average distance will be

$r = 6.86 \times 10^{12} km$