Physics

Gravitation and Orbital Mechanics

522 Questions

Gravitation and orbital mechanics focus on planetary motion, elliptical orbits, and satellite deployment. Questions examine astrodynamics fundamentals, including geostationary orbits and perturbation theory. These topics are highly relevant for civil services and specialized technical examinations.

Planetary orbitsSatellite dynamicsGeostationary orbitsPerturbation theoryOrbital eccentricity

Gravitation and Orbital Mechanics Questions

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

The period of rotation of the geostationary satellite is ______ hours.

  1. 12

  2. 24

  3. 6

  4. 48
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A geostationary satellite is an earth-orbiting satellite, placed at an altitude of approximately 35,800 kilometers (22,300 miles) directly over the equator, that revolves in the same direction the earth rotates (west to east). 

At this altitude, one orbit takes $24 hours $, the same length of time as the earth requires to rotate once on its axis. 
The term geostationary comes from the fact that such a satellite appears nearly stationary in the sky as seen by a ground-based observer. 

Hence correct answer is option $B$ 

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

The orbital angular velocity vector of a geostationary satellite and the spin angular velocity vector of the earth are

  1. always in the same direction

  2. always in opposite direction

  3. always mutually perpendicular

  4. inclined at 23 1/2 to each other
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For the satellite to be 'synchronous' with the Earth, its period of revolution should be equal to Earth's rotation. For this, the satellite has to revolve along the direction of Earth's rotation thus their angular velocity vector always point in the same direction.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

A synchronous satellite should be at a proper height moving

  1. From West to East in equatorial plane

  2. From South to North in polar plane

  3. From East to West in equatorial plane

  4. From North to South in polar plane
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For the satellite to be 'synchronous' with the Earth, its period of revolution should be equal to Earth's rotation. For this, the satellite has to revolve along the direction of Earth's rotation that is from West to East.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

A satellite placed in an orbit around Earth with certain speed will revolve in_______ as seen from Earth

  1. A helical path

  2. A circular path

  3. Straight line

  4. A parabolic path
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The centrifugal force acting on the satellite, revolving around the earth with certain velocity, is balanced by the gravitational force acting on it due to earth. The satellite keeps revolving around the earth in circular path of certain radius as seen from the earth.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

Parking orbit for a geostationary satellite is

  1. at 45 degrees north west of equator

  2. is in equatorial plane of earth

  3. in west-east direction.

  4. along the north direction
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Parking orbit for a geostationary satellite is in equatorial plane of earth, since it has to be at rest always with respect to equator

The correct option is option (b)

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

A geostationary satellite is at rest, relative to earth only for points in the 

  1. equitorial plane

  2. plane passing through the poles of the earth

  3. plane along magnetic north and south of the earth

  4. planes that are isoclinic
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A geostationary satellite is at rest, relative to earth only for points in the equitorial plane.

The correct option is (a)

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

Two satellites of masses $m _{1}$ and $m _{2} (m _{1} > m _{2})$ are revolving round the earth in circular orbits of radii $r _{1}$ and $r _{2}(r _{1} > r _{2})$ respectively. Which of the following statements is true regarding their speeds $v _{1}$ and $v _{2}$?

  1. $v _{1} = v _{2}$
  2. $v _{1} < v _{2}$
  3. $v _{1} > v _{2}$
  4. $(v _{1}/r _{1}) = (v _{2}/r _{2})$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Velocity of satellite $=\sqrt { \dfrac { GM }{ R+h }  } $

Now, 
        ${ V } _{ 1 }=\sqrt { \dfrac { GM }{ { r } _{ 1 } }  } $
        ${ V } _{ 2 }=\sqrt { \dfrac { GM }{ { r } _{ 2 } }  } $
As ${ r } _{ 1 }>{ r } _{ 2 }$
So  ${ V } _{ 1 }<{ V } _{ 2 }$

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

An artificial satellite is moving around earth in a circular orbit with speed equal to one fourth the escape speed of a body from the surface of earth. The height of satellite above earth is : ($R$ is radius of earth)

  1. $3R$
  2. $5R$
  3. $7R$
  4. $8R$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let's consider,

$r=$ height  of the satellite above the earth

$R=$ radius of the earth

$G=$ gravitational constant

$g=$ acceleration due to gravity

The escape velocity of a body from the surface of earth,

$v _e=\sqrt{\dfrac{2GM}{R}}$

$\dfrac{1}{4}.v _e=\dfrac{1}{4}\sqrt{\dfrac{2GM}{R}}$. . . . . .(1)

The orbital velocity of the satellite is given by

$v _o=\sqrt{\dfrac{GM}{r}}$. . . . . .(2)

Equation equation (1) and (2), we get

$\sqrt{\dfrac{GM}{r}}=\dfrac{1}{4}\sqrt{\dfrac{2GM}{R}}$

$\dfrac{GM}{r}=\dfrac{1}{16}.\dfrac{2GM}{R}$

$r=8R$

The correct option is D.
Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

Suppose that the moon travels in a circle about the earth at a distance $ 3.84 \times 10^8 m$ once in every 28.3 days and that has a mass of $7.4 \times 10^{22}$ . Then the speed of the moon is most nearly:

  1. $10 m/s $
  2. $10^3 m/s$
  3. $10^5 m/s$
  4. $10^7 m/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed v = 2*pi*r / T. r = 3.84 * 10^8 m, T = 28.3 days = 28.3 * 24 * 3600 seconds approx 2.44 * 10^6 s. v = 2 * 3.14 * 3.84 * 10^8 / 2.44 * 10^6 approx 1000 m/s.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

Satellite is revolving around the earth. If it's radius of orbit is increased to $4$ times the radius of geostationary satellite, what will become its time period ?

  1. $8\ days$
  2. $4\ days$
  3. $2\ days$
  4. $16\ days$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given,
$r _1=r$ 
$r _2=4r$
$T _1=1day$
The time period of the geostationary satellite is given by
$T=2\pi \sqrt{\dfrac{r^3}{Gm _E}}$. . . . . .(1)
where, $G=$ gravitational constant 
From equation (1),
$T\propto \sqrt{r^3}$
$\dfrac{T _2}{T _1}=\sqrt{\dfrac{r _2^3}{r _1^3}}$
$T _2=T _1\sqrt{\dfrac{4r\times 4r\times 4r}{r^3}}=8T _1 days$
$T _2=8\times 1=8days$
The correct option is A.

Multiple choice evs artificial satellite types of artificial satellites geostationary orbits moon and stars in sky

The relay satellite transmits the television programme continuously from one part to another because its : 

  1. Period is greater than the period of rotation of the earth about its axis

  2. Period is less than the period of rotation of the earth about its axis

  3. Period is equal to the period of rotation of the earth about its axis

  4. Mass is less than the mass of earth
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Relay satellite has to forces on the are unstartly suppose if the satellite is stable in space of a certain position, then as the earth rotate satellite can show once one part and later another part which is absorb movement. Therefore the satellite has to revolve around the earth with same angular speed. Therefore the time period of satellite revolution should be same as time period of the rotation of earth and rotation of the satellite should be about axis of earth's rotation. So its period is equal to period of rotation of the earth about its axis.