Question

The orbit of the comet Encke has a perihelion distance of 0.331 AU and an eccentricity of 0.850. Suppose that the arrival of the comet at its perihelion distance happens to occur at a point directly in line between the Sun and the Earth. Roughly how many years will it be before such an event happens again?

a) about 9 months

b) about 17 months

c) about 13 years

d) about 76 years

Answer 1

The time period of an elliptical orbit is

Where M is the mass of sun = 1.989*10³⁰ kg

a, the semi major axis is given by

a = q/(1-e)

q is the perihelion distance = 0.331 AU

e = 0.850

So, a = 0.331/(1-0.85) = 2.2067 AU = 2.2067*1.496*10¹¹ m = 3.3012232*10¹¹ m

G = 6.674*10^-11 m³/kgs²

So,

The orbits will come in line, when the period of orbit of comet is an integral multiple of the period of earth.

That is: n*T becomes almost a whole number.

For n = 4, 4*3.27 = 13.1, which is close to a whole number. So, the event will happen after 13 years