In March 2006, two small satellites were discovered orbiting Pluto, one at a distance of 48,000 km and the other at 64,000 km. Pluto already was known to have a large satellite, Charon, orbiting at 19,600 km with an orbital period of 6.39 days.

Required:
Assuming that the satellites do not affect each other, find the orbital periods T1 and T2 of the two small satellites without using the mass of Pluto.

Time period for first satellites 24.46 days and for second satellites 37.67 days

Explanation:

Given :

Distance of first satellites m

Distance of second satellites m

Distance of charon m

Time period of charon days

From the kepler's third law,

Square of the time period is proportional to the cube of the semi major axis.

For first satellites,

days

For second satellites,

days

Therefore, time period for first satellites = 24.46 days and for second satellites 37.67 days

grav potential energy

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y