A satellite is in a circular orbit around an unknown planet. The satellite has a

Question

A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 250km/s. The radius of the orbit is 4000km. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 7500km.

9. What is period of the first satellite

a. 96s

b. 134s

c. 233s

d. 239s

10. What is the period of the second satellite?

a. 96s

b. 342s

c. 180s

d. 244s

e. 450s

11. What is the speed of the second satellite?

a. 96km/s

b. 342km/s

c. 180km/s

d. 244km/s

e. 450km/s

12. What is the centripetal acceleration of the first satellite in m/s?

a. 1.2*104

b. 3.33*102

c. 1.6*105

d. 1.6*104

e. 3.33*106

13. If the second satellite has a mass of 3000kg, what must be the centripetal force?

a. 1.33*107 N

b. 1.35*104 N

c. 3.9*109 N

d. 6.2*108 N

Explanation / Answer

Given

two satellites are orbiting a planet of mass M

satellite 1

Vorbit V1 = 250 km/s , orbit radius R1 = 4000 km

satellite 2

Vorbit V2 = ? km/s , orbit radius R2 = 7500 km

we know that the orbital speed V = sqrt(G*M/R)

wehre G is universal gravitational constant G = 6.67*10^-11 Nm2/kg2 , M is mass of planet  

so the mass of the planet is M = V^2*R/G = 250000^2*4000000 /(6.67*10^-11) kg = 3.748126*10^27 kg

the relation for time period is  

V = 2pi*R/T

T = 2pi*R/V

T = 2pi*r/(sqrt*G*M/r) = 2pi sqrt(r^3/G*M)

9. Period of first satellite is  

T1 = 2pi*sqrt(R1^3/G*M)

T1 = 2pi*sqrt(4000000^3/(6.67*10^-11*3.748126*10^27)) s

T1 = 100.531 s

10. T2 = 2pi*sqrt(R2^3/G*M)

T2 = 2pi*sqrt(7500000^3/(6.67*10^-11*3.748126*10^27)) s

T2 = 258.108 s

11. speed of second satellite is V = sqrt(G*M/R2) = sqrt((6.67*10^-11*3.748126*10^27)/(7500000)) m/s

V = 182574.187368 m/s = 182.574187368 km/s = 180 km/s

12. centripetalacceleration of first satellite is a = G*M/R1^2

a1= (6.67*10^-11*3.748126*10^27)/(4000000)^2 m/s2

a1 = 15625.0002625 m/s2 = 1.6*10^4 m/s2

13. if m2 = 3000 kg then a2 =?

centripetalacceleration of first satellite is a2 = G*M/R2^2

a2= (6.67*10^-11*3.748126*10^27)/(7500000)^2 m/s2

a1 = 4444.44452 m/s2 = 4.444*10^4 m/s2

now centripetal force is F = m*a2 = 3000*4.444*10^4 N = 133320000 N = 1.33*10^8 N

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