Respuesta :
Answer:
The speed of orbit when it crosses Mercury, v = 5.4 x 10⁴ m/s
Explanation:
Given,
The mass of the comet, m = 1.5 x 10³³ Kg
The mass of the sun, M = 1.99 x 10³⁰ Kg
The velocity of the comet at the orbit of mars, V = 3.1 x 10⁴ m/s
The radius of orbit of mars, R = 2.28 x 10⁸ km
= 2.28 x 10¹¹ m
The radius of orbit of mercury, r = 5.79 x 10⁷ Km
= 5.79 x 10¹⁰ m
The velocity of orbit at a distance R from the sun is given by the formula
[tex]V = \sqrt{\frac{GM}{R} }[/tex]
Substituting the given values in the above equation
[tex]V = \sqrt{\frac{6.67X10^{-11}X1.99X10^{30}}{2.28X10^{11}}}[/tex]
= 2.41 x 10⁴ m/s
Given that the velocity of a comet passing the orbit of mars is 3.1 x 10⁴ m/s
The discrepancy in the velocity is 0.7 x 10⁴ m/s
This is due to the high eccentricity of the orbit of a comet.
The velocity of a comet crossing the orbit of mercury is
[tex]v = \sqrt{\frac{6.67X10^{-11}X1.99X10^{30}}{5.79X10^{10}}}[/tex]
= 4.7 x 10⁴ m/s
Adding the discrepancy to the above value gives
v = 5.4 x 10⁴ m/s
Hence, the velocity of the comet crossing the orbit of mercury is, v = 5.4 x 10⁴ m/s
