Space Dynamics & Orbital Mechanics

Subtopic: Kepler's Laws & Two-Body Problem

An earth satellite has the instantaneous position vector r⃗ and velocity vector v⃗ as given below. Here p̂ and q̂ denote the unit vectors along the x and y axes of the perifocal frame, respectively. Assume that the value of gravitational parameter is 398600 km3/s^2. Which one of the following trajectories does the satellite follow? r⃗ = (8000p̂ + 9000q̂) km and v⃗ = (-6p̂ + 6q̂) km/s

Subtopic: Kepler's Laws & Two-Body Problem

An earth satellite moves in an elliptical orbit with a perigee altitude of 300 km and an apogee altitude of 3000 km. Assume that the radius of the earth is 6378 km. The eccentricity of the orbit is __________ (rounded off to three decimal places).

Subtopic: Kepler's Laws & Two-Body Problem

F and G denote two points on a spacecraft's orbit around a planet, as indicated in the figure. O is the center of the planet, P is the periapsis, and the angles are as indicated in the figure. If OF = 8000 km, OG = 10000 km, $\theta$F = 0 deg, and $\theta$G = 60 deg, the eccentricity of the spacecraft's orbit is ____ (rounded off to two decimal places).

Subtopic: Kepler's Laws & Two-Body Problem

Which of the following statements is/are correct about a satellite moving in a geostationary orbit?

Subtopic: Rocket Trajectory & Staging

Consider an artificial satellite moving around the Moon in an elliptic orbit. The altitude of the satellite from the Moon's surface at the perigee is 25 km and that at the apogee is 134 km. Assume the Moon to be spherical with a radius of 1737 km. The trajectory is considered with reference to a coordinate system fixed to the center of mass of the Moon. The ratio of the speed of the satellite at the perigee to th at at the apogee is ___________ (rounded off to 2 decimal places).

Subtopic: Kepler's Laws & Two-Body Problem

The universal gravitational constant is 116.67 10 - Nm2/kg2. For a planet of mass 236.4169 10 kg and radius 3390 km, the escape velocity is _____ km/s. (round off to one decimal place). Q. 63 A satellite is in a circular orbit around Earth with a time period of 90 minutes. The radius of Earth is 6370 km, mass of Earth is 245.98 10 kg and the universal gravitational constant is 116.67 10 - Nm2/kg2. The altitude of the satellite above mean sea level is ____ km. (round off to the nearest integer)

Subtopic: Kepler's Laws & Two-Body Problem

A satellite is in a circular orbit around Earth with a time period of 90 minutes. The radius of Earth is 6370 km, mass of Earth is $5.98 \times 10^{24}$ kg and the universal gravitational constant is $6.67 \times 10^{-11}$ N m$^2$/kg$^2$. The altitude of the satellite above mean sea level is ____ km. (round off to the nearest integer)

Subtopic: Rocket Trajectory & Staging

Consider a high Earth-orbiting satellite of angular momentum per unit mass $h$ and eccentricity $e$. The mass of the Earth is $M$ and $G$ is the universal gravitational constant. The distance between the satellite's center of mass and the Earth's center of mass is $r$, the true anomaly is $\theta$, and the phase angle is zero. Which of the following statements is/are true?

Subtopic: Hohmann Transfer & Orbital Maneuvers

An aerospace system operating under standard sea level conditions is governed by Space Dynamics & Orbital Mechanics (Hohmann Transfer & Orbital Maneuvers). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Subtopic: Rocket Trajectory & Staging

Burnout velocity of a space vehicle in a circular orbit at an angle $5^\circ$ above the local horizon around earth is 13.5 km/s. The velocity vector orientation indicates the orbit trajectory nature is:

Subtopic: Kepler's Laws & Two-Body Problem

The product of earth's mass ($M$) and the universal gravitational constant ($G$) is $GM = 3.986 \times 10^{14}$ m$^3$/s$^2$. The circular orbital speed of a spacecraft at an altitude of 300 km above the Earth's surface (radius of Earth $R_E = 6370$ km) is _________ km/s (round off to 2 decimal places).

