Answer to Question #103345 in Astronomy | Astrophysics for sakshi

Question

comet has an aphelion distance of 6 .1 ×10¹¹ m and periphelion distance of 5.1× 10¹¹m. The mass of the sun is 2.0 ×10^30 calculate the speed of the comet at the perihelion and the aphelion.

Answer 1

1) The speed of the comet at the perihelion 

$v^2_p=GM\left(\frac{2}{r_p}-\frac{1}{a}\right)$

$r_p=a(1-e)$

$\frac{r_p}{r_a}=\frac{5.1}{6.1}=\frac{(1-e)}{(1+e)}\to e=0.0893$

$5.1\cdot 10^{11}=a(1-0.0893)$

$a=5.6\cdot 10^{11}\ m$

$v^2_p=(6.67\cdot 10^{-11})(2\cdot 10^{30})\left(\frac{2}{5.1\cdot 10^{11}}-\frac{1}{5.6\cdot 10^{11}}\right)$

$v_p=1.7\cdot 10^{4}\frac{m}{s}$

2) The speed of the comet at the aphelion

$v^2_a=GM\left(\frac{2}{r_a}-\frac{1}{a}\right)$

$v^2_p=(6.67\cdot 10^{-11})(2\cdot 10^{30})\left(\frac{2}{6.1\cdot 10^{11}}-\frac{1}{5.6\cdot 10^{11}}\right)$

$v_a=1.4\cdot 10^{4}\frac{m}{s}$