Answer to Question #159034 in Classical Mechanics for syuhada

Question

There are many comets in our solar system. A comet is located at a distance r_c = 16 AU from the sun moving at a speed v_c = 0.26vE where v_E is the average speed of Earth orbital motion. At that particular instant the position vector r_c makes an angle ϕ = 68^o with velocity vector v_c .

a) Determine eccentricity ε of the orbit.

b) If the semi-major axis of the orbit a = 13.7 AU, write the equation of the orbit for the comet.

c) Determine the period of the comet. Can you identify the most probable name for the comet?

Answer 1

1)

$r=a(1-ecos (180°-\phi)),$ $⇒$

$e=\frac{1-\frac ra}{cos(180°-\phi)},$

$e=\frac{1-\frac {16}{13.7}}{cos(112°)}\approx0.4482.$

2)

$r=\frac{p}{1+ecos\theta},$

$p=a(1-e^2)=10.9484,$

$r=\frac{10.9484}{1+0.4482cos\theta}.$

3)

$T=a^{\frac 32}=50.7$ years.

Comet 166P/NEAT.