Physics

Gravitation and Orbital Mechanics

500 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 physics science in daily life introduction to science contribution of physics in technology and society physics in relation to other sciences

Geo-stationary satellite revolves at ____________.

  1. Any height

  2. Fixed height

  3. Height above pole

  4. Height which depends upon its mass
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A geostationary satellite orbits the Earth at a specific altitude (approximately 35,786 km) above the equator, allowing it to remain fixed relative to a point on the Earth's surface.

Multiple choice physics the universe types of galaxies galaxies constellations

Solar system revolves around the Milky Way galaxy with the speed of:

  1. $2.5$ $\text{light years} / s$
  2. $250\ km/s$
  3. $250\ \text{light years} / s$
  4. $2.5\ km/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The Solar System is travelling at an average speed of $250\ km/s$ on its trajectory around the galactic center.
The Earth belongs to Milky Way galaxy.
Multiple choice physics constellations and galaxies light year evolution and end stages of stars in the world of stars

If light travelling from the Sun at the speed of $3\times {10}^{8}\ m/s$, reach a planet $A$ in $25\ min\  30\ sec$. Then what is the distance between the Sun and the planet? 

(1 light year $=9.461\times {10}^{12}\ km$)

  1. $3$ light minutes
  2. $0.48\times {10}^{-4}$ light year
  3. $1.96\times {10}^{4} $light year
  4. $2.5$ light years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Speed of light $=3\times {10}^{8}\ m/s$
Time taken $=25\ min\ 30\ sec = 1530\ sec$
By using the formula, 
$Speed=\cfrac{Distance}{Time}$
or 

$Distance=Speed \times Time$ $=3\times {10}^{8}\times 1530$ $=4590\times {10}^{8}\ m$ $=4590\times {10}^{5}\ km$
Distance (in light year) $=\cfrac{4590\times {10}^{5}}{9.461\times {10}^{12}}$ $=0.48\times {10}^{-4}$ light year.

Multiple choice physics our solar system planets of the solar system solar system and sun introduction to solar system

Planets do not collide with each other because

  1. those are of different sizes

  2. those have fixed, non-intersecting individual orbits

  3. those rotate from West to East

  4. each planet has a different time of rotation and revolution
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Every planet is at a different distance from the Sun and has a fixed orbit in which it revolves around the Sun. The Sun"s gravitational force holds the planets in this place and they do not collide with each other as their orbits are non-intersecting.

Multiple choice physics our solar system planets of the solar system solar system and sun introduction to solar system
The time taken by a planet for one complete revolution changes according to:

  1. its distance from the Sun

  2. its size

  3. its mass

  4. the shape of its orbit
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

As the distance between the Sun and the planet increases, the time taken by the planet to complete one revolution around the Sun also increases as the planet has to cover more distance as compared to the planets before it.

Multiple choice physics our solar system planets of the solar system solar system and sun introduction to solar system

The earth revolves about the sun in an elliptical orbit with mean radius $9.3 \times 10^7\ m$ in a period of $1$ year. Assuming that there are no outside influences, then

  1. The earth's kinetic energy remains constant.

  2. The earth's angular momentum remains constant.

  3. The earth's potential energy remains constant.

  4. All the statements above are correct.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

As the earth orbits the sun in an elliptical path, central gravitational force exerts zero torque about the sun, which keeps the angular momentum constant. Speed and potential energy vary along the orbit.

Multiple choice physics our solar system planets of the solar system solar system and sun introduction to solar system

Two plates move around the Sun. The periodic times and the mean radii of the orbits are $T _1, T _2$ and $r _1, r _2$ respectively. The ratio $\dfrac{T _1}{T _2}$ is equal to.

  1. $\left (\dfrac{r _1}{r _2} \right)^{\dfrac{1}{2}}$
  2. $\left (\dfrac{r _1}{r _2} \right)$
  3. $\left (\dfrac{r _1}{r _2} \right)^{2}$
  4. $\left (\dfrac{r _1}{r _2} \right)^{\dfrac{3}{2}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Kepler's Third Law of Planetary Motion states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit (T^2 proportional to r^3). Therefore, T1/T2 = (r1/r2)^(3/2).

