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**Q1:**MATINS BETERE 1) If an object is in Earth's orbit (a=1.000 A.U., e=0.0167) and suddenly increases its energy by 10 per cent without increasing its angular momentum [perhaps it fires a rocket engine towards the Sun, accelerating it directly outwards]: what is the final semi-major axis and eccentricity of the object's orbit? Note: E<0. Therefore increasing E by 10% means less negative or 90% of the original value. (Marks: 4) 2) The Earth was last at perihelion on January 3, 2022. The period of the Earth's orbit is 365.25 days. (a) If the Earth's orbit was a perfect circle when (give the actual calendar date in your answer!) would it reach a True Anomaly (angle with respect to perihelion) of 160 degrees? (b) But given that the Earth's orbit is slightly elliptical (e-0.0167), when (calendar date) will the Earth actually be at True Anomaly of 160 degrees? (c) How far will the Earth be from the Sun at that time? (d) How fast will the Earth be moving in its orbit on that day? (e) (for comparison to (c) and (d)) what is the distance (from the Sun) and speed of the Earth when it is at perihelion? (Marks 10) 3) How bright will Pluto appear in reflected or scattered sun-light (total Flux received in W/m²) at the Earth when Pluto is at Opposition and a distance from the Sun of 40.0 A.U.? Assume that Pluto has an albedo of 0.60 and a radius of 1.2 x 10³ km. (Marks: 6) DELLSee Answer**Q2:**The University of Queensland, School of Mechanical and Mining Engineering MECH2210 Dynamics and Orbital Mechanics Section B1- Tutorial Problems 2022 Assignment B1, Submit: 0.3 & 17 due Mon wk 11 Online Dynamics Revision Quiz The following problems cover orbital mechanics material - please attempt all: Module/Question - 1/7, 2/12, 2/21, 3/5-12, 4/5, 6/3. (Answers online) F ᏛᎾ . B m Problem 1 Explorer No.1 launched in January 1958 had perigee and apogee heights above the Earth's surface of 360 km and 2550 km and an inclination of 33.2°. Calculate the: a) orbit period, b) its eccentricity, c) the total energy (per unit mass of the orbit) d) the angular momentum (per unit mass of the orbit), e) the maximum and minimum speeds and orbit positions f) the minimum impulse to change the inclination to 0° assuming the satellite passes the equator at its perigee, g) the minimum impulse Av required to escape Earth. (Answers: 1.92hr,0.14, -25.4 MJ/kg, 5.53x1010 m²/s, 8.2p & 6.2a km/s, 3.54 km/s, 2.67 km/s) Problem 2 An earth satellite is tracked from ground stations and is observed to have an altitude of 2200 km, a velocity magnitude 7 km/s and a radial velocity of 2.7 km/s. Determine: a) the total orbital energy per unit mass b) the orbital eccentricity e c) the minimum altitude and the maximum speed and d) the true anomalies at the observed position and at the point of maximum speed. e) Identify any potential difficulties with the orbit. (Answers: -22 MJ/kg, 0.389, -835km & 10 km/s, 105.3deg & 0 deg, crash into Earth) Problem 3 An early warning defence system detects an UFO travelling at 800km above earth's surface with a horizontal (perpendicular) speed of 8 km/s and a vertical (radial) speed of 1.3 km/s. Determine: a) the total energy (per unit mass of the orbit) b) the angular momentum (per unit mass of the orbit), c) the eccentricity of the orbit e d) the minimum and maximum radii of the orbit e) the true anomaly 9 at the point of observation. f) whether the UFO is possibly a missile, Earth satellite or comet and explain your answer. g) the minimum measured speed v of the UFO for it to be a comet and explain why. (Tot. 21 mks = 3 x 7) Problem 4See Answer**Q3:**For the following line elements and vector V", write down the metric, the inverse metric, and See Answer**Q4:**Consider a metric in a D-dimensional space. Evaluate the following expressions.See Answer**Q5:**Consider the line element of the sphere of radius a: The only non-vanishing Christoffel symbols are (a) write down the metric and the inverse metric, and use the definitionSee Answer**Q6:**Please explain to the class the questions below: Are these statements True or False? Justify your answer for one of them. 1. The neap tides occur at the new moon and full moon. 2. Spring tides occur during the new and full lunar phases. 3. Special relativity states the relationship between energy and mass as E = m0c2. 