Question

The comet hale-bopp has a period of about 3000 years. what is its mean distance from the sun in au (astronomical units)? (note that the earth has period of about 1 year and a distance of 1au from the sun.)

Answer 1

As we know by Kepler's law

Square of time period is always proportional to the cube of time period

it is given by

`(T_1^2)/(T_2^2) = (r_1^3)/(r_2^3)`

here we have

T1 = 3000 years

r1 = distance of comet

T2 = 1 year

r2 = 1AU

now by above equation we will have

`(3000^2)/(1^2) = (r_1^3)/(1^3)`

`9*10^6 = r_1^3`

`r_1 = 208 AU`

so the distance of comet will be 208 AU.