×
×

# In March 2006, two small satellites were discovered ISBN: 9780321675460 31

## Solution for problem 26E Chapter 13

University Physics | 13th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants University Physics | 13th Edition

4 5 1 381 Reviews
10
5
Problem 26E

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. Assuming that the satellites do not affect each other, find the orbital periods of the two small satellite? ithout? using the mass of Pluto.

Step-by-Step Solution:

Solution 26E Step 1 Gravitational force between pluto and charon = Centripetal force exerted by charon 2 2 That is, GMm/R = m R Where, R - Radius of charon orbiting around pluto M - mass of pluto m - Mass of charon - angular speed of charon 3 2 Or, GM/R = We know that, = 2 / T 3 2 2 That is, GM/R = 4 / T 2 2 3 Or, we can write, T = 4 R / GM 2 3 Since, G and M are constants for Pluto, we can write, T R Step 2 We can write, the square of the orbital period of Charon is directly proportional to the cube of the orbital radius of Charon around Pluto. 2 3 Or, T /R = a constant For the other satellite 1 having an orbital radius of 48000 km, the ratio, 2 3 T1R 1 = a constant 2 3 2 3 So, we can write, T /R = T /R 1 1 Provided, orbital radius of charon, R = 19600 km and orbital radius of satellite 1, R = 48000 km 1 2 3 3 2 3 3 Therefore, T /19600 km = T /48000 km 1 Provided, orbital period of charon is, T = 6.39 days Therefore, 6.39 days /19600 km = T /48000 km 3 2 3 3 1 Or, T 2 = (48000 km / 19600 km ) 6.39 days 3 2 2 1 T 2= 14.688 × 40.832 days 2 1 2 2 T1 = 600 days Taking square roots on both sides, T = 24.5 days 1

Step 3 of 3

##### ISBN: 9780321675460

This textbook survival guide was created for the textbook: University Physics, edition: 13. Since the solution to 26E from 13 chapter was answered, more than 820 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Pluto, satellite, satellites, Small, orbital. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. University Physics was written by and is associated to the ISBN: 9780321675460. The answer to “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. Assuming that the satellites do not affect each other, find the orbital periods of the two small satellite? ithout? using the mass of Pluto.” is broken down into a number of easy to follow steps, and 68 words. The full step-by-step solution to problem: 26E from chapter: 13 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

Unlock Textbook Solution