Subtopic: Kepler's Laws & Two-Body Problem

A combustor is operating with a fuel -air ratio of 0.03. If the stoichiometric fuel -air ratio of the fuel used is 0.06, the equivalence ratio of the combustor will be _______ (accurate to two decimal places). /Artifact <</Attached [/Top ]/Subtype /Header /Type /Pagination >>BDC q 0 0 595.44 841.68 re W* n BT /GS0 gs /TT0 8.04 Tf 54 798.36 Td [(G)20.995 (A)21.007 (T)13.993 (E )-33.993 (2)-6.007 (0)-5.995 (1)-5.995 (8)-6.007 ( )-2.998 ( )-2.998 ( )-2.998 ( )-3.01 ( )-2.998 ( )]TJ ET Q q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf 0.03 Tc 105.86 798.36 Td ( \ )Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf 0.03 Tc 307.87 798.36 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf 438.46 798.36 Td [(A)20.995 (e)11.007 (r)5 (o)7.002 (sp)-6.007 (a)-2.998 (c)-2.998 (e)10.995 ( )-2.998 (En)-7.002 (g)7.002 (i)-5 (n)-5.995 (e)10.995 (e)10.995 (r)5 (i)-5 (n)-5.995 (g)]TJ ET Q q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf 513.34 798.36 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n 52.56 795 490.44 0.48 re f* EMC Q /Artifact <</Attached [/Bottom ]/Subtype /Footer /Type /Pagination >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf -0.165 Tc 54 37.824Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf 64.704 37.824 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n 52.56 46.104 317.95 0.48 re f* Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 530.86 37.704 Td (5)Tj ET Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 534.96 37.704 Td (/)Tj ET Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 537.12 37.704 Td (9)Tj ET Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 541.08 37.704 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 0 >>BDC q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf -0.0029 Tc 54 775.56 Td (Q. )Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 70.584 775.56 Td (26)Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 83.544 775.56 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n BT /C2_0 12.96 Tf 86.784 775.56 Td <00B1>Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 93.264 775.56 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 96.504 775.56 Td [(Q.)-8.002 ( )]TJ ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 113.18 775.56 Td (55)Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 126.14 775.56 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 129.38 775.56 Td [(carry)-10 ( tw)-8.997 (o )-8.002 (m)8.997 (arks e)-8.997 (ach.)]TJ ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 253.73 775.56 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 1 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 11.04 Tf 54 750.7 Td ( )Tj ET EMC Q q 59.424 667.42 33.96 80.64 re W* n /P <</Lang (en-US)/MCID 2 >>BDC q 59.424 667.42 33.96 80.64 re W* n BT /TT0 12 Tf 64.824 737.26 Td (Q.26)Tj ET Q q 59.424 667.42 33.96 80.64 re W* n BT /TT2 12 Tf 88.464 737.26 Td ( )Tj ET Q q 59.424 667.42 33.96 80.64 re W* n BT /TT0 12 Tf 100.82 737.26 Td ( )Tj ET EMC Q Q q 93.384 708.82 452.14 39.24 re W* n /P <</Lang (en-US)/MCID 3 >>BDC q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 99.144 730.9 Td [(The)5 ( sol)]TJ ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 134.78 730.9 Td [(uti)-3 (on of)3 ( the dif)3 (fe)7 (r)-6 (e)4 (nti)-3 (a)4 (l equa)6 (ti)-3 (on )]TJ ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 296.83 738.58 Td <0BD7>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 7.56 Tf 302.83 741.82 Td <0C2E>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 307.63 738.58 Td <0BEC>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 296.95 724.3 Td <0BD7>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 302.95 724.3 Td <0BEB>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 7.56 Tf 308.59 727.06 Td <0C2E>Tj ET Q 296.83 734.26 16.8 0.84 re f* q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 316.51 730.9 Td <0D45>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 329.11 730.9 Td <0375>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 0.009 Tc 338.47 738.58 Td <0BD70BEC>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 0.009 Tc 338.59 724.3 Td <0BD70BEB>Tj ET Q 338.47 734.26 11.64 0.84 re f* q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 353.71 730.9 Td <0D4C>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 367.03 730.9 Td <0372>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12.96 Tf 374.23 730.9 Td (,)Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12.96 Tf 377.47 730.9 Td ( )Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 380.71 730.9 Td [(g)10 (iven th)-9 (a)4 (t )]TJ ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 431.38 730.9 Td <0755>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 442.54 730.9 Td <0D4C>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 455.86 730.9 Td <0372>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 463.06 730.9 Td <0003>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 465.94 730.9 Td <008300900086>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 0.009 Tc 488.86 738.58 Td <0BD70BEC>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 0.009 Tc 488.98 724.3 Td <0BD70BEB>Tj ET Q 488.86 734.26 11.64 0.84 re f* q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 504.22 730.9 Td <0D4C>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 517.54 730.9 Td <0373>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 524.62 730.9 Td ( )Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 527.62 730.9 Td [(a)4 (t )]TJ ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 99.144 711.7 Td <0754>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 110.06 711.7 Td <0D4C>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 123.38 711.7 Td <0372>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 130.58 711.7 Td <0003>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 0.024 Tc 133.46 711.7 Td (is)Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 141.5 711.7 Td ( )Tj ET EMC Q Q q 93.384 667.42 101.06 34.2 re W* n /P <</Lang (en-US)/MCID 4 >>BDC q 93.384 667.42 101.06 34.2 re W* n BT /TT0 12 Tf 98.784 689.26 Td [(\(A)5 (\) )]TJ ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 118.46 689.26 Td <0754>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 125.78 689.26 Td <123A>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 131.18 689.26 Td <0373>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 141.26 689.26 Td <0D46>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 153.86 689.26 Td <0741>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 9 Tf 160.94 694.06 Td <0B3F>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 9 Tf 167.54 694.06 Td <0B37>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 9 Tf 172.7 694.06 Td <0BEB>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 178.85 689.26 Td <123B>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /TT0 12 Tf 184.25 689.26 Td ( )Tj ET EMC Q Q q 194.45 667.42 103.46 34.2 re W* n /P <</Lang (en-US)/MCID 5 >>BDC q 194.45 667.42 103.46 34.2 re W* n BT /TT0 12 Tf 199.85 686.62 Td [(\(B)10 (\) )]TJ ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 9 Tf 218.81 694.3 Td <0B35>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 9 Tf 218.81 680.02 Td <0B37>Tj ET Q 218.81 689.98 5.16 0.84 re f* q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 12.96 Tf 226.25 687.34 Td <123A>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 12.96 Tf 231.65 686.62 Td <0373>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 12.96 Tf 241.73 686.62 Td <0D46>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 12.96 Tf 254.33 686.62 Td <0741>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 9 Tf 261.41 691.42 Td <0B3F>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 9 Tf 268.01 691.42 Td <0B37>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 9 Tf 273.17 691.42 Td <0BEB>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 12.96 Tf 279.29 687.34 Td <123B>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /TT0 12 Tf 284.69 686.62 Td ( )Tj ET EMC Q Q q 297.91 667.42 126.02 34.2 re W* n /P <</Lang (en-US)/MCID 6 >>BDC q 297.91 667.42 126.02 34.2 re W* n BT /TT0 12 Tf 303.31 686.62 Td (\(C\) )Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 9 Tf 325.27 694.3 Td <0B35>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 9 Tf 325.27 680.02 Td <0B37>Tj ET Q 325.27 689.98 5.16 0.84 re f* q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 12.96 Tf 332.71 686.62 Td <123A>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 12.96 Tf 338.11 686.62 Td <0373>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 12.96 Tf 348.19 686.62 Td <0D45>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 12.96 Tf 360.79 686.62 Td <0741>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 9 Tf 367.87 691.42 Td <0B3F>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 9 Tf 374.47 691.42 Td <0B37>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 9 Tf 379.63 691.42 Td <0BEB>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 12.96 Tf 385.75 686.62 Td <123B>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /TT0 12 Tf 391.15 686.62 Td ( )Tj ET EMC Q Q q 423.94 667.42 121.58 34.2 re W* n /P <</Lang (en-US)/MCID 7 >>BDC q 423.94 667.42 121.58 34.2 re W* n BT /TT0 12 Tf 429.34 683.98 Td [(\(D)5 (\) )]TJ ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 9 Tf 452.02 691.66 Td <0B35>Tj ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 9 Tf 452.02 677.38 Td <0B37>Tj ET Q 452.02 687.34 5.16 0.84 re f* q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 12.96 Tf -0.0547 Tc 459.34 683.98 Td <07540741>Tj ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 7.56 Tf 473.38 695.38 Td <0C37>Tj ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 7.56 Tf 479.02 695.38 Td <0C2F>Tj ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 7.56 Tf 483.46 695.38 Td <0CE3>Tj ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 7.56 Tf 478.54 685.54 Td <0C2E>Tj ET Q 473.38 692.38 14.76 0.6 re f* q 423.94 667.42 121.58 34.2 re W* n BT /TT0 12 Tf 488.86 683.98 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 8 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 656.62 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 9 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 642.82 Td ( )Tj ET EMC Q q 59.424 488.83 33.96 150.98 re W* n /P <</Lang (en-US)/MCID 10 >>BDC q 59.424 488.83 33.96 150.98 re W* n BT /TT0 12 Tf 64.824 629.02 Td (Q.27)Tj ET Q q 59.424 488.83 33.96 150.98 re W* n BT /TT2 12 Tf 88.464 629.02 Td ( )Tj ET Q q 59.424 488.83 33.96 150.98 re W* n BT /TT0 12 Tf 100.82 629.02 Td ( )Tj ET EMC Q Q q 93.384 612.22 452.14 27.6 re W* n /P <</Lang (en-US)/MCID 11 >>BDC q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 99.144 629.02 Td [(The)5 ( )]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 120.5 629.02 Td [(re)7 (l)-11 (a)4 (ti)-3 (on )20 (be)4 (twe)4 (e)4 (n)-9 ( )20 (pre)-2 (ssure)]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 242.69 629.02 Td ( )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 245.45 629.02 Td (\()Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT3 12 Tf 249.41 629.02 Td (p)Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 255.41 629.02 Td (\))Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 259.37 629.02 Td ( )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 262.25 629.02 Td [(a)4 (nd )20 (ve)4 (lo)-11 (c)4 (it)-13 (y)]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 320.95 629.02 Td ( )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 323.83 629.02 Td (\()Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT3 12 Tf 327.79 629.02 Td (V)Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT3 12 Tf 335.23 629.02 Td (\))Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 339.19 629.02 Td ( )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 