Question

Suppose NASA wants to repair a malfunctioning spacecraft from a circular orbit at 1,050 km altitude at the ISS located at 400 km altitude orbit. The Hohmann Transfer technique is used to bring the spacecraft from the higher orbit down to the lower orbit. What is the spacecraft velocity along the transfer elliptical orbit at 600 km altitude location?

	7.1559 km/s
	B.	7.3254 km/s
	C.	7.4125 km/s
	D.	7.6686 km/s

Answer 1

Answer :-

Given data :-

Distance of malfunctioning space craft = 1050 km

Distance from center R = 6371 +1050 = 7421 km

Distance of ISS = 400 km

Distance from center r = 6771 km.

To reach at malfunctioning space craft,

The velocity of escape the orbit =    

where = GM = 3.99 × 10¹⁴ m³/s²

putting the values and calculating we get

   

u = 5372.24 ÷√1000 (for taking in meter) = 169.88 m/s

similarly velocity to enter the orbit

putting the values

v = 5496.8 ÷√1000 = 173.82 m/s

So, Taking increase in velocity gradually,

Speed at 400 km = 169.88 m/s

Speed at 1050 km = 173.82 m/s

So speed at 600 km =

169.88 +

So speed at 600 km = 171.09 m/s