4. (15 pts) You have to plan a mission from Earth to Venus in following question

Question

4. (15 pts) You have to plan a mission from Earth to Venus in following questions assuming that their orbits around the Sun are co-planar. There are total 6 parts in Q. 4, 5, 6. Use following data: a) Launch site coordinates: 2831' N, 80°39' w, b) Earth radius: 6,371 km; c) Venus radius: 6,051.8 km; d) Earth orbit radius: 149,600,000 km; e) Venus orbit radius: 108,208,000 km; f) Sun gravitational parameter: 132,712,440,000 km3/s'; g) Earth orbital period: 365.256378 day; and h) Venus orbital period: 224.7 day. (a) What is the condition on the parking orbit to begin the mission? (b) Compute the 's to escape the Earth sphere of influence from a 500 km orbit and to orbit around Venus with optimal capture. 5. (20 pts)

Explanation / Answer

a) the parking orbit is same as the inclination site.Since every point on earth between tropics crosses the plane of ecliptic twice a day, can we use that fact.If we time the lauch can we get directly in the plane of ecliptic.and hence the parking orbit should be 28'31.

b)To get out of the earth the veolcity required is 42.1km/s, earth is moving at a speed of 29.78km/s. so 42.1-29.78 = 12.32 km/s.

v=29.78 km/s or 12.32 km/s=(2(v2/2GM/r))1/2

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