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

`(T_1^2)/(T_2^2) = (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

`(1^2)/(309.1^2) = (1^3)/(r^3)`

from above equation we have

`r = 45.7 AU`

as we also know that

`1 AU = 1.5 * 10^(11) km`

so average distance will be

`r = 6.86 * 10^(12) km`