A comet has a very elliptical orbit with a period of 137.6 y. If the closest approach of the comet to the Sun is 0.09 AU, what is its greatest distance from the Sun

53.35 AU

Explanation:

Using Kelper's third law

The relation between  the time period (T) and the semi-major axis  of the comet can be expressed as:

T²∝a³

T² = Ka³

where;

(a) = length of the semi-major axis

Making (a) the subject of the axis

a³

a = 26.72 AU

Finally, the greatest distance from the Sun is:

d = 2(26.72) - 0.09

d =53.44 - 0.09

d = 53.35 AU

Thus, the greatest distance from the Sun = 53.35 AU