341.95 629.02 Td [(for)6 ( )20 (a)4 ( )20 (st)-12 (e)4 (a)4 (d)-19 (y)20 (, )20 (isentropi)-9 (c)4 ( )20 (fl)]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 460.78 629.02 Td (ow )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 478.18 629.02 Td [(a)4 (t )18 (two )20 (point)-3 (s )]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 99.144 615.22 Td [(a)4 (long)8 ( )-9 (a)4 ( stre)4 (a)4 (m)]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 168.98 615.22 Td [(li)-3 (ne)4 ( )]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 190.01 615.22 Td (is, \()Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT3 12 Tf 208.13 615.22 Td (c)Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 213.41 615.22 Td ( )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 216.41 615.22 Td [(is a c)5 (onst)-2 (a)4 (nt\))]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 279.77 615.22 Td ( )Tj ET EMC Q Q q 93.384 576.22 452.14 28.8 re W* n /P <</Lang (en-US)/MCID 12 >>BDC q 93.384 576.22 452.14 28.8 re W* n BT /TT0 12 Tf 98.784 588.7 Td [(\(A)5 (\))]TJ ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 115.46 588.7 Td <0003>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 118.1 588.7 Td <0003>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 120.74 588.7 Td <0003>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 123.38 588.7 Td <073F>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 129.26 588.7 Td <123A>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 134.3 588.7 Td <074C>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 140.54 585.22 Td <0B36>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 141.26 594.82 Td <0C0A>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 149.66 588.7 Td <0D46>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 161.3 588.7 Td <0003>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 163.94 588.7 Td <074C>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 169.94 585.22 Td <0B35>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 170.9 594.82 Td <0C0A>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /TT0 12 Tf 176.69 588.7 Td [(\) =)7 ( )]TJ ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 193.49 595.78 Td <0BCF>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 6.96 Tf 197.69 593.74 Td <0C2D>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 6.96 Tf 199.49 599.14 Td <0C2E>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 196.25 582.7 Td <0B36>Tj ET Q 193.49 591.7 10.56 0.84 re f* q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 206.81 588.7 Td <0D46>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 217.01 588.7 Td <0003>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 221.09 595.78 Td <0BCF>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 6.96 Tf 225.29 593.74 Td <0C2E>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 6.96 Tf 227.09 599.14 Td <0C2E>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 223.85 582.7 Td <0B36>Tj ET Q 221.09 591.7 10.56 0.84 re f* q 93.384 576.22 452.14 28.8 re W* n BT /TT0 12 Tf 231.53 588.7 Td ( )Tj ET EMC Q Q q 93.384 544.75 452.14 31.464 re W* n /P <</Lang (en-US)/MCID 13 >>BDC q 93.384 544.75 452.14 31.464 re W* n BT /TT0 12 Tf 98.784 555.91 Td [(\(B)10 (\))]TJ ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 114.74 555.91 Td <0003>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 117.38 555.91 Td <0003>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 120.02 555.91 Td <073F>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 126.02 555.91 Td <123A>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 131.06 555.91 Td <074C>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 137.3 551.83 Td <0B36>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 142.7 571.03 Td <0D02>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 138.02 561.67 Td <0D02>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 142.46 561.67 Td <0C37>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 147.62 561.67 Td <0C2D>Tj ET Q 138.02 568.15 13.92 0.6 re f* q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 154.94 555.91 Td <0D46>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 166.58 555.91 Td <0003>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 169.22 555.91 Td <074C>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 175.22 551.83 Td <0B35>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 180.89 571.03 Td <0D02>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 176.21 561.67 Td <0D02>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 180.77 561.67 Td <0C37>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 185.93 561.67 Td <0C2D>Tj ET Q 176.21 568.15 13.92 0.6 re f* q 93.384 544.75 452.14 31.464 re W* n BT /TT0 12 Tf 190.61 555.91 Td [(\) =)7 ( )]TJ ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 207.41 562.99 Td <0BCF>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 211.61 560.95 Td <0C2D>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 213.41 566.35 Td <0C2E>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 210.17 549.91 Td <0B36>Tj ET Q 207.41 558.91 10.56 0.84 re f* q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 220.61 555.91 Td <0D46>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 230.93 555.91 Td <0003>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 234.89 562.99 Td <0BCF>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 239.09 560.95 Td <0C2E>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 240.89 566.35 Td <0C2E>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 237.65 549.91 Td <0B36>Tj ET Q 234.89 558.91 10.56 0.84 re f* q 93.384 544.75 452.14 31.464 re W* n BT /TT0 12 Tf 245.45 555.91 Td ( )Tj ET EMC Q Q q 93.384 517.63 452.14 27.12 re W* n /P <</Lang (en-US)/MCID 14 >>BDC q 93.384 517.63 452.14 27.12 re W* n BT /TT0 12 Tf 98.784 523.87 Td (\(C\))Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 114.74 523.87 