# ESA 380/3 Orbital Mechanics Mekanik Orbit

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1 -1- UNIVERSITI SAINS MALAYSIA First Semester Examination Academic Session 2010/2011 November 2010 ESA 380/3 Orbital Mechanics Mekanik Orbit Duration : 3 hours Masa : 3 jam INSTRUCTIONS TO CANDIDATE: ARAHAN KEPADA CALON : Please check that this paper contains EIGHT (8) printed pages, ONE (1) page appendix and SIX(6) questions before you begin the examination. Sila pastikan bahawa kertas soalan ini mengandungi LAPAN(8) mukasurat bercetak, SATU (1) mukasurat lampiran dan ENAM (6) soalan sebelum anda memulakan peperiksaan. Answer FIVE (5) questions. Jawab LIMA (5) soalan. Answer all questions in English OR Bahasa Malaysia OR a combination of both. Calon boleh menjawab semua soalan dalam Bahasa Malaysia ATAU Bahasa Inggeris ATAU kombinasi kedua-duanya. Answer to each question must begin from a new page. Jawapan untuk setiap soalan mestilah dimulakan pada mukasurat yang baru. In the event of any discrepancies, the English version shall be used. Sekiranya terdapat sebarang percanggahan pada soalan peperiksaan, versi Bahasa Inggeris hendaklah diguna pakai. 1. Appendix A1/Lampiran A1: [1 page/mukasurat] 2/-

2 -2-1. Figure 1: Displacement of a rigid body Rajah 1: Pengalihan objek tegar (a) From the figure 1 define the equation below. Daripada Rajah 1, takrifkan persamaan di bawah. A A sinφ (30 marks/markah) An earth satellite is in an orbit with perigee altitude 400 and apogee altitude at Find Sebuah satelit di orbit Bumi dengan ketinggian perigee adalah 400 dan ketinggian apogee adalah Cari (i) The eccentricity Keeksentrikan (ii) Angular momentum Momentum sudut 3/-

3 -3- (iii) Orbital speeds at perigee and apogee Kelajuan orbit pada perigee dan apogee (iv) The period Tempoh (40 marks/markah) (c) Draw the location of the equilibrium points that also known as Lagrangian Points for Earth-Sun system. If a spacecraft with sun monitoring mission is planned to be launched, which point of Lagrangian Point is suitable for this mission? Explain. Lukiskan lokasi titik keseimbangan yang juga dikenali sebagai titik Lagrange untuk sistem bumi - matahari. Jika sebuah kapal angkasa yang mempunyai misi untuk memerhati matahari bakal dilancarkan, titik Lagrange manakah yang bersesuai untuk misi ini? Terangkan. (30 marks/markah) 4/-

4 -4-2. (a) Illustrate all of the orbital elements in three dimensions. Lukiskan elemen-elemen orbit dalam tiga dimensi. (30 marks/markah) Find the orbital elements of a geocentric satellite whose inertial position and velocity vectors in a geocentric equatorial frame are Cari elemen-elemen orbit satelit geopusat yang mana kedudukan awal dan vektor halajunya berada dalam bingkai geopusat khatulistiwa seperti berikut / / (70 marks/markah) 5/-

5 -5-3. The geocentric equatorial position vectors of a satellite at three separate times are Vektor keadaan geopusat khatulistiwa sebuah satelit pada tiga masa berbeza adalah (a) Find Cari (50 marks/markah) Find the orbital elements. Cari elemen-elemen orbit. (50 marks/markah) 6/-

6 -6-4. (a) Calculate the local sidereal time (in degrees) at Vladivostok, Russia (east longitude ) at 8:00 UT on 21st March Kira masa hari ikut bintang tempatan (dalam darjah) bagi Vladivostok, Russia (longitud ke timur ) 8:00 UT pada 21 Mac (50 marks/markah) Define all forces that can cause orbit perturbation. Nyatakan kesemua daya yang boleh menyebabkan gangguan orbit. (40 marks/markah) (c) A small remote sensing satellite is operated at LEO orbit. Discuss the perturbation forces that this satellite is exposed to and define the orbital parameter that affected towards these forces. Sebuah satelit penderiaan jauh beroperasi pada orbit LEO. Bincangkan daya gangguan yang dialami oleh satelit ini dan nyatakan elemen orbit yang terganggu akibat daya-daya tersebut. (10 marks/markah) 7/-

7 -7-5. A spacecraft is in a 300 km circular earth orbit. Calculate Sebuah kapal angkasa berada pada orbit bulat 300 km. Kira (a) The total required for a Hohmann transfer to a 3000 km altitude coplanar circular earth orbit, see Figure 2. Jumlah yang diperlukan untuk perpindahan Hohmann ke altitud 3000 km orbit bulat Bumi sesatah, lihat Rajah 2. (70 marks/markah) The total transfer time. Jumlah masa perpindahan. (30 marks/markah) Figure 2/ Rajah 2 8/-

8 -8-6. (a) Find the total ΔV required for a Hohmann transfer from Mars orbit to Jupiter s orbit. Refer Figure 3. Cari jumlah ΔV yang diperlukan untuk perpindahan Hohmann dari orbit Marikh ke orbit Musytari. Rujuk Rajah 3. (40 marks/markah) Figure 3/Rajah 3 Estimate the total ΔV requirement for a Hohmann transfer from earth to Mercury, assuming a 150 km circular parking orbit at earth and a 150 km circular capture orbit at Mercury. Furthermore, assume that the planets have coplanar circular orbits with radii equal to the semi major axes listed in Table A1. (see appendix). Anggarkan jumlah ΔV yang diperlukan untuk perpindahan Hohmann dari Bumi ke Utarid, dengan anggapan orbit letak bulat Bumi ialah 150 km dan orbit tangkap bulat Utarid ialah 150 km. Tambahan lagi, anggap bahawa semua planet mempunyai orbit bulat koplanar dengan jejari sama dengan paksi semimajor yang diberi dalam Jadual A1(lihat lampiran). (60 marks/markah) -oooooooo- 9/-

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