2. Determine the following orbital parameters associated with a spacecraft in va

Question

2. Determine the following orbital parameters associated with a spacecraft in various orbits around the sun:
a) Velocity of a spacecraft in circular orbit around the Sun at the mean radius of Jupiter measured from the Sun,
b) Minimum velocity change required to modify the trajectory of the spacecraft in Question 2a to an elliptical trajectory that has a perihelion (at the mean radius of Earth from the Sun (i.e., 1 AU),
c) Time required to transit from Jupiter to Earth along the trajectory in Question 2b,
d) Velocity change required at perihelion to circularize the orbit around the Sun at the mean radius of Earth.

Explanation / Answer

Answer a- velocity of spacecraft around the circular orbit around the sun at the Jupiter radius from the sun depends upon 2 things

1- the distance between the sun and Jupiter and is 2- the orbital period

the distance between the sun and Jupiter is 5.2 AU or 778,547,200km

the orbital period of Jupiter is around 4332 days or 103968 hours

so the orbital velocity of the spacecraft in Jupiter trajectory would be 778547200/103968 = 7488.3 km/h

B- now the spacecraft changes its trajectory from Jupiter to earth

at the perihelion condition, the distance between the earth and the sun is 146 million year

and the orbital period is 365.25days or 8770 hours

So now the orbital velocity would be 146,000,000/8770km/hour = 16667.6km/h

c- the time required for trajectory from change its path would be

t= d2-d1/v2-v1

=778-146/9179.3 = 68850.5 hours= 2678.75 days

d- the velocity change required at perihelion to circularize the orbit around the sun the mean orbit ofthe earth

the distance between earth and sun at circular orbit is 149,597,870km

the orbital period of the earth 365.25days or 8770 hours

the orbital velocity would be = 17057.9km/h

the change in velocity required at perihelion to circularize the orbit around the sun at the mean radius to the earth is = 390km/h

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