Td <0003>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 117.38 523.87 Td <0003>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 120.02 523.87 Td <073F>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 126.02 523.87 Td <123A>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 131.06 523.87 Td <074C>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 137.3 519.79 Td <0B36>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 138.02 538.99 Td <0D02>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 142.46 538.99 Td <0C37>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 147.62 538.99 Td <0C2D>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 142.7 529.63 Td <0D02>Tj ET Q 138.02 536.11 13.92 0.6 re f* q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 154.94 523.87 Td <0D46>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 166.58 523.87 Td <0003>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 169.22 523.87 Td <074C>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 175.22 519.79 Td <0B35>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 176.21 538.99 Td <0D02>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 180.77 538.99 Td <0C37>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 185.93 538.99 Td <0C2D>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 180.89 529.63 Td <0D02>Tj ET Q 176.21 536.11 13.92 0.6 re f* q 93.384 517.63 452.14 27.12 re W* n BT /TT0 12 Tf 190.61 523.87 Td [(\) =)7 ( )]TJ ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 207.41 530.95 Td <0BCF>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 211.61 528.91 Td <0C2D>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 213.41 534.31 Td <0C2E>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 210.17 517.87 Td <0B36>Tj ET Q 207.41 526.87 10.56 0.84 re f* q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 220.61 523.87 Td <0D46>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 230.93 523.87 Td <0003>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 234.89 530.95 Td <0BCF>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 239.09 528.91 Td <0C2E>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 240.89 534.31 Td <0C2E>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 237.65 517.87 Td <0B36>Tj ET Q 234.89 526.87 10.56 0.84 re f* q 93.384 517.63 452.14 27.12 re W* n BT /TT0 12 Tf 245.45 523.87 Td ( )Tj ET EMC Q Q q 93.384 488.83 452.14 28.8 re W* n /P <</Lang (en-US)/MCID 15 >>BDC q 93.384 488.83 452.14 28.8 re W* n BT /TT0 12 Tf 98.784 501.31 Td [(\(D)5 (\))]TJ ET Q q 93.384 488.83 452.14 28.8 re W* n BT /TT0 12 Tf 115.34 501.31 Td ( )Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 121.46 501.31 Td <073F>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 127.34 501.31 Td <123A>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 132.38 501.31 Td <074C>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 138.62 497.83 Td <0B36>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 139.34 507.43 Td <0C0A>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 144.5 507.43 Td <0B3F>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 150.74 507.43 Td <0B35>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 158.78 501.31 Td <0D46>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 170.42 501.31 Td <0003>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 173.06 501.31 Td <074C>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 179.09 497.83 Td <0B35>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 180.05 507.43 Td <0C0A>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 185.33 507.43 Td <0B3F>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 191.57 507.43 Td <0B35>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /TT0 12 Tf 196.97 501.31 Td [(\) =)7 ( )]TJ ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 213.77 508.39 Td <0BCF>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 6.96 Tf 217.97 506.35 Td <0C2D>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 6.96 Tf 219.77 511.75 Td <0C2E>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 216.53 495.31 Td <0B36>Tj ET Q 213.77 504.31 10.56 0.84 re f* q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 227.09 501.31 Td <0D46>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 237.29 501.31 Td <0003>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 241.37 508.39 Td <0BCF>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 6.96 Tf 245.57 506.35 Td <0C2E>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 6.96 Tf 247.37 511.75 Td <0C2E>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 244.13 495.31 Td <0B36>Tj ET Q 241.37 504.31 10.56 0.84 re f* q 93.384 488.83 452.14 28.8 re W* n BT /TT0 12 Tf 251.81 501.31 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 16 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 11.04 Tf 54 478.87 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 17 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 11.04 Tf 54 466.27 Td ( )Tj ET EMC Q q 59.424 385.49 33.96 78.024 re W* n /P <</Lang (en-US)/MCID 18 >>BDC q 59.424 385.49 33.96 78.024 re W* n BT /TT0 12 Tf 64.824 452.71 Td (Q.28)Tj ET Q q 59.424 385.49 33.96 78.024 re W* n BT /TT2 12 Tf 88.464 452.71 Td ( )Tj ET Q q 59.424 385.49 33.96 78.024 re W* n BT /TT0 12 Tf 100.82 452.71 Td ( )Tj ET EMC Q Q q 93.384 407.47 452.14 56.04 re W* n /P <</Lang (en-US)/MCID 19 >>BDC q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 99.144 452.71 Td [(A )-27 (thi)-3 (n )-29 (a)4 (irf)4 (oil)-3 ( )-29 (is )-32 (mount)-3 (e)4 (d )-29 (in )-31 (a)4 ( )-29 (low)]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 262.01 452.71 Td (-)Tj ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 265.97 452.71 Td [(spe)-6 (e)4 (d, )-29 (subsoni)-3 (c)-5 ( )-29 (wind )-29 (tunnel, )-29 (in )-31 (whic)4 (h )-29 (th)-11 (e)4 ( )-29 (Ma)3 (c)4 (h )-29 (numb)-11 (e)4 (r )]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 99.144 437.95 Td [(is )-52 (0.1. )-49 (At)10 ( )-49 (a)4 ( )-49 (point)6 ( )-49 (on )-49 (the)12 ( )-39 (a)4 (irf)4 (oil)-3 (, )-49 (the )-47 (pre)7 (ssure)5 ( )-49 (c)4 (oe)4 (f)-6 (f)-6 (icie)4 (nt )-51 (is )-52 (mea)6 (sure)6 (d )-49 (to )-51 (be)4 ( )]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /C0_0 12 Tf 459.94 437.95 Td <0010>Tj ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 466.54 437.95 Td [(1.2. )-59 (I)23 (f )-46 (the )-47 (flow)3 ( )]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 99.144 424.27 Td [(ve)4 (locit)-11 (y)20 ( )-29 (is )-32 (incr)5 (e)-5 (a)4 (se)3 (d )-29 (suc)-6 (h )-29 (that )-29 (the )-27 (fr)6 (e)4 (e)]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 284.33 424.27 Td (-)Tj ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 288.29 424.27 Td [(str)-9 (e)4 (a)4 (m )-31 (Ma)-6 (c)4 (h )-29 (number)5 ( )-29 (is )-32 (0.6, )-29 (the)]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 441.82 424.27 Td ( )Tj ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 445.18 424.27 Td [(pre)-2 (ssure)5 ( )-29 (c)4 (oe)4 (f)-6 (fic)5 (ient )]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 99.144 410.47 Td [(a)4 (t t)-3 (he)4 ( sa)3 (me point on t)-3 (he)4 ( a)-5 (irf)4 (oil)-3 ( will)-3 ( a)4 (pprox)-6 (im)-3 (a)4 (tel)-9 (y)30 ( )-9 (be)4 (: )]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 360.43 410.47 Td ( )Tj ET EMC Q Q q 93.384 385.49 106.22 14.784 re W* n /P <</Lang (en-US)/MCID 20 >>BDC q 93.384 385.49 106.22 14.784 re W* n BT /TT0 12 Tf 98.784 388.49 Td [(\(A)5 (\) )]TJ ET Q q 93.384 385.49 106.22 14.784 re W* n BT /C0_0 12 Tf 118.34 388.49 Td <0010>Tj ET Q q 93.384 385.49 106.22 14.784 re W* n BT /TT0 12 Tf 124.94 388.49 Td (3.5)Tj ET Q q 93.384 385.49 106.22 14.784 re W* n BT /TT0 12 Tf 140.06 388.49 Td ( )Tj ET EMC Q Q q 199.61 385.49 106.34 14.784 re W* n /P <</Lang (en-US)/MCID 21 >>BDC q 199.61 385.49 106.34 14.784 re W* n BT /TT0 12 Tf 205.01 388.49 Td [(\(B)10 (\) )]TJ ET Q q 199.61 385.49 106.34 14.784 re W* n BT /C0_0 12 Tf 223.85 388.49 Td <0010>Tj ET Q q 199.61 385.49 106.34 14.784 re W* n BT /TT0 12 Tf 230.45 388.49 Td (2.9)Tj ET Q q 199.61 385.49 106.34 14.784 re W* n BT /TT0 12 Tf 245.57 388.49 Td ( )Tj ET EMC Q Q q 305.95 385.49 106.2 14.784 re W* n /P <</Lang (en-US)/MCID 22 >>BDC q 305.95 385.49 106.2 14.784 re W* n BT /TT0 12 Tf 311.35 388.49 Td (\(C\) )Tj ET Q q 305.95 385.49 106.2 14.784 re W* n BT /C0_0 12 Tf 330.31 388.49 Td <0010>Tj ET Q q 305.95 385.49 106.2 14.784 re W* n BT /TT0 12 Tf 336.91 388.49 Td (1.5)Tj ET Q q 305.95 385.49 106.2 14.784 re W* n BT /TT0 12 Tf 351.91 388.49 Td ( )Tj ET EMC Q Q q 412.15 385.49 133.37 14.784 re W* n /P <</Lang (en-US)/MCID 23 >>BDC q 412.15 385.49 133.37 14.784 re W* n BT /TT0 12 Tf 417.58 388.49 Td [(\(D)5 (\) )]TJ ET Q q 412.15 385.49 133.37 14.784 re W* n BT /C0_0 12 Tf 440.14 388.49 Td <0010>Tj ET Q q 412.15 385.49 133.37 14.784 re W* n BT /TT0 12 Tf 446.74 388.49 Td (0.75)Tj ET Q q 412.15 385.49 133.37 14.784 re W* n BT /TT0 12 Tf 467.86 388.49 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 24 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 374.69 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 25 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 360.89 Td ( )Tj ET EMC Q q 59.424 293.93 33.96 63.96 re W* n /P <</Lang (en-US)/MCID 26 >>BDC q 59.424 293.93 33.96 63.96 re W* n BT /TT0 12 Tf 64.824 347.09 Td (Q.29)Tj ET Q q 59.424 293.93 33.96 63.96 re W* n BT /TT2 12 Tf 88.464 347.09 Td ( )Tj ET Q q 59.424 293.93 33.96 63.96 re W* n BT /TT0 12 Tf 100.82 347.09 Td ( )Tj ET EMC Q Q q 93.384 330.29 452.14 27.6 re W* n /P <</Lang (en-US)/MCID 27 >>BDC q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 99.144 347.09 Td [(A )-97 (soli)-4 (d )-99 (c)4 (irc)5 (ular)5 ( )-99 (sha)-6 (ft )-98 (of)-6 ( )-99 (diame)4 (ter)5 ( )]TJ ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT3 12 Tf 268.25 347.09 Td (d)Tj ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 274.25 347.09 Td ( )Tj ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 278.45 347.09 Td [(is )-102 (unde)4 (r )-96 (pu)-9 (r)-6 (e)4 ( )-99 (torsion )-101 (of )-96 (ma)-7 (g)10 (nit)-3 (ude)4 ( )]TJ ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT3 12 Tf 454.42 347.09 Td (T)Tj ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 461.14 347.09 Td [(. )-99 (The)5 ( )-99 (max)-7 (im)-3 (u)10 (m)8 ( )]TJ ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 99.144 333.29 Td [(tensil)-2 (e)4 ( stre)4 (ss ex)-7 (pe)4 (rie)5 (nc)4 (e)4 (d)-9 ( a)4 (t an)-17 (y)20 ( point)-3 ( on the sha)5 (ft )-8 (is )]TJ ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 353.83 333.29 Td ( )Tj ET EMC Q Q q 93.384 293.93 106.22 29.16 re W* n /P <</Lang (en-US)/MCID 28 >>BDC q 93.384 293.93 106.22 29.16 re W* n BT /TT0 12 Tf 98.784 308.93 Td [(\(A)5 (\))]TJ ET Q q 93.384 293.93 106.22 29.16 re W* n BT /TT0 12 Tf 115.34 308.93 Td ( )Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /TT0 12 Tf 118.34 308.93 Td ( )Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /C2_1 8.52 Tf -0.0131 Tc 121.7 316.01 Td <0B370B36>Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /C2_1 8.52 Tf 131.54 316.01 Td <0BCD>Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /C2_1 8.52 Tf 121.46 302.93 Td <0C17>Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /C2_1 8.52 Tf 127.22 302.93 Td <0BD7>Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /C2_1 6.96 Tf 132.86 305.45 Td <0C2F>Tj ET Q 121.46 311.93 15.96 0.84 re f* q 93.384 293.93 106.22 29.16 re W* n BT /TT0 12 Tf 137.42 308.93 Td ( )Tj ET EMC Q Q q 199.61 293.93 106.34 29.16 re W* n /P <</Lang (en-US)/MCID 29 >>BDC q 199.61 293.93 106.34 29.16 re W* n BT /TT0 12 Tf 205.01 308.93 Td [(\(B)10 (\))]TJ ET Q q 199.61 293.93 106.34 29.16 re W* n BT /TT0 12 Tf 220.85 308.93 Td ( )Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /TT0 12 Tf 223.85 308.93 Td ( )Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /C2_1 8.52 Tf -0.0131 Tc 227.21 316.01 Td <0B350B3A>Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /C2_1 8.52 Tf 237.05 316.01 Td <0BCD>Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /C2_1 8.52 Tf 226.97 302.93 Td <0C17>Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /C2_1 8.52 Tf 232.85 302.93 Td <0BD7>Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /C2_1 6.96 Tf 238.49 305.45 Td <0C30>Tj ET Q 226.97 311.93 15.96 0.84 re f* q 199.61 293.93 106.34 29.16 re W* n BT /TT0 12 Tf 242.93 308.93 Td ( )Tj ET EMC Q Q q 305.95 293.93 106.2 29.16 re W* n /P <</Lang (en-US)/MCID 30 >>BDC q 305.95 293.93 106.2 29.16 re W* n BT /TT0 12 Tf 311.35 308.93 Td (\(C\) )Tj ET Q q 305.95 293.93 106.2 29.16 re W* n BT /C2_1 8.52 Tf -0.0131 Tc 333.55 316.01 Td <0B370B36>Tj ET Q q 305.95 293.93 106.2 29.16 re W* n BT /C2_1 8.52 Tf 343.39 316.01 Td <0BCD>Tj ET Q q 305.95 293.93 106.2 29.16 re W* n BT /C2_1 8.52 Tf 333.31 302.93 Td <0C17>Tj ET Q q 305.95 293.93 106.2 29.16 re W* n BT /C2_1 8.52 Tf 339.19 302.93 Td <0BD7>Tj ET Q q 305.95 293.93 106.2 29.16 re W* n BT /C2_1 6.96 Tf 344.83 305.45 Td <0C30>Tj ET Q 333.31 311.93 15.96 0.84 re f* q 305.95 293.93 106.2 29.16 re W* n BT /TT0 12 Tf 349.27 308.93 Td ( )Tj ET EMC Q Q q 412.15 293.93 133.37 29.16 re W* n /P <</Lang (en-US)/MCID 31 >>BDC q 412.15 293.93 133.37 29.16 re W* n BT /TT0 12 Tf 417.58 308.93 Td [(\(D)5 (\) )]TJ ET Q q 412.15 293.93 133.37 29.16 re W* n BT /C2_1 8.52 Tf -0.0131 Tc 440.5 316.01 Td <0B350B3A>Tj ET Q q 412.15 293.93 133.37 29.16 re W* n BT /C2_1 8.52 Tf 450.34 316.01 Td <0BCD>Tj ET Q q 412.15 293.93 133.37 29.16 re W* n BT /C2_1 8.52 Tf 440.26 302.93 Td <0C17>Tj ET Q q 412.15 293.93 133.37 29.16 re W* n BT /C2_1 8.52 Tf 446.02 302.93 Td <0BD7>Tj ET Q q 412.15 293.93 133.37 29.16 re W* n BT /C2_1 6.96 Tf 451.66 305.45 Td <0C2F>Tj ET Q 440.26 311.93 15.96 0.84 re f* q 412.15 293.93 133.37 29.16 re W* n BT /TT0 12 Tf 456.22 308.93 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 32 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 11.04 Tf 54 283.97 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 33 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 270.41 Td ( )Tj ET EMC Q q 59.424 97.224 33.96 170.18 re W* n /P <</Lang (en-US)/MCID 34 >>BDC q 59.424 97.224 33.96 170.18 re W* n BT /TT0 12 Tf 64.824 256.61 Td (Q.30)Tj ET Q q 59.424 97.224 33.96 170.18 re W* n BT /TT2 12 Tf 88.464 256.61 Td ( )Tj ET Q q 59.424 97.224 33.96 170.18 re W* n BT /TT0 12 Tf 100.82 256.61 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 35 >>BDC q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 99.144 256.61 Td [(A )12 (c)4 (lampe)4 (d)]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 151.34 256.61 Td (-)Tj ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 155.3 256.61 Td [(c)4 (lampe)4 (d)-9 ( )10 (be)4 (a)-5 (m, )8 (subj)-2 (e)4 (c)4 (ted )12 (to a )12 (point)-3 ( )10 (lo)-11 (a)4 (d )10 (P)-3 ( )10 (a)4 (t )8 (the)-7 ( )10 (mi)-3 (dspa)3 (n, )10 (is )7 (sh)-10 (own )12 (in )8 (the )12 (fi)-8 (g)10 (u)-9 (re)7 ( )]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 99.144 242.81 Td [(be)4 (low. The)5 ( )]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 156.02 242.81 Td [(ma)-7 (g)10 (nit)-3 (ude)4 ( )]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 209.69 242.81 Td [(of)-6 ( the )]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 240.41 242.81 Td [(mom)-3 (e)4 (nt re)5 (a)4 (c)4 (ti)-3 (on a)4 (t t)-13 (he)4 ( two f)3 (ix)-11 (e)4 (d e)4 (nds of the)4 ( )-9 (be)4 (a)4 (m i)-3 (s)]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 495.1 242.81 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 36 >>BDC q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 475.42 118.34 Td ( )Tj ET EMC Q q 93.384 97.224 106.22 13.8 re W* n /P <</Lang (en-US)/MCID 37 >>BDC q 93.384 97.224 106.22 13.8 re W* n BT /TT0 12 Tf 98.784 100.22 Td [(\(A)5 (\) )]TJ ET Q q 93.384 97.224 106.22 13.8 re W* n BT /TT0 12 Tf 118.34 100.22 Td [(P)-13 (L)21 (/2)]TJ ET Q q 93.384 97.224 106.22 13.8 re W* n BT /TT0 12 Tf 141.74 100.22 Td ( )Tj ET EMC Q Q q 199.61 97.224 106.34 13.8 re W* n /P <</Lang (en-US)/MCID 38 >>BDC q 199.61 97.224 106.34 13.8 re W* n BT /TT0 12 Tf 205.01 100.22 Td [(\(B)10 (\))]TJ ET Q q 199.61 97.224 106.34 13.8 re W* n BT /TT0 12 Tf 220.85 100.22 Td ( )Tj ET Q q 199.61 97.224 106.34 13.8 re W* n BT /TT0 12 Tf 223.85 100.22 Td [(P)-13 (L)11 (/4)]TJ ET Q q 199.61 97.224 106.34 13.8 re W* n BT /TT0 12 Tf 247.25 100.22 Td ( )Tj ET Q q 199.61 97.224 106.34 13.8 re W* n BT /TT0 12 Tf 250.37 100.22 Td ( )Tj ET EMC Q Q q 305.95 97.224 106.2 13.8 re W* n /P <</Lang (en-US)/MCID 39 >>BDC q 305.95 97.224 106.2 13.8 re W* n BT /TT0 12 Tf 311.35 100.22 Td (\(C\))Tj ET Q q 305.95 97.224 106.2 13.8 re W* n BT /TT0 12 Tf 327.31 100.22 Td ( )Tj ET Q q 305.95 97.224 106.2 13.8 re W* n BT /TT0 12 Tf 330.31 100.22 Td [(P)-13 (L)21 (/8)]TJ ET Q q 305.95 97.224 106.2 13.8 re W* n BT /TT0 12 Tf 353.59 100.22 Td ( )Tj ET Q q 305.95 97.224 106.2 13.8 re W* n BT /TT0 12 Tf 359.71 100.22 Td ( )Tj ET EMC Q Q q 412.15 97.224 133.37 13.8 re W* n /P <</Lang (en-US)/MCID 40 >>BDC q 412.15 97.224 133.37 13.8 re W* n BT /TT0 12 Tf 417.58 100.22 Td [(\(D)5 (\))]TJ ET Q q 412.15 97.224 133.37 13.8 re W* n BT /TT0 12 Tf 434.14 100.22 Td ( )Tj ET Q q 412.15 97.224 133.37 13.8 re W* n BT /TT0 12 Tf 437.14 100.22 Td [(P)-13 (L)21 (/16)]TJ ET Q q 412.15 97.224 133.37 13.8 re W* n BT /TT0 12 Tf 466.42 100.22 Td ( )Tj ET Q q 412.15 97.224 133.37 13.8 re W* n BT /TT0 12 Tf 472.54 100.22 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 41 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 86.424 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 42 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 72.624 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 43 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 58.824 Td ( )Tj ET EMC Q /P <</MCID 44 >>BDC q 93.36 118.32 452.04 149.16 re W* n q 311.4 0 0 121.56 163.32 118.32 cm /Im0 Do Q EMC Q 6/9

