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

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

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

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