Please show how you did the work, this question was long and confusing just tryi

Question

Please show how you did the work, this question was long and confusing just trying to understand how to do it. Thank you in advance.

(17%) Problem 2: A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v 105 x 104 m/s. The mass of the planet is M-6.06 x 1024 kg. The mass of the satellite is m = 4.7 × 103 kg > 10% Part (a) Enter an expression for the kinetic energy KE of the satellite in terms of m and v Grade Summary 0% 100% 7 89 HOME Submissions Attempts remaining: 7 (3% per attempt) detailed view END VO BACKSPACE DE CLEAR give up! Hints: 0% deduction per hint. Hints remaining:- Feedback: 0% deduction per feedback. i 10% Part (b) Calculate the value of KE in Joules. as 10% Part (c) Enter an expression for the magnitude of the gravitational force F in terms of M, R, m and the gravitational constant G 10% Part (d) Enter an expression for the centripetal acceleration of the satellite ac in terms of the speed of the satellite, v, and R 10% Part (e) Enter an expression for the radius R in terms of G, M and v 10% Part (f) Calculate the value of R in meters. 10% Part (g) Enter an expression for the gravitational potential energy PE in terms of G, M, m, and R 10% Part (h) Calculate the value of PE in Joules. à 10% Part (i) Enter an expression for the total energy E of the satellite in terms of mt and v -là 10% Part (j) Calculate the value of the total energy E in Joules.

Explanation / Answer

a)

KE of satellite = (0.5) m v2

b)

KE of satellite = (0.5) m v2 = (0.5) (4700) (10500)2 = 2.6 x 1011 J

c)

F = GMm/R2

d)

ac = v2/R

e)

orbital speed is given as

v = sqrt(GM/R)

R = GM/v2

f)

R = GM/v2 = (6.67 x 10-11) (6.06 x 1024) /(1.05 x 104)2 = 3.7 x 106 m

g)

PE = - GMm/R

h)

PE = - GMm/R = (6.67 x 10-11) (6.06 x 1024) (4700)/(3.7 x 106) = - 5.1 x 1011 J

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