Astronomy help SPACEFLIGHT A TRIP TO MARS AND BACK You are planning a round trip

Question

Astronomy help

SPACEFLIGHT A TRIP TO MARS AND BACK You are planning a round trip to Mars. Assume that Earth is in a circular orbit at 1.00AU from the Sun and Mars is in a circular orbit 1.52 AU from the Sun. Also assume that the orbits of Earth and Mars are coplanar. The orbit you plan to use for your trip is an ellipse with the Sun at one focus. The perihelion of the ellipse is at Earth's orbit at 1.00 AU and the aphelion is at Mars' orbit at 1.52 AU For this problem assume that the orbital period of Earth is 365 days and the orbital period of Mars is 684 days. a) Check that Kepler's Third Law holds for Earth and Mars. b) What is the semi-major axis a of the spacecraft's orbit? What is the eccentricity e of the spacecraft's orbit? What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take to get back? d) When (at what Earth Mars configuration) do you launch to go? In other words, where does Mars need to be relative to Earth in order for you to get to Mars successfully? e) Where is Earth when you arrive at Mars? f) Where does Earth need to be relative to Mars for you to return safely to Earth? g How long to you have to wait on Mars before you can launch for home? h) What is your total trip time? Care to go? i) If you miss your launch configuration in part (d) or part (f), how long do you have to wait for the next one?

Explanation / Answer

a)Kepler's third law holds good for both mars and earth. The square of orbital velocity of both is equal to the cube of gravity prevailing in the planet.

b)The semi major axis of the space craft should be greater than the radius of earth and mars. The eccentricity is given equal to the ratio of difference of the radii of earth and mars to the sum of radii of earth and mars.

Eccentricity=(6371-3390)/(6371+3390)=0.305

c)The orbital period of spacecraft would be in between the orbital period of earth and mars.From earth it would take nearly 225million km to travel to mars.

Similarly it has to travel the same distance to return back.

d)The spacecraft should be exactlt at the center of the earth so that it would reach mars at its edges.

e)From mars,when earth is viewed,it would appear to be smaller in size and it would act as if it would take more than 225million km to travel to earth.

f)On earth the place from.where the spacecraft was launched would.be correct if the satellite again lands there.

g)Nearly 684days we have to wait on mars before returning back as it is the orbital period.

h)Total trip time would be =684 days.

i)If we miss our launch configuration,we need to wait for another 684days=684+684=1368days.

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