A comet (assumed to be in an elliptical orbit around the sun) is at a distance of 0.4 AU from the sun at the perihelion. If the time period of the comet is 125 years, what is the aphelion distance ? AU : Astronomical Unit.

Options

A. 50AU
B. 25AU
C. 49.6AU
D. 24.6AU

Answer

C

Explanation

`thereforer=(0.4+y)/2`

Also `((T_1)/(T_2))^(2)=((r_1)/(r_2))^(3)` by Kepler’s law of time – period
(`T_1,r_1` are taken for earth)
`therefore((1y)/(125y))^2=((1AU)/(((0.4+y)/2)AU))^(3)`
Solving we get y =49.6 AU