Question

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.

Answer #1

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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...

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 a 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,...

Assumptions for following two problems: 1) Space is almost vacuum,
so almost no air. 2) Orbits are circular instead of
elliptical.
You might find following information useful. Mass of Earth: 5.972 ×
1024 kg Mass of Mangalyaan: 1,337.2 kg Radius of earth: 6,378 km
Apogee: the point in the orbit of the moon or a satellite at which
it is furthest from the earth.
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