Universe
Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 12, Problem 50Q
To determine

The mass of Jupiter by using the orbital data for Jovian satellite of any choice (see Appendix 3). Also, explain the manner in which this answer is compared with the mass quoted in Table 12-1.

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The value we have just calculated is the combined masses of Jupiter and Callisto!  Their mass is in units of the Sun's Mass (MS) - we can convert this to units which are more familiar to us like kilograms by multiplying this answer by the scale factor (1.99x1030 kg/1 MS):  (MJupiter + MCallisto)   =   (               MS) (1.99x1030 kg/1 Solar Mass)  =   _______x_10___ kg (I have already written the x 10 so you are reminded to write the exponenet of 10 in the scientific notation expression of your answer).  Since you know from looking at pictures of Jupiter with its Galilean Satellites (look in your book at a picture if you have not already), that Callisto is much smaller than Jupiter - in fact it is less than 0.001 of Jupiter's size or mass, so the number we have just calculated for (MJupiter + MCallisto) is almost the same as MJupiter .  How much more massive is Jupiter than the Earth? (The mass of Earth is about 5.98 x 1024 kg)
I would like you to compare the size of some of the largest moons of the solar system to their host planets. Using diameters of 12,700 km, and 140,000 km, 116,000 km for Earth, Jupiter, and Saturn respectively, please provide the ratios of the following moons to their host planets (you can use Table 12.1 from the book to get the diameters of the moons): Luna (Earth's moon), Io, Callisto, Ganymede, Europa, and Titan. After collecting those ratios, please tell me one thing that you notice that stands out about those results.
Calculate the gravitational field strength on a planet with a diameter of 15487.3 km and the escape velocity of 11 km s-1. Give your answer in SI units.
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