Question

Can you write out all formulas as well? Explain like I've never seen the problem before.

Two planets are orbiting a star in a distant galaxy. The first has a semi major axis of 150x10^6 km, an eccentricity of 0.20 and a period of 1.0 Earth years. The second has a semimajor axis of 250x10^6 km, an eccentricity of 0.30 and a period of:

Answer 1

solution Let the semi minor axis = b semi major axis = a = 150X106 km and eccentricity = e then b2= a² (1-e2) = (150x106)2(1-0.04) 1. = 1150x106) 2(0.96) = b = lsoxiob 10.96 km = 150 X 0.9797959x10 - 146, 97 x 106 km to the average radius of Planet = n. n = atb = 150+ 146.97X106 km = 148.4847X106 km Similarles for second planets 2' - (250x10612(1-0.99) OR b = 250 x0,95394 X 106 . 238.4848 X 106km to r2 = at = 244.2424X106 km How from Kepler's law - (Iyear)) ? = K 1148,4847X1065 () = (244, 2424x1067 2 T2 = 1244.2494 3 2 2 T2 = 14814847) 3/2 OR T = (1164489944082) = 2.10964 years' T 210964 Į Earth years.