how far from the Sun is Venus?
(R3/T2)earth = (R3/T2)venus (1.003/3652)earth = (R3/2252)venus Now cross-multiply and you get, R3 = 50625/133225 R3 = 0.38 R = 0.79 AU, or 67.4 million miles Example 2: OK. This is a little tougher than just setting up a ratio. And since many of you have questions on this, let’s try a little example. (I’ll let you work out the math). Our galaxy (Milky Way) has an estimated mass of 4 x 1041 kg. The earth is located at a distance of 2.84 x 1020 m. Can we determine the time it takes for the Sun to orbit the center of the Galaxy? Well, yeh, but Kepler won’t help us much here. Newton, however, will: Since the gravitational attraction of the Galaxy MUST supply the centripetal force holding the Sun in place, we can equate these two forces: Centripetal force: F = msunv2/r Gravitational force: F = GMgalaxymsun/r2 Let’s equate them: msunv2/r = GMgalaxymsun/r2 v2/r = GMgalaxy/r2 But we need to input the Period, T. We can do this by noticing that, v = 2pr/T Now, substituting this in for v, we get
