Question

5. NASA decides to send a spacecraft to Neptune by the simple Hohmann transfer de- scribed in Example 8.6 of the text book. The spacecraft starts in a circular orbit near the Earth and must end up in a circular orbit near Neptune at 30 times greater dis- tance from the Sun. Using Kepler's 3rd law, show that the transfer will take about 31 years to complete. What thrust factor =V/v is required to start the spacecraft on its journey?

Answer 1

Ans: Given that. The space craft starts in a arcular hot orbit near the earth and must end up in a circular orbit near neptune Msk mass of sunt mst mass of spacerrart Distance betwem earth and sun Ri= I AU=1.50x10lm Distance of Neptune dem sun Rg = 30 AD = 30 X1,5X10" R3 = 45* 10lm Rs Ms path 2 is an ellipse semimator axis of that ellipse a= RitRg a 1+30 as a = 15.5 AO = 15.58 1.58101 = 23.25 810lm. now According to keplens 3rd law 47293 M where 1= Reelweed mass oo system u= Msms a ms Ms » ms and Y = GMsms Mstms Mstms a Ms Got unnarsal gravitational constant G = 6.874 x 1011 m3 Msf mass of sun = 1.989x1080 kg. 2 - T2 = 492a3ms & GK2 93 GM s ms GMs a X (3,14) 2x (23.25 8101113 (6.674 X 10-11) (1.984 x 1080) 1.92858 109 T2² = 3.71995 % 1018 T2 = 1.9285 X109 s T₂ = now lyear = 31,577600 S

T, = 1.9285 x 109 31,577,600 1 T2 = 61.08 time of transter years To = 22 = 30.504 ~ 31 years. The to Journey thrust factor required start the space crade on its 2 RB RITR3 2x 45 x 1011 ✓ 1.50x1011+458 lol! 11.93548 7 = 1.3912 to start its jourou The space coaft must boost its speed about 39% in dep tranfer orbit near to Neptune.