Subtopic: Kepler's Laws & Two-Body Problem

A spacecraft forms a circular orbit at an altitude of 150 km above the surface of a spherical Earth. Assuming the gravitational parameter, µ = 3.986 × 10 14 m^3/s2 and radius of earth, RE = 6,400 km, the velocity required for the injection of the spacecraft, parallel to the local horizon, is _______________ (accurate to two decimal places).

Subtopic: Hohmann Transfer & Orbital Maneuvers

The aircraft velocity (m/s) components in body axes are given as [ u, v, w] = [100, 10, 10]. The air velocity (m/s), angle of attack (deg) and sideslip angle (deg) in that order are

Subtopic: Kepler's Laws & Two-Body Problem

A satellite is injected at an altitude of 350 km above the Earth's surface, with a velocity of 8.0 km/s parallel to the local horizon. (Earth radius=6378 km, µE (GM=Gravitational constant × Earth mass) = 3.986×1014 m3s-2). The satellite

Subtopic: Kepler's Laws & Two-Body Problem

An aerospace system operating under standard sea level conditions is governed by Space Dynamics & Orbital Mechanics (Kepler's Laws & Two-Body Problem). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Subtopic: Hohmann Transfer & Orbital Maneuvers

An aerospace system operating under standard sea level conditions is governed by Space Dynamics & Orbital Mechanics (Hohmann Transfer & Orbital Maneuvers). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Subtopic: Kepler's Laws & Two-Body Problem

Considering R as the radius of the moon, the ratio of the velocities of two spacecraft orbiting moon in circular orbit at altitudes R and 2R above the surface of the moon is ________. Q. 26 - Q. 55 carry two marks each.

Subtopic: Kepler's Laws & Two-Body Problem

Lift-off distance for a given aircraft of weight W is SLO. If the take-off weight is reduced by 10%, then the magnitude of percentage change in the lift-off distance (assume all other parameters to remain constant) is _______.

Subtopic: Kepler's Laws & Two-Body Problem

Consider the low earth orbit (LEO) and the geo synchronous orbit (GSO). Then

Subtopic: Kepler's Laws & Two-Body Problem

Q. 26 to Q. 55 carry two marks each. Questions Q.26 to Q. 30 are numerica l answer type. The answer to each of these questio ns is either a positive whole number, or a positive real number with maximum of 2 decimal places. Consider a cantilever beam having length L=1 m, square cross-section (width = depth = 0.01 m) and Young's modulus 50 GPa. The beam is subjected to a transverse load P = 1 N at the mid-span (L/2) at the center of the cross-section. Unde r the small deformation theory, the transverse deflection of the beam (in mm) at its free-end is

Subtopic: Kepler's Laws & Two-Body Problem

The angular momentum, about the centre of mass of the earth, of an artificial satellite in a highly eiliptical orbit is

Subtopic: Kepler's Laws & Two-Body Problem

Ignoring compressibility effects, the cruising speed of the aircraft is approximately

Subtopic: Kepler's Laws & Two-Body Problem

The life of a geo-stationary communications satellite is limited by

Subtopic: Kepler's Laws & Two-Body Problem

Mars to the escape velocity from the surface of earth is approximately

Subtopic: Kepler's Laws & Two-Body Problem

Which of the following quantities remains constant for a satellite in an elliptical orbit around the earth?

Subtopic: Kepler's Laws & Two-Body Problem

A planet is observed to be at its slowest when it is at a distance r, from the sun and at its fastest when it is at a distance r2 from the sun. The eccentricity e of the planet's orbit is given by

Subtopic: Kepler's Laws & Two-Body Problem

The velocity required for a spacecraft to escape earth's gravitational field depends on

Subtopic: Kepler's Laws & Two-Body Problem

The Earth's radius is $6.37 \times 10^6\text{ m}$ and the acceleration due to gravity on its surface is $9.81\text{ m/s}^2$. A satellite is in a circular orbit at an altitude of $6.30 \times 10^5\text{ m}$ above the Earth's surface. The minimum additional speed it needs to escape from the Earth's gravitational field is:

Subtopic: Kepler's Laws & Two-Body Problem

The velocity change needed to make the orbit equatorial is:

Subtopic: Kepler's Laws & Two-Body Problem

Dutch-roll mode will be

Subtopic: Hohmann Transfer & Orbital Maneuvers

P 0.8 0.4 0 In the above figure, c, refers to the section lift coefficient, C, refers to the lif coefficient of the wing, y is the coordinate along the span and s is the span of the wing. A designer prefers to use a wing for which the stall begins at the root. Which of the wings will he choose?