Question

A spacecraft with mass 1500 kg is in a circular orbit at an altitude 200 km above the surface of Earth.

A) Use the Law of Universal Gravitation and Newton's 2nd law for circular motion to derive and find the speed of the spacecraft in this orbit.

B) How much mechanical energy does the spacecraft have in this orbit?

C) How much work must the spacecraft engines perform to get it into the above circular orbit from the surface of Earth? Ignore the effect of Earth's rotation about its axis.

Answer 1

Mass of Spacecraft Radins I$ 00K ciTular orbit of Spacecxaft, RE+2 00 Km =6400 +200)km Radius oearth, R 6400 Km = 6600km E Mabs eayth M:6 x1024 Newton's 2nd fox Cixcular moliom (A) Nom GMm be the Speed of Spacecraft in 4he bit Ahexe, GM ravitahional Con stant 24 x 6 X10 11 6.67 X1o 6600 x10 V7786.93 m The Sped ofSpace ca ft in bit So 7786.93 ms this

k.E. Spauecft, Km GMM 2 and Potential everg Spacaft, U GMM mechanical eneyg paccraft GMm 27 GMM GMM E : K tU 1-7 20 -V XIS00 J 2 x 6600 x10 10 1.S47 x to E - mechanical eherg So, Spacecraft s 1.547 x1010 muct Space ciat gines 0OYK done peufom G MM 2 R.+ 200 ( GMM 1-1 2 R

24 6.67x10 x6 X10 XIS00 N 6600x103 6400 x10 2 J (4.1942 X10 ) 17 -.0015 x 10 1.42 x lo J t done So, 142 x101 J
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