4 Mass of the Sun Kepler 3rd Law can be used to estimate the mass of the Sun M5 2 2_ 4.75 3 T_GMSr Where r represents the mean distance of the planet to the Sun. Go online (for example lg) to find the data for the distance r and orbital period T of each planet of the solar system. 26. Would the plot of Tvs r be linear? Calculate and make a plot of T2 vs r3. 27. What is the numerical value of the slope? (kg/Nmz) 28. What is the mass of the Sun? (kg) The expected value is M3 = 1.989 X 1030 kg. 29. Calculate the % error Planetary Fact Sheet - Metric MERCURY VENUS EARTH MOON MARS JUPITER SATURN URANUS NEPTUNE PLUTO Mass (1024kg) 0.330 4.87 5.97 0.073 0.642 1898 568 86.8 102 0.0130 Diameter (km) 4879 12,104 12,756 3475 6792 142,984 120,536 51,118 49,528 2376 Density (kg/m3) 5429 5243 5514 3340 3934 1326 687 1270 1638 1850 Gravity (m/s2) 3.7 8.9 9.8 1.6 3.7 23.1 9.0 8.7 11.0 0.7 Escape Velocity (km/s) 4.3 10.4 11.2 2.4 5.0 59.5 35.5 21.3 23.5 1.3 Rotation Period (hours) 1407.6 5832.5 23.9 655.7 24.6 9.9 10.7 -17.2 16.1 153.3 Length of Day (hours) 4222.6 2802.0 24.0 708.7 24.7 9.9 10.7 17.2 16.1 153.3 Distance from Sun (10% km) 57.9 108.2 149.6 0.384* 228.0 778.5 1432.0 2867.0 4515.0 5906.4 Perihelion (10% km) 46.0 107.5 147.1 0.363* 206.7 740.6 1357.6 2732.7 4471.1 4436.8 Aphelion (10% km) 69.8 108.9 152.1 0.406* 249.3 816.4 1506.5 3001.4 4558.9 7375.9 Orbital Period (days) 88.0 224.7 365.2 27.3* 687.0 4331 10,747 30,589 59,800 90,560 Orbital Velocity (km/s) 47.4 35.0 29.8 1.0* 24.1 13.1 9.7 6.8 5.4 4.7 Orbital Inclination (degrees) 7.0 3.4 0.0 51 1.8 1.3 2.5 .8 18 17.2 Orbital Eccentricity. 0.206 0.007 0.017 0.055 0.094 0.049 0.052 0.047 0.010 0.244 Obliquity to Orbit (degrees) 0.034 177.4 23.4 6.7 25.2 3.1 26.7 97.8 28.3 122.5 Mean Temperature (C) 167 464 15 -20 -65 -110 140 -195 200 -225 Surface Pressure (bars) 0 92 0 0.01 Unknown* Unknown* Unknown* Unknown* 0.00001 Number of Moons 0 0 1 0 2 79 32 27 14 5 Ring System? No No No No No Yes Yes Yes Yes No Global Magnetic Field? Yes No Yes No No Yes Yes Yes Yes Unknown MERCURY VENUS EARTH MOON MARS JUPITER SATURN URANUS NEPTUNE PLUTO