2016年IOAA理论第9题-火星环绕任务

英文题目

(T9) Mars Orbiter Mission 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 × 10⁵kg 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_a above the surface of the Earth, after this engine burn?

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