3. Such a solar system must have formed in a way, which differs from formation of our solar system, at least in detail. The basic model for the formation of our solar system (contraction of a revolving gas cloud) leads directly to a flat disk structure, with all planetary orbits moving in the same direction. It is difficult to produce planetary orbits with a wide range of inclinations and directions using this process, unless the planetary orbits started too close to one another, and thus gravitational interactions between different planets were important early on. The angular momentum problem in theories of solar system formation would be more acute in such a strange solar system.
10. a) From the text, Jupiter reflects 3 x 10-10 of the Sun light. At a distance of the Earth from the Sun, the planet would intercept 52 = 25 times as much as light as it does at its distance from the Sun. A planet 10 times diameter of Jupiter would also reflect 102 = 100 times as much as light as Jupiter, so a planet 10 times the size of Jupiter in Earth's orbit would reflect
25 x 100 = 2500 times as much light as Jupiter, or
2500 x 3 x 10-10 = 7.5 x 10-7 the light of Sun.
If the eclipse were complete, then the ratio of area of the planet and Sun would be 10-2 that for Jupiter and Sun, which is about 1%. Therefore, the eclipse would be essentially complete in this case. The angular separation at a distance of 10.000 AU would be
206,265/10,000 = 20.63 seconds of arc
(as distance of Earth is 1 AU)
b) Again from the text, the Earth reflects 7.5 x 10-11 the light of Sun, Mercury is about 2.6 closer to the Sun than the Earth, so the Earth would reflect (2.6)2 = 6.7 times as much sunlight, or 5 x 10-10 the light of the Sun.
The ratio of areas for the Earth and Sun is given by
(12,756/ 1,391,400)2 = 0.008%
so the eclipse would dim the Sun by much less than 1%.
The angular separation would be
(0.387)(206,265)/(10,000) = 8 arcseconds
So wavelength = (300,000 km/sec)/ 1.2 x 108= 0.0025 km = 2.5 m
b) now frequency from the same formula be
frequency = speed of light / wavelength
= 3 x 1017 cycles / second
8. The mass of Sun is approximately 2 x 1030kg, while the total mass of planets is approx 2.7 x 1027kg, so the Sun is about
2 x 1030kg/2.7 x 1027 = 750 times as massive as all the planets.
The Earth is composed of different mix of elements than the Sun because only those materials that condense at relative high temperature were able to avoid being evaporated and swept out of the inner solar system by the intense heat of the Sun, and thus be incorporated into the Earth. Since most of the mass in the solar system resides in Sun, the most abundant elements in the solar system are most abundant elements making up the Sun, Hydrogen, followed by Helium