Question

Only solve part (d) please. The formula derived in part (b) is

1 Dimensional Analysis 34 1.4. The luminosity of certain giant and supergiant stars varies in a periodic manner. It is hypothesized that the period p depends upon the star's average radius r, its lllass ข, alul i.he nravii.aiional cousiałí. G. (a) Newton's law of gravitation asserts that the attractive force between two bodies is proportional to the product of their masses divided by the square of the distance between them, that is, Gm1m2 d2 where G is the gravitational constant. From this determine the (funda- mental) dimensions of G. (b) Use dimensional analysis to determine the functional dependence of p on m, r, and G (Arthur Eddington used the theory for thermodynamic heat engines to show that 2yGp where ρ is the average density of the star and γ is the ratio of specific heats for stellar material. How does this differ from your result? (d) In Figure 1.8 the data for a pulsating star are given. Explain how you could use data like this to complete the formula you derived in part (b) 14 12 0 oO 8 6 1998 2003 Time 2008 Figure 1.8 Luminosity of a Mira type variable star, 1621+19 U Herculis (AAVSO [2009]) VmG

Answer 1

that Magaiude (d) prom tg35 to 2003-toe-see- bas complefed& qucles and another in betoen oo3 to 8 hsthe period is cycles a ed mer in to ind oud o por tionality k 20 nct a the constant e 2 6 0 ass ot star 163 U Herculis