PLEASE SHOW ALL WORK AND COMPLETE FULL QUESTION FOR THUMBS UP The International

Question

PLEASE SHOW ALL WORK AND COMPLETE FULL QUESTION FOR THUMBS UP

The International Space Station (ISS) stays in a circular orbit with radius 6.7×103 km from the center of the earth. (a) What is the period of ISS orbital motion? (b) What is the orbital speed of ISS? (c) If we can ignore the ground speed due to earth rotation, how much energy is minimally required to send 1 kg of cargo from the earth surface onto ISS?  (G = 6.67 × 10-11 N·m2/kg2 ; earth mass ME 6.0 × 1024 kg; earth radius RE 6.4 × 103 km).

Explanation / Answer

a) for circular motion,

gravitational force on ISS = mass of ISS x radial acc.

G Me m / (Re + h)^2 = m w^2 (Re + h)

Me - mass of earth

Re - radius of earth

(6.67 x 10^-11 x 5.972 x 10^24 ) / (6371000 + 6700000)^3 = w^2

w = 4.223 x 10^-4 rad/s

Time period. T = 2pi / w = 2pi / (4.223 x 10^-4)

T = 14877.17 sec

b) v= w . (Re + h)

v = (4.223 x 10^-4) (6371000 + 6700000)

v = 5520 m/s

c) Potential energy at the surface of earth = - G Me m / Re

            = - (6.67 x 10^-11 x 5.972 x 10^24 x 1 ) / (6371000)

      = - 62522743.78 J

Potential when it reaches at the surface of iSS
= - (6.67 x 10^-11 x 5.972 x 10^24 x 1 ) / (6371000 + 6700000)

      = - 30474516.1 J

Using enery conservation,

PE+ KE at surafce of earth = at ISS

- 62522743.78 + KE = - 30474516.1

KE =3.205 x 10^7 J ...Ans

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