Many years hence, your grandchild is a member of an advance party that will trav
ID: 1596777 • Letter: M
Question
Many years hence, your grandchild is a member of an advance party that will travel to the ultra-cool dwarf star Trappist-1 to explore the possibility of colonizing one of the planets discovered. The plan is for the starship to travel to that far away solar system and to orbit the star at a distance that is mid-way between planets Trappist d and Trappist e, which are expected to be most like Earth. Trappist d orbits the star with a period of 4.05 Earth days with an orbital radius .021 times the orbital radius of Earth around the sun. Trappist e orbits the star with a period of 6.1 Earth days with an orbital radius that is only .028 times the orbital radius of Earth around the sun. You are concerned that if the starship does not slow down to just the right velocity, it will either overshoot its target or crash into the star and the mission will fail.. If the starship is to enter a circular orbit, how fast must it be moving and in what direction when it reaches its target distance from the star? The orbital radius of Earth is 150 million kilometers.
Explanation / Answer
distance between the d and e = (0.028 - 0.021)*Au
= 0.007 AU
radius of orbit of starship, r = 0.021 + 0.007/2
= 0.00245 AU
=0.00245*1.5*10^11 m
= 3.675*10^8 m
we know, Orbital speed, vo = sqrt(2*G*Msun/r)
= sqrt(2*6.67*10^-11*1.99*10^30/(3.675*10^8))
= 8.50*10^5 m/s <<<<<<<----------------Answer
direction : tangent to the circular path
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