A)some comets are in highly elongated orbits that come very close to the sun at perihelion. the distance from one such comet to the center of the sun is 6.00×10^9m at perihelion and 3.00×10^12m at aphelion. for this comet's orbit, find the semi-major axis. b)in 2017 astronomers discovered a planet orbiting the star hats-43. the orbit of the planet around hats-43 has semi-major axis 7.41×109m, eccentricity 0.173, and period 4.39 days. find the distance between hats-43 and the planet at its closest approach. express your answer with the appropriate units

A) 1.50x10¹² m

B) 6.13x10⁹ m

Explanation:

A) The semi-major axis is the average of the perihelion and the aphelion distances:  

where SMA: is the semi-major axis, P: is the perihelion distance and A: is the aphelion distance

So, the semi-major axis for the comet's orbit is 1.50x10¹² m.

B) To find the distance between the star and the planet at its closest approach, that is to say, at the perihelion, we need to use the Kepler's Law of orbits:

where e: is the eccentricity

Therefore, the distance from the planet to the star HATS-43 is 6.13x10⁹ m at perihelion.  

I hope it helps you!  

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