4. There is no gravity in space. 5. Newton's first law of motion is essentially a restatement of Galileo's law of inertia.See Answer**Q7:**1)All the planets in the Solar System revolve in a clockwise motion.See Answer**Q8:**2)The inner planets are composed of rock and metal, and the outer planets are rich in low-density gases such as hydrogen and helium.See Answer**Q9:**3)Terrestrial planets grew slowly and the Jovian planets grew quickly.See Answer**Q10:**4)There are nearly 4000 known extrasolar planets.See Answer**Q11:**5)The Terrestrial planets do not have rings. Why T or F?See Answer**Q12:**33 A satellite is orbiting at a distance of 4.2 x 106 m from the surface of the Earth. The radius of the Earth is 6.4 x 106 m. What is the ratio of gravitational force on the satellite in orbit/gravitational force on the satellite on the surface of the Earth? A 0.36 B 0.42 C 0.51 D 0.64 Answer give DSee Answer**Q13:**34 A satellite of mass 1 600 kg is orbiting the Earth with radius 2R. R is the radius of the Earth which is equal to 6.37 × 106 m. What is the centripetal force acting on the satellite? [G = 6.67 × 10-¹1 N m² kg-2, mass of the Earth = 5.97 x 1024 kg] A 1744 N B 1806 N C 1960 N D 3 925 NSee Answer**Q14:**Analyze and Interpret 1. Describe the pattern on your graph. 2. The Sun's spectral type is about G2. Use your chart to predict the Sun's absolute magnitude. 3. Vega's spectral type is A0. Predict Vega's absolute magnitude. 4. Predict the absolute magnitude of a star whose spectral type is B5. Conclude and Communicate 5. Summarize how you can use this pattern to predict a main- sequence star's absolute magnitude if you know its spectral type.See Answer**Q15:**Problem 4 (10 pts.): Two elliptical orbits share the same central body and apsidal line as shown in below figure. Point A lies at the apogee of orbit 1. Point B lies at the apogee of orbit 2. Perform a Hohmann transfer from point A to point B. All numbers have been non-dimensionalzed such that μ 1. The apogee and perigee of orbit 1 and 2 are given by = = 10 and Respectively. What is the total Av for the maneuver? 11p₁ = 4 √√₁2 = 8 (p2 = 3 Point BSee Answer**Q16:**1. (10 pts) Manually draw the layout and patterns of motion of the solar system. Please include the Sun and all planets. Draw the orbits of all planets around the Sun (2 pts) Label the orbit direction and spin direction of all planets. Label the spin direction of the Sun. (2 pts) Label the planets' average orbital distances from the Sun in AU and their orbital periods in Earth years (2 pts) Label the size of the Sun and each planet as compared to Earth's radius (e.g. 0.5 Earth radius, 2 Earth radii,...) (2 pts) Point out the exceptions to the patterns of motion (2 pts). (The sizes and distances do not need to be drawn to scale, which is impossible to do on letter sized paper anyway.) • •See Answer**Q17:**2. (6 pts) Formation of the solar system (nebula theory) a) From what you drew for Question 1, you should be able to tell the spin direction of the protoplanetary disk (the disk formed from the collapse and flattening of the original nebula) during the formation of the solar system. What is the spin direction? (2 pts) b) Where is the frost line with respect to the planets' orbits? (2 pts) c) Why are most icy bodies (e.g. icy moons, comets, dwarf planets) found outside the frost line? (2 pts)See Answer**Q18:**3. (2 pts) Manually draw a bound orbit and an unbound orbit around a planet. Mark where the planet is with respect to the orbits.See Answer**Q19:**4. (6 pts) Planetary geology a) What is the difference between lithosphere and crust? (2 pts) b) Describe convection in a terrestrial planet. How does it cool the planetary interior? (4 pts)See Answer**Q20:**Problem 2 An earth satellite is tracked from ground stations and is observed to have an altitude of 2200 km, a velocity magnitude 7 km/s and a radial velocity of 2.7 km/s. Determine: a) the total orbital energy per unit mass b) the orbital eccentricity e c) the minimum altitude and the maximum speed and d) the true anomalies at the observed position and at the point of maximum speed. e) Identify any potential difficulties with the orbit. (Answers: -22 MJ/kg, 0.389, -835km & 10 km/s, 105.3deg & 0 deg, crash into Earth)See Answer

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