Newton had the data listed in Table 6–4, plus the relative sizes of these objects: in terms of the Sun’s radius R , the radii of Jupiter and Earth were 0.0997 R and 0.0109 R . Newton used this information to determine that the average density ρ (= mass/volume) of Jupiter is slightly less than of the Sun, while the average density of the Earth is four times that of the Sun. Thus, without leaving his home planet. Newton was able to predict that the composition of the Sun and Jupiter is markedly different than that of Earth. Reproduce Newton’s calculation and find his values for the ratios ρ J / ρ Sun and ρ E / ρ Sun (the modern values for these ratios are 0.93 and 3.91, respectively).
Newton had the data listed in Table 6–4, plus the relative sizes of these objects: in terms of the Sun’s radius R , the radii of Jupiter and Earth were 0.0997 R and 0.0109 R . Newton used this information to determine that the average density ρ (= mass/volume) of Jupiter is slightly less than of the Sun, while the average density of the Earth is four times that of the Sun. Thus, without leaving his home planet. Newton was able to predict that the composition of the Sun and Jupiter is markedly different than that of Earth. Reproduce Newton’s calculation and find his values for the ratios ρ J / ρ Sun and ρ E / ρ Sun (the modern values for these ratios are 0.93 and 3.91, respectively).
Newton had the data listed in Table 6–4, plus the relative sizes of these objects: in terms of the Sun’s radius R, the radii of Jupiter and Earth were 0.0997 R and 0.0109 R. Newton used this information to determine that the average density ρ(= mass/volume) of Jupiter is slightly less than of the Sun, while the average density of the Earth is four times that of the Sun. Thus, without leaving his home planet. Newton was able to predict that the composition of the Sun and Jupiter is markedly different than that of Earth. Reproduce Newton’s calculation and find his values for the ratios ρJ/ρSun and ρE/ρSun (the modern values for these ratios are 0.93 and 3.91, respectively).
The mean diameters of Mars and Earth are 6.9 * 103 km and 1.3 * 104 km, respectively. The mass of Mars is 0.11 times Earth’s mass. (a) What is the ratio of the mean density (mass per unit volume) of Mars to that of Earth? (b)What is the value of the gravitational acceleration on Mars? (c) What is the escape speed on Mars?
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 • 1011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0 • 104 light years from its center.
a) What should the orbital period of that star be in years?
b) If its period is 6.0 • 107 years instead, what is the mass of the galaxy in solar masses? Such calculations are used to imply the existence of “dark matter” in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
The mean diameters of X and Y, two planets in the same solar system, are 6.5 x 10³ km and 1.2 x 104 km, respectively. The mass of x is 0.21 times the mass of Y. The value of g on Y is 8.1 m/s².
(a) What is the ratio of the mean density of X to that of Y (Px / Py)?
(b) What is the value of g on X?
m/s²
(c) The mass of Y is 4.372 x 1024 kg. What is the escape speed on X?
m/s
Chapter 6 Solutions
Physics for Scientists and Engineers with Modern Physics
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