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MANIPAL UNIVERSITYII SEM MTech (A&SE) Examinations 2012

ASTRONAUTICS-II (ICE 504)

Time: 3 hrs. (16-05-2012) [Max. Marks: 100]

Answer any fivefull questions.

1(A) Obtain an expression for the radius of sphere of influence. (06)

(B) Define synodic period and derive an expression for the same. (06)

(C) On 6 February 2006, when the earth is 147.410 km from the sun, a spacecraft parked in a

200 km altitude circular earth orbit is to be launched directly into an elliptical orbit around

the sun with perihelion of 120106km and aphelion equal to the earthsdistance from the

sun on the launch date. Calculate the delta-v required and vof the departure hyperbola.

[sun=132,712,439,935.5 km3/s

2, earth=398600.4 km

3/s

2]

(08)

2(A) Derive expressions for the velocity, delta-v and true anomaly for an entry ellipse in the

deorbit (phase A) of re-entry.

(08)

(B) Discuss about blackout phase during re-entry. (04)

(C) A returning spacecraft enters the sphere of influence of earth with a VHEof 7200 km/hr on a

hyperbolic trajectory with a perigee altitude of 55.2 km within the planetary atmosphere.Assume that the velocity at perigee is reduced by 1800 km/hr on each pass through the

atmosphere.

(a)Find the eccentricity of the original entry hyperbola as well as the velocity at

perigee.

(b)Find the characteristics of the modified trajectory after the first pass to include a, ra,

ha, vaand the rpof the second pass.

(c)

What will the apoapsis altitude and eccentricity be after the second pass?

(08)

3(A) Derive Lagranges quantic equation for Euler configuration of three body problem. (08)

(B) Briefly explain about stability and dynamics at Eulerian points. (06)

(C) Explain Cowells method of numerical perturbation calculation. (06)

P.T.O.

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4(A) The orbit of a satellite around an unspecified planet has an inclination of 40 , and its

perigee advances at the rate of 70per day. At what rate does the node line regress?

(06)

(B) What are the criteria in choosing a numerical integration method? (06)

(C) For a spacecraft in the perifocal reference frame, the following orbital parameters are given:

e=1.5, perigee altitude=300 km, i=350, =130

0, =115

0.Calculate and at perigee in the

geocentric equatorial frame.

(08)

5(A) The geocentric equatorial position vectors of a satellite at three separate times are:

Use Gibbs method to find v2.

(15)

(B) Derive an expression for eccentricity using Lamberts method. (05)

6(A) Relative to a tracking station whose local sidereal time is 117 and latitude is +51 , the

azimuth and elevation angle of a satellite are 27.51560and 67.5556

0, respectively. Calculate

the topocentric right ascension and declination of the satellite.

(06)

(B) Derive Eulers equations of rotational motion. (08)

(C) Relative to an , , , frame of reference the components of angular momentum L are given

by:

(kg m2/s)

where, x, yand zare the components of the angular velocity . Find the components of

such that , where the magnitude of is 20 rad/s.

(06)