Question

What is the period of revolution for a comet with aphelion at 5 AU and perihelion at the orbit of Earth?

Answer 1

Given:

For the comet:

Aphelion = 5 AU

Solution:

For the Comet:

Perihelion = 1 AU

So, the length of the major axis, a = Aphelion + Perihelion = 1 + 5 = 6 AU

the length of the semi major axis = radius, R =
`(a)/(2) = (6)/(2)` = 3 AU

According to Kepler's third law of planetary motion:

`T^(2) = R^(3)` (1)

where,

T = Time period of rervolution for comet

Using eqn (1):

`T = \sqrt R^(3)`

`T = \sqrt (3)^(3)`

T = 5.196 ≈ 5.2 years