Space Dynamics - Flight Mechanics & Space Dynamics - Aerospace Engineering Previous Year Questions

1

2007 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2007

Two identical earth satellites A and B are in circular orbits at altitudes h_A and h_B above the earth's surface respectively, with h_A > h_B. If E denotes the total mechanical energy, T the kinetic energy and V the gravitational potential energy of a satellite, then:

A

E_A > E_B and V_A < V_B

B

E_A > E_B and T_A > T_B

C

E_A < E_B and T_A > T_B

D

E_A > E_B and T_A < T_B

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2

2007 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2007

The lateral-directional characteristic equation for an airplane gave the following set of roots: λ_1 = -0.6, λ_2 = -0.002, λ_3,4 = -0.06 ± j1.5, where j = √-1. The damping ratio corresponding to the Dutch-roll mode will be

A

0.04

B

0.66

C

0.35

D

0.18

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3

2007 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2007

The on-board rocket motor of a satellite of initial mass 2000 kg provides a specific impulse of 280 seconds. If this motor is fired to give a speed increment of 500 m/s along the direction of motion, the mass of propellant consumed is:

A

685 kg

B

333 kg

C

1666 kg

D

167 kg

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4

2008 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2008

To transfer a satellite from an elliptical orbit to a circular orbit having radius equal to the apogee distance of the elliptical orbit, the speed of the satellite should be

A

increased at the apogee

B

decreased at the apogee

C

increased at the perigee

D

decreased at the perigee

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5

2008 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2008

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

A

Kinetic energy

B

Product of speed and radial distance from the center of the earth

C

Rate of area swept by the radial vector from the center of the orbit

D

Rate of area swept by the radial vector from the center of the earth

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6

2008 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2008

In the definition of the aircraft Euler angles \(\phi\) (roll), \(\theta\) (pitch), and \(\psi\) (yaw), the correct sequence of rotations required to make the inertial frame coincide with the aircraft body frame is

A

first \(\psi\) about z axis, second \(\theta\) about y axis, third \(\phi\) about x axis

B

first \(\theta\) about y axis, second \(\phi\) about x axis, third \(\psi\) about z axis

C

first \(\phi\) about x axis, second \(\theta\) about y axis, third \(\psi\) about z axis

D

first \(\psi\) about z axis, second \(\phi\) about x axis, third \(\theta\) about y axis

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7

2009 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2009

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

A

the working life of the on-board electronic circuitry

B

the time it takes for its orbit to decay due to atmospheric drag

C

the quantity of on-board fuel available for station-keeping

D

the number of meteorite impacts that the satellite structure can withstand before breaking up

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8

2009 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2009

Let \(M_0\) be the total mass of a single stage rocket, \(M_P\) be the total mass of propellant, \(M_L\) be the mass of payload carried by the rocket and \(M_S\) be the mass of inert structural components. If \(I_{sp}\) is the specific impulse of the propulsion system (in seconds) and \(g\) is the acceleration due to gravity, then the maximum velocity that can be attained by the rocket vehicle in the absence of gravity and atmospheric drag is given by

A

\(g I_{sp} \ln \left( \frac{M_0}{M_P} \right)\)

B

\(g I_{sp} \ln \left( \frac{M_0}{M_L + M_S} - 1 \right)\)

C

\(g I_{sp} \ln \left( \frac{M_0}{M_S} \right)\)

D

\(g I_{sp} \ln \left( \frac{M_0}{M_0 - M_P} \right)\)

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9

2009 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2009

An airplane flying at 100 m/s is pitching at the rate of 0.2 deg/s. Due to this pitching, the horizontal tail surface located 4 metres behind the centre-of-mass of the airplane will experience a change in angle of attack, which is

A

0.01 deg

B

0.008 deg

C

0.04 deg

D

0.004 deg

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10

2009 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2009

The linearized dynamics of an aircraft (which has no large rotating components) in straight and level flight is governed by the equations \[\frac{d\vec{x}}{dt} = \begin{bmatrix} [A] & [B] \\ [C] & [D] \end{bmatrix} \vec{x}\] where \(\vec{x} = [u \; w \; q \; \theta \; v \; p \; r \; \phi]^T\), \([\;]^T\) represents the transpose of a matrix, \([A], [B], [C]\) and \([D]\) are 4×4 matrices and \([0]\) is the 4×4 null matrix. Which of the following is true ?

