Answer to Question #165487 in Classical Mechanics for dinie syafikh

Question

Comet d'Arrest was discovered in June 28, 1851 and its orbit about the sun has a semimajor axis a = 3.49 AU. Recently it was observed that the comet has a velocity vc = 0.45V E e_v when it was spotted at position r_c = 2.91RE e_r from the sun at which the velocity vector v_c makes an angle ϕ = 60^o with vector rc (V_E and R_E = 1 AU are the average speed and radius of the Earth orbital motion around the sun respectively). Calculate i. the eccentricity of the comet's orbit. ii. the period of the comet in Earth years. iii. the perihelion, aphelion and the latus rectum of the orbit. 

Answer 1

1)

$e=\frac{r_c}{a}sin^2 \phi \approx 0.625,$

2)

$T=a^{1.5}\approx 6.520 ~a,$

3)

$r_p=a(1-e)=1.309 ~AU,$

$r_a=a(1+e)=5.671~AU,$

$p=a(1-e^2)=2.127~AU.$