Question

Mass of earth: 5.972x10^24 kg Mass of Mangalyaan: 1,337.2 kg Radius of earth: 6,378 km Apogee:...

Mass of earth: 5.972x10^24 kg
Mass of Mangalyaan: 1,337.2 kg
Radius of earth: 6,378 km
Apogee: The point in the orbit of the moon or satellite at which it is furthest from the earth.

On Nov. 5th of 2013, a space probe known as Mangalyaan was launched and it reached its apogee of 23,500 km. Mangalyaan, then went through 7 different apogee raising maneuvers before its trans-mars injection on Nov. 30th, 2013. Before its final maneuver to trans-mars injection, the apogee was 192,874 km.

a.) Draw a free body diagram for forces acting on mangalyaan just after it reaches its first apogee.
b.) What is the equation of orbital velocity for Mangalyaan?
c.) Write down the equation that relates orbital velocity to the force of attraction between Mangalyaan and earth.
d.) Calculate the orbital speed (in m/s) of Mangalyaan at its first apogee and before its final maneuver.
e.) Calculated the period for both apogees.

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