Question

The planet Gliese 163 c, discovered in 2012, is a potentially habitable world which is approxi- mately 7 times same mass as the Earth, orbiting a small red dwarf star that is only 0.4 times mass of the Sun. Completing its entire orbit in only a little over 25 days, Gliese 163 c orbits at a distance from its star at a speed of 1.78 times that of the speed of the Earth around the Sun. Approximating that both the Earth’s orbit and Gliese 163 c’s orbit can be taken to be nearly circular, with gravity providing centripetal force, what must be its average orbital distance from its star compared with the Earth's average orbital distance to the Sun?

Answer 1

For Earth-Sun system, Gravity providing the centripetal force  

---(1)

For planet Gliese and its red dwarf star,

Gravity providing the centripetal force  

----(2)

Given that , Mass of Gliese is 7 times same mass as the Earth  

Mass of  red dwarf star that is only 0.4 times mass of the Sun

Speed of Gliese around red dwarf star is 1.78 times that of the speed of the Earth around the Sun ,

Average orbital distance from Gliese to Red dwarf star is times the average orbital distance from Earth to Sun.