RBSE Class 11 Physics Notes Chapter 8 Gravitation

These comprehensive RBSE Class 11 Physics Notes Chapter 8 Gravitation will give a brief overview of all the concepts.

RBSE Class 11 Physics Chapter 8 Notes Gravitation

Solar system:
A small part of the universe in which Sun is covered by eight planets alongwith earth and many satellites alongwith comets, is called a solar system.

Planets:
The celestial bodies revolving around the Sun, are called planets. There are eight planets alongwith earth in our solar system.

Satellites:
The celestial bodies revolving around the planets, are called satellites. For example; moon is only natural satellite of the earth.

Kepler’s laws:

• Each planet revolves around the Sun in elliptical orbits and sun is situated at one of its foci.
• The areal velocity of the planet remains constant i.e., the line joining the Sun and planet sweeps equal areas in equal time.
• Square of time period of the planet is directly proportional to cube of average distance between Sun and the planet.

 

Newton’s law of gravitation:
According to this law, “The gravitational attraction force acting between two bodies is directly proportional to the product of their masses and inversely proportional to the square of distance between them.”

Universal constant of gravity:
Universal constant of gravity is equal to gravitational force acting between two bodies of unit masses and situated a unit distance (i.e., 1 m).

Acceleration due to gravity:
The acceleration produced by gravitational force, is called acceleration due to gravity. It is denoted by g’.

Variation of acceleration due to gravity:

• Value of g decreases with increasing height form the earth’s surface.
• Value of g decreases with increasing depth from the earth’s surface.
• Value of g is maximum at poles and minimum at the equator.

Intensity of gravitational field:
Force acting on unit mass at any point in gravitational field is called the intensity of gravitational field at that point.

Gravitational potential energy:
Gravitational potential energy of a body at any point in gravitational field is equal to work done in bringing the body from infinity to that point.

Gravitational potential:
Work done in bringing unit mass from infinity to any point in gravitational field is called the gravitational potential at that point.

Escape velocity:
The minimum velocity with which a projected body escapes i.e., reaches to infinity and never returns back, is called escape velocity.

Binding energy of a satellite:
The energy required by a satellite for escaping from its orbit forever, is called the binding energy of the satellite.

Goestationary satellite:
The satellite which is been always above a particular part of earth, is called geostationary satellite. Its time of revolution is 24 hours.

→ Kepler’s second law, areal velocity
\(\frac{\Delta \vec{A}}{\Delta t}=\frac{\vec{L}}{2 m}\) = constant

→ Kepler’s third law, T² ∝ r³ or T³ = Kr³

→ Newton’s law of gravitation,
F = \(\frac{G m_1 m_2}{r^2}\)

→ Gravitational acceleration at distance r from the centre of the earth, g = \(\frac{G M_e}{r^2}\) and on the surface of the earth, g = \(\frac{G M_e}{R_e^2}\)

→ Intensity of gravitational field at point situated at a distance r from the centre of the earth
I = \(\frac{G M_e}{r^2}\)
and on the earth's surface I = \(\frac{G M_e}{R_e^2}\)

→ Gravitational acceleration at height h from the earth’s surface.
g' = \(\frac{g}{\left(1+\frac{h}{R_e}\right)^2}\)
If h < < R_e, then g; = g(1 - \(\frac{2 h}{R_e}\))

→ Gravitational acceleration at a depth d from the earth’s surface,
g' = g(1 - \(\frac{d}{R_e}\))

→ Gravitational acceleration on the earth’s surface, at latitude λ,
g' = g - R_eω² cos² λ

→ Gravitational potential energy at distance r from the centre of the earth,
U = -\(\frac{G M_e m}{r}\)

→ Gravitational potential at distance r from the centre of the earth,
V_G = -\(\frac{G M_e}{r}\)

→ Change in gravitational potential energy on going upto height h from the earth’s surface,
ΔU = \(\frac{m g h}{\left(1+\frac{h}{R_e}\right)}\)

→ Velocity of projection v = \(\sqrt{\frac{2 g h}{\left(1+\frac{h}{R_e}\right)}}\)

→ Maximum height attained by a projectile
h = \(\frac{v^2 R_e}{2 g R_e-v^2}\)

→ Relation between gravitational potential and intensity of gravitational field,
V_G = -I × r

→ Orbital velocity of a satellite,
v_o = \(\sqrt{\frac{G M_e}{r}}=\sqrt{\frac{G M_e}{R_e+h}}=\sqrt{\frac{g R_e}{1+\frac{h}{R_e}}}=\sqrt{g R_e}\)
(for h < < R_e)

→ Time period of a satellite,
T = 2 \(\pi \sqrt{\frac{r^3}{G M_e}}=2 \pi \sqrt{\frac{R_e^3}{G M_e}}=\sqrt{\frac{3 \pi}{G \rho}}=2 \pi \sqrt{\frac{R_e}{g}}\)

→ Potential energy of a satellite,
U = -\(\frac{G M_e m}{r}\)

→ Kinetic energy of a satellite,
K = \(\frac{1}{2} \frac{G M_e m}{r}\)

→ Total energy of a satellite,
E_t = -\(\frac{1}{2} \frac{G M_e m}{r}\)

→ Binding energy of a satellite
E_p = \(\frac{1}{2} \frac{G M_e m}{r}\)

→ Escape velocity v_e = \(\sqrt{\frac{2 G M_e}{R_e}}=\sqrt{2 g R_e}\)

→ Relation between escape velocity and orbital speed of a satellite revolving near the earth’s surface,
v_e = v₀√2

→ Solar system:
System of Sun, its planets (eight), their satellites and comets confined to small part of the universe is called solar system.

→ Planets:
Celestial bodies which revolve around the Sun, are called planets e.g. earth is a planet.

→ Satellites:
The celestial bodies which revolve around the planets, are called satellites, e.g. moon is only natural satellite of the earth.

→ Gravitational potential:
Gravitational potential at a point is equal to the work done in bringing unit mass from infinity to that point.

→ Escape velocity:
The minimum velocity with which projecting a body, it escapes and never returns back, is called escape velocity.