The gravitational force between Pluto and Charon is 3 point 6 1 times 10 to the 18th power cap n Pluto has a mass of 1 point 3 times 10 to the 22th power kilograms , which is only slightly greater than Charon’s mass of 1 point 6 times 10 to the 21th power kilograms How far apart are Pluto and Charon?
Answer
A
2 point 4 times 10 to the 12th power m
B
5 point 8 times 10 to the 24th power m
C
2 point 0 times 10 to the 7th power m
D
3 point 8 times 10 to the 14th power m
Explanation
Use Newton’s law of gravitation, F = Gm₁m₂/r², and solve for distance: r = √(Gm₁m₂/F). Substituting the values gives r = √[(6.67 × 10⁻¹¹)(1.3 × 10²²)(1.6 × 10²¹)/(3.61 × 10¹⁸)] ≈ 2.0 × 10⁷ m. Therefore, Pluto and Charon are about 2.0 × 10⁷ meters apart, which is choice C.
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