Johannes Kepler proposed Kepler’s law in the early 1600s. Kepler offered three laws of planetary motion: 

• Kepler first law (The law of orbits): According to the first law, all planets revolve around the sun in an elliptical orbit with the Sun at one focus. Moreover, the sum of the distances of any two planets from two foci is constant. This elliptical orbit causes a change of seasons.
• Kepler’s second law  (The law of equal areas) states that the planet moves faster if it is nearer to the sun, and similarly, its speed decreases with the increase in distance between the sun and the planet.
• Kepler’s third law (The law of periods)- As per the third law of Kepler, the square of the time of revolution is directly proportional to the cube of its semi-major axis.

 T² ∝ a³

The Universal law of gravitation was proposed by Newton. According to this law, every particle present in this universe gets attracted with force. That force is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.

Where F is the gravitational force, G is the gravitational force, and m1 and m2 are the masses of the bodies, and r is the distance between centres of bodies.

The Gravitational Constant

The gravitational constant is represented as G. The gravitational constant is the gravitational force between two different bodies of different masses separated through a unit distance. As it is a universal constant, therefore its value remains the same at every place on earth. 

The value of the gravitational constant is 6.6734 × 10^-11 N m²/kg² globally. 

Acceleration due to gravity of the earth

The acceleration of anybody by the gravitational force is the acceleration due to gravity. It is a vector quantity as it has both directions as well as magnitude. Its SI unit is m/s2, and g denotes the acceleration due to gravity.

The value of acceleration due to gravity on earth and at sea level is 9.8 m/s².

Mathematically, g = GM/r²

Acceleration due to gravity below and above the surface of the earth

The mathematical expression for acceleration due to gravity above the surface of the earth is-

gh= gRE2/(RE+h)2

The mathematical expression for acceleration due to gravity below the surface of the earth is-

gd= g(1−d/RE)

Where g = acceleration due to gravity,

RE= Radius of earth,

H= height of the surface,

And d= depth from the surface.

Gravitational potential energy is the energy of any object by its change in position when present in a gravitational field.

In other words, Gravitational potential energy is the energy stored in a body at that position. The SI unit of Gravitational potential energy is J/Kg, and its dimensional formula is M⁰L²T^-2. The potential energy at infinity is zero. It is represented by ‘U’.

Where m= mass in kilograms

g= acceleration due to gravity

h= height in meters.

Escape speed

The minimum amount of speed of any object which is necessary for the object to escape from the earth’s gravitational field is the Escape speed.

The mathematical expression for the escape speed is derived from the law of conservation of energy. The mathematical expression for the escape speed of spherical bodies such as planets stars is-

Where ve= escape speed

G= universal gravitational constant

M= mass of a massive body

r= distance from centre to object.

The unit of escape speed is metres per second (m.s-1), and the dimensional formula is  M⁰L¹T^-1.

Earth possesses only a single natural satellite, i.e. the moon. The moon revolves around the sun and is a non-luminous object. It gets its light via the Sun. Moreover, some other objects resonate with earth and are therefore termed NEOs (Near Earth Objects). They are referred to as the second moon of the blue planet, i.e. the Earth.

The artificial earth satellites are any temporary or permanent objects revolving around the earth. The first-ever idea of an artificial satellite was given by Sir Isaac Newton. The satellite should fall on the earth’s surface, but its momentum causes it to descend along a curve path.

Artificial earth satellites are Sputnik, Landsat 8, Envisat, Aqua, Quickboard, etc.

The energy of an orbiting satellite

The energy of an orbiting satellite is always negative, which states that the satellite cannot escape the earth’s gravity. The total energy of the orbiting satellite is the sum of its potential and kinetic energy.

T.E. = K.E. + P.E.

Geostationary and polar satellites

Geostationary satellites are satellites that rotate around the earth in the same plane (equatorial plane) with the same speed and direction as the earth itself. These types of satellites are synchronous and are used for communication purposes. The first-ever geostationary satellite was Telstar.

The polar satellite revolves in a different orbit that is perpendicular to the equatorial orbit and passes through different points on earth. The polar satellites are helpful in the scanning of other parts of the Earth. SPOT is an example of a polar satellite.

Weightlessness

It is the sensation of complete or almost complete lack of any sensation of weight. It happens with astronauts orbiting the earth. It happens when you cannot sense the force of gravity. It results due to the absence of any contact forces between two objects. It is also felt by any object at free-fall as there are no-contact forces.

Question 1- What are the three laws of Kepler?

Answer 1- The three laws of Kepler are-

• The first law is the law of Orbit.

• The second law is the law of equal areas.

• The third law is the law of periods.

Question 2- What is the Universal law of gravitation?

Answer 2- The class 11 Physics chapter 8 NCERT solutions have every information regarding the universal law of gravitation. The universal law of gravitation states that every particle present in this universe gets attracted with force. That force is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.

Where F = gravitational force, 

G is the gravitational force, 

And m1 and m2 are the masses of the bodies 

r= distance between centres of bodies.               

Question 3- What are some interesting and important points for class 11 physics Gravitation?

Answer 3- Some important points to remember from the gravitation chapter of class 11 are-

• It is a conservative force and is also the weakest force in nature.
• Gravitational force is applicable for every object of the earth of any shape or size.
• It is independent of the medium between objects.

Question 4- Define satellite?

Answer 4- A satellite refers to any object that revolves around the earth in a definite orbit. It can be a natural or an artificial satellite. Earth has only one natural satellite that is the moon. Some artificial satellites of the earth are Sputnik, Landsat 8, Envisat, Aqua etc.

Question 5- How to prepare for the Gravitation chapter of class 11?

Answer 5- For the beginning, read the whole chapter thoroughly. Firstly master the basics of the chapter, which will play a significant role in further understanding the topics. Highlight all the important points and make your notes which you can quickly revise before the examination. Last but most important, practice as many questions as you can.