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The Sun and Planets Class Exercise 1. Exercise 1. Spring Semester 2017 Prof Dr Ravit Helled The view from Earth The Solar System is a planetary system with one star (the Sun) and eight planets.1 The four planets nearest to the Sun are rocky planets. We call these these the terrestrial planets. In order of increasing distance from the Sun, these are: Mercury, Venus, Earth, and Mars. The remaining outer four planets are the gas giants. Continuing outwards from Mars, they are Jupiter, Saturn, Uranus, and Neptune. In this exercise we will gain a more intuitive understanding of sizes and distances in the Solar System. To achieve this, we begin by converting the typical units of measurement to a scale better suited to astronomical distances and sizes. We do this by normalizing the SI units (e.g., meters, kilograms) into Earth masses and Earth radii (i.e., 1 distance unit ≡ 1 Earth radii and 1 mass unit ≡ 1 Earth mass). Use this new system of units to complete the following table: Table 1. — Fill in the missing values Object Radius (km) Radius (R⊕ ) Earth 6’378.14 1.0 Moon 1’737.5 Mercury 2’439.7 Venus 6’051.8 Mars 3’389.5 Jupiter 69’911 Saturn 58’232 Uranus 25’362 Neptune 24’622 Sun 695’700 † Ganymede 2’634.1 Mass (1024 kg) 5.97219 0.07346 0.330104 4.86732 0.641693 1’898.13∗ 568.319∗ 86.8103 102.410 1’989’000∗ 0.14819 Mass (M⊕ ) 1.0 † Ganymede is the largest and most massive moon of Jupiter ∗ Corrected masses for Jupiter, Saturn, and the Sun Exercise 2. “To infinity... and beyond!” In astronomy and physics, we can measure distances by the time that it takes light to travel between two points. We can do this because the speed of light is finite and we have measured its value to great accuracy. The most common unit in this distance scale is the lightyear (sometimes abbreviated as “ly”), which is just short of 9 trillion kilometers (1 ly = 9.461 × 1012 km). As defined by the International Astronomical Union (IAU), a lightyear is the distance that light travels in vacuum in one Julian year (365.25 days). 1 Sorry, Pluto. 1 For instance, the distance between Earth and the Sun is 149.6 billion meters. The speed of light is c = 3 × 108 m/s. tlight = 149.6 × 109 m = 498.7 s 3 × 108 m/s (1) Therefore it takes 8 minutes and 19 seconds for sunlight to reach the Earth. We will now use this distance scale to understand some distances in the Solar System. In the following table calculate the time it takes light to travel between (or traverse) the object(s): Table 2. — Light Travel Time Scale Distance (m) Sun–Earth 1.47 × 1011 Sun diameter 1.39 × 109 Earth diameter 1.27 × 107 Earth–Moon 3.69 × 108 Sun–Mars 2.17 × 1011 Sun–Jupiter 7.79 × 1011 Sun–Pluto 5.91 × 1012 Nearest star (Prox. Cen.) 4.02 × 1016 Milky Way diameter† 9.50 × 1020 Milky Way–Andromeda† 2.37 × 1022 Milky Way–GN-z11† 1.27 × 1023 light travel time 8m19s † Ignore all cosmological effects (e.g., expansion, general relativity, etc.). Exercise 3. The Scale of Systems The satellite (i.e., moon) systems of giant planets are often referred to as “miniature solar systems”. In this exercise we will make a few calculations to test whether or not this comparison makes sense. Calculate the ratio of the mass of the Sun to the total mass of the planets. Compare it to the ratio of the mass of Jupiter to the mass of its satellites. Use whichever mass units you are most comfortable with. Table 3. — Ratios Central Body Planets/Satellites Sun planets Jupiter Jovian moons Mass Ratio Note that you can neglect the masses of the terrestrial planets because they are very small compared to the mass of the gas giants. How similar are these two ratios? What does this mean for the comparison above? 2