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

A satellite is orbiting the earth at 17,500 MPH, a rock is released from the satellite. Identify what would happen to the rock.

  1. The rock would orbit the earth at a velocity of 17,500 MPH next to the satellite

  2. As the rock cannot generate its own force, it will slow down

  3. Gravity will pull the rock towards earth

  4. As the rock is smaller than the satellite, it will accelerate and orbit at a greater velocity

  5. As the rock is smaller than the satellite, its inertia will pull it further away from earth
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The satellite moves in the orbit with a constant speed in circular path, with centripetal acceleration being provided by the force of gravity on it.

The radius of orbit can be found by 
$\dfrac{GMm}{R^2}=\dfrac{mv^2}{R}$
$\implies R=\dfrac{GM}{v^2}$ which is independent of the mass of projectile(satellite)
When the stone is released from the orbiting satellite, it moves with the same speed. Its mass is much lesser than that of satellite, but the orbital radius is independent of its mass, depending only upon the speed which is same. Thus is would also orbit the earth with same speed in same orbit as that of satellite.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

For satellite in elliptical orbit which of the following quantities does not constant 

  1. Angular momentum

  2. Momentum

  3. Areal velocity

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

In an elliptical orbit, the gravitational force is central, so angular momentum and areal velocity (Kepler's second law) are conserved. Total energy is also conserved. However, the velocity vector changes in both magnitude and direction, so linear momentum is not constant.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

To overcome the effect weightlessness in an artificial satellite

  1. the satellite is rotated around its axis with compartment of astronaut at the centre of the satellite.

  2. the satellite is shaped like wheel.

  3. the satellite is rotated around and around till weightlessness disappears.

  4. the compartment of astronaut is kept on the periphery of rotating wheel like satellite.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

On a rotating body, as we move away from center of rotation the centrifugal force increases. So, the centrifugal force is maximum at the periphery of a rotating wheel. Thus, having the astronaut room there would solve some of the weightlessness problem in satellite.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

The radius and mean density of the earth are $R$ & $p$ respectively . the critical orbital speed of a satellite for a low altitude orbit is 

  1. $ 2 \sqrt {\dfrac { \pi G p}{3R}} $
  2. $ 2R \sqrt {\dfrac { \pi Gp}{3}} $
  3. $ 2R \sqrt {\dfrac {2 \pi G p}{3}} $
  4. $ 2R \sqrt {\dfrac { \pi Gp}{2}} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Orbital speed v = sqrt(GM/R). Mass M = density * volume = p * (4/3) * pi * R^3. Substituting M: v = sqrt(G * p * 4/3 * pi * R^3 / R) = sqrt(4/3 * pi * G * p * R^2) = 2R * sqrt(pi * G * p / 3).

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

A body is suspended from a spring balance kept in a satellite The reading of the balance is $\displaystyle W _{1}$ when the satellite goes in an orbit of radius $R$ and is $\displaystyle W _{2}$ when it goes in an orbit of radius $2R$ Then

  1. $\displaystyle W _{1}=W _{2}$
  2. $\displaystyle W _{1}< W _{2}$
  3. $\displaystyle W _{1}>W _{2}$
  4. $\displaystyle W _{1}\neq W _{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Answer is A.

The reading on the spring balance is independent of the radius and thus both weight will be the same. Also, there is no gravitational force acting on a satellite.
 
Hence, ${ W } _{ 1 }={ W } _{ 2 }$.

Multiple choice physics gravitation: planets and satellites weightlessness application of newton's law of motion escape velocity

Consider a satellite going round the earth in a circular orbit. Which of the following statements is wrong?

  1. It is a freely falling body

  2. It is a moving with constant speed.

  3. It is acted upon by a force directed away from the centre of the earth which counter- balances the gravitational pull.

  4. Its angular momentum remains constant.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Satellite going around the earth in circular orbit is in state of free fall, and its speed is constant. speed depends upon the radius of orbit of satellite.

So Its angular velocity($\omega=v\times r$) is also constant and thus angular momentum $m\omega$ is also constant.
Apart from gravitational pull of the earth, there is no other force on the satellite. So option C is incorrect.