Chapter 13, Problem 031 The mean diameters of planets A and B are 7.4 × 10 3 km
ID: 1563078 • Letter: C
Question
Chapter 13, Problem 031
The mean diameters of planets A and B are 7.4 × 103 km and 2.5 × 104 km, respectively. The ratio of the mass of planet A to that of planet B is 0.74. (a) What is the ratio of the mean density of A to that of B? (b) What is the ratio of the gravitational acceleration on A to that on B? (c) What is the ratio of escape speed on A to that on B?
Chapter 13, Problem 031
The mean diameters of planets A and B are 7.4 × 103 km and 2.5 × 104 km, respectively. The ratio of the mass of planet A to that of planet B is 0.74. (a) What is the ratio of the mean density of A to that of B? (b) What is the ratio of the gravitational acceleration on A to that on B? (c) What is the ratio of escape speed on A to that on B?
Chapter 13, Problem 031 The mean diameters of planets A and Bare 7.4 x 103 km and 2.5 x 104 km, respectively. The ratio of the mass of planet A to that of planet Bis 0.74 (a) What is the ratio of the mean density of A to that of B? b) What is the ratio of the gravitational acceleration on A to that on B (c) What is the ratio of escape speed on A to that on B? (a) Number Units (b) Number Units (c) Number Units Click if you would like to Show Work for this question: Open Show WorkExplanation / Answer
(a) We know that the density is given by = Mass/volume
volume = (4/3)Pi*R3
Density for planet A (pA) = MA /((4/3)*Pi*RA3)
Density for planet B (pB) = MB /((4/3)*Pi*RB3)
pA/pB = (MA /MB)*(RB/RA)3 = 0.74*(2.5*104/7.4*103)3 = 28.534
(b) We know that gravitational acceleration is given by = GM/R2
therefore
gA/gB = (MA/MB)(RB /RA)2 = 0.74*(25/7.4)2 = 8.446
(c) We know that escape velocity is given by
= (GM/r)1/2
VA /VB = ((MA/MB)(RB /RA))1/2 = 1.5811
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