Question

(a) Explain the relationship between the universal gravitational constant G and the acceleration due to gravity at the earth's surface g. Therefore, calculate g from G using the relationships given below. Justify the choice of units for G (Nm kg?). F= mg The mass of the earth is 5.98 x 1024 kg, it's radius is Tg = 6.38 x 10 m, and G = 6.67 x 10-11 Nm?kg (10 marks) (b) Explain, including performing the integral, how the work done to lift an object up from the earth's surface to an altitude h can be calculated using: GMm (5 marks) (c) By equating the force due to gravity given in part (b) to a centripetal force, it is possible to obtain an expression for the speed v of a planet executing a circular orbit at radius r around the sun, of mass M:

Answer 1

Date: Page Ans.(a) by Newton's and Law E-mg - by grautational force formula F= Gmm - © put equation (17= equation (2) Big = Gora I= Gm7 m-kg. r m2 This shows Relationship between og and G. g = m/s2 sueen of and & m G= m/s.ma kg. multiply and deride by kg O G = Kg. m/s.m • kg ml² = Newton 6- Nima i Kga F- Grm s3 s is Radius of earth Totel height karth his attitude

APCU - Date : Page: As we know work done is W =- Fode here o to R Gnm ds W =- Fior -- W-. Gmm r W-– Gmm R (7 by gravitational force f-Gom 82 • centabetal force F=mra compare (19 = (2) By – Grm 824 V? Gm