A

\([A] \neq [0]; \; [B] \neq [0]; \; [C] = [0]; \; [D] \neq [0]\)

B

\([A] = [0]; \; [B] \neq [0]; \; [C] \neq [0]; \; [D] = [0]\)

C

\([A] \neq [0]; \; [B] = [0]; \; [C] = [0]; \; [D] \neq [0]\)

D

\([A] \neq [0]; \; [B] = [0]; \; [C] \neq [0]; \; [D] = [0]\)

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11

2009 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2009

The velocity vector of an aircraft along its body-fixed axis is given by \(\vec{V} = \begin{bmatrix} u \\ v \\ w \end{bmatrix}\). If \(V\) is the magnitude of \(\vec{V}\), \(\alpha\) is the angle of attack and \(\beta\) is the angle of sideslip, which of the following set of relations is correct ?

A

\(u = V \sin \beta \cos \alpha; \; v = V \sin \beta; \; w = V \cos \beta \sin \alpha\)

B

\(u = V \cos \beta \cos \alpha; \; v = V \sin \beta; \; w = V \cos \beta \sin \alpha\)

C

\(u = V \cos \beta \cos \alpha; \; v = V \sin \beta; \; w = V \sin \beta \sin \alpha\)

D

\(u = V \cos \beta \cos \alpha; \; v = V \sin \beta; \; w = V \cos \beta \sin \alpha\)

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12

2010 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2010

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

A

a maximum when the satellite is farthest from the earth

B

a constant

C

proportional to the speed of the satellite

D

proportional to the square of the speed of the satellite

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13

2010 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2010

A uniform cross-section rigid rod of mass \(m\) and length \(l\) is hinged at its upper end and suspended like a pendulum. Its natural frequency for small oscillations is

A

\(\sqrt{\frac{g}{2l}}\)

B

\(\sqrt{\frac{g}{l}}\)

C

\(\sqrt{\frac{2g}{l}}\)

D

\(\sqrt{\frac{3g}{2l}}\)

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14

2011 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2011

For an airplane to be statically stable, its centre of gravity must always be

A

ahead of wing aerodynamic centre

B

aft of the wing aerodynamic centre

C

ahead of neutral point

D

aft of neutral point

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15

2011 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2011

An elliptic orbit has its perigee at 400 km above the Earth’s surface and apogee at 3400 km above the Earth’s surface. For this orbit, the eccentricity and semi-major axis respectively are (assume radius of Earth = 6400 km)

A

0.18 and 8300 km

B

0.18 and 1900 km

C

0.22 and 8300 km

D

0.22 and 1900 km

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16

2012 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2012

The maximum distance that the centre of gravity can be behind aerodynamic centre without destabilizing the wing-tail combination is

A

0.4 m

B

1.4 m

C

2.4 m

D

3.4 m

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17

2014 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2014

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 ______.

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18

2016 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2016

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, \(\mu_E\) (GM=Gravitational constant × Earth mass) = 3.986×10⁵ km³/s²). The satellite

A

forms a circular orbit.

B

forms an elliptic orbit.

C

escapes from Earth’s gravitational field.

D

falls back to earth.

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19

2017 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2017

The period of revolution of earth about the sun is 365.256 days, approximately. The semi-major axis of the earth’s orbit is close to 1.4953 x 10¹¹ m. The semi-major axis of the orbit of Mars is 2.2783 x 10¹¹ m. The period of revolution of Mars, about the sun, is ________ Earth days (in three decimal place)

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20

2018 · Aerospace Engineering · Flight Mechanics & Space Dynamics · Space Dynamics

Aerospace Engineering (AE) 2018

The tangential velocity component ‘\( V \)’ of a spacecraft, which is in a circular orbit of radius ‘\( R \)’ around a spherical Earth (\( \mu = GM \) → gravitational parameter of Earth) is given by the following expression.

A

\(V = \sqrt{\frac{\mu}{2R}} \)

B

\(V = \sqrt{\frac{\mu}{R}} \)

C

\(V = \frac{2\pi R}{\sqrt{\mu}} \)

D

\(V = \frac{2\pi}{\sqrt{\mu R^2}} \)

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