IOAA 2016, theory — Задача 9. Mars Orbiter Mission

Theoretical Examination · 20 т.

Условие

India's Mars Orbiter Mission (MOM) was launched using the Polar Satellite Launch Vehicle (PSLV) on 5 November 2013. The dry mass of MOM (body + instruments) was 500 kg and it carried fuel of mass 852 kg. It was initially placed in an elliptical orbit around the Earth with perigee at a height of 264.1 km and apogee at a height of 23903.6 km, above the surface of the Earth. After raising the orbit six times, MOM was transferred to a trans-Mars injection orbit (Hohmann orbit).

The first such orbit-raising was performed by firing the engines for a very short time near the perigee. The engines were fired to change the orbit without changing the plane of the orbit and without changing its perigee. This gave a net impulse of $1.73 \times 10^{5}\ \mathrm{kg\ m\ s^{-1}}$ to the satellite. Ignore the change in mass due to burning of fuel.

T9.1 What is the height of the new apogee, $h_{\mathrm{a}}$ above the surface of the Earth, after this engine burn? [14 т.]

T9.2 Find the eccentricity ($e$) of the new orbit after the burn and the new orbital period ($P$) of MOM in hours. [6 т.]

Решение

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Оригинал в Архива: theory-qp.pdf · официални решения: theory_sol.pdf