The Solar System
The Solar System
9th Edition
ISBN: 9781305804562
Author: Seeds
Publisher: Cengage
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Chapter 4, Problem 8RQ
To determine

Is the sphere of Eudoxus is a scientific model.

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thanks. Moon is at the distance 384400 km from Earth and orbits the Earth every ∼28 days. If the radius of the Moon is 1737 km (consider it to be spherical), what is the area of the moon as measured by the observer on Earth? (Hint: Length contraction
The mass of Jupiter is 1/1047 of the Sun's mass (that's 0.000955). We want to confirm this using Newton's version of Kepler's Third Law, following the examples in Lecture 7. We'll use the approximate data for two different moons of Jupiter to see how close the results are. Pick the closest answer in each case: (a) Ganymede is the third moon from the inside. It has an orbital period around Jupiter of approximately 0.0194 Earth years. Its semimajor axis is 0.0071 AU. Which of these comes closest to the mass of Jupiter (in solar masses) when using these data?       (b) Europa is the second moon from the inside. It has an orbital period around Jupiter of approximately 0.0096 Earth years. Its semimajor axis is 0.0045 AU. Which of these comes closest to the mass of Jupiter (in solar masses) when using these data?
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)

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Kepler's Three Laws Explained; Author: PhysicsHigh;https://www.youtube.com/watch?v=kyR6EO_RMKE;License: Standard YouTube License, CC-BY