Question

please wrute clearly and explain your steps

8.5 continued) Geodesics for the Surface of a Sphere can integrate equation 8.42 quite easily to get sino = const. = f - - Rsine (8.43) a unitless but otherwise arbitrary constant (since R has units of s, includ- art of the constant of integration makes it clearer how the units work out). Substituting this into equation 8.41 yields de- cos sin c* cose Rsin'e = R sine (8.44) This differential equation would be very difficult to solve directly. In this case, using the definition of the pathlength (equation 8.16) really helps us with the integration. In this metric, the definition reads 1 = R(DL) + Rºsin’e de (8.45) Substituting dolds from equation 8.43 and solving for dolds yields de = + Rsinov sin°8 – 2 (8.46) Exercise 8.5.2. Verify that equation 8.46 is correct.

Answer 1

eqn 8.46 is correct if it obeys eqh (8:45) it means, if I used do = = Rino sinze me? in Ritlis of egn (8:45) and df = from 8.43 is the the Rsino result results should be l.fl. His! and solve R.His • His then then F Then, I have de = + I J tip de -c? Rsino alls and do = Roinho then Rittis of ego (8:45) * R24992+rsino leta = Relime Jumbres)in tine (and a (sinto -c²) R&rinke. c² R² sinho R² sine WA T = 1 ERAL = L.His - This, do is correcto