Question

1. In May of 2016, Pluto was 32.65 AU from the Earth. Pluto and its largest moon Charon orbit one another in 6.3872304 days; their angular separation in May was 0.8265”.

   1. a) [2] Calculate the actual distance between Charon and Pluto. (Answer: 1.95 x 10^7 m)

   2. b) [3] Determine the combined mass of Pluto and Charon, in kg. (Answer: 1.449 x 10^22 kg)

2. [5 marks] The barycentre (center of mass) of the Pluto-Charon system is 0.7405” from Charon.

   1. a) [2] Calculate the semi-major axis of both Charon’s and Pluto’s orbit around the barycentre.

   2. b) [3] Using your answer to question 1(b), determine the individual masses of Pluto and Charon, in kg. If you didn’t get a reliable answer, use 1.60 x 1022 kg.

Only need the answer for number 2 but it requires info from the previous question to complete.

Answer 1

If a is the distance between the centers of the two bodies (the semi-major axis of the system), r₁ is the semi-major axis of the primary's orbit around the barycenter, and r₂ = a − r₁ is the semi-major axis of the secondary's orbit.

The barycentre (center of mass) of the Pluto-Charon system is 0.7405” from Charon.

the distance between Charon and Pluto a=1.95 x 10^7 m

the combined mass of Pluto and Charon

m1+m2=1.449 x 10^22 kg