JEE Main 2023 Gravitation Revision Notes

Here are the important topics:

• Kepler’s first law (law of elliptical orbit):

A planet moves around the sun in an elliptical orbit with the sun situated at one of its foci.

• Kepler’s second law (law of areal velocities):

A planet moves around the sun in such a way that its areal velocity is constant.

• Kepler’s third law (law of time period):

A planet moves around the sun in such a way that the square of its period is proportional to the cube of the semi-major axis of its elliptical orbit.

• Law of gravitation by Newton:-

Every particle of matter attracts every other particle with a force that varies directly as the product of masses of two particles and inversely as the square of the distance between them in this universe .

Formula of dimensional of G: G = Fr2/Mm =[MLT-2][L2]/[M2] = [M-1L3T-2]

Gravity from acceleration (g):- g = GM/R2

Variation of g along with altitude:- g' = g(1- 2h/R),  if h<<R. Here Radius of the earth is r and h is the height of the body above the surface of the earth.

Variation of g along with depth:- g' = g(1- d/R). Here g' be the value of acceleration due to gravity at the depth d.

Variation with latitude:-

At poles:- θ = 90°, g' = g

At equator:- θ = 0°, g' = g (1-ω2R/g)

Here ω is the angular velocity.

As g = GMe/Re2 , therefore gpole > gequator

Mass of Gravitational:- m = FR2/GM

Field intensity Gravitational:-

E = F/m

= GM/r2

Weight:- W= mg

On the earth Gravitational intensity (Es):-

Es = 4/3 (πRρG)

Here R is the radius of the earth, G is the gravitational constant and ρ is the density of earth.

Gravitational potential energy (U):- U = -GMm/r

(a) Two particles: U = -Gm1m2/r

(b) three particles: U = -Gm1m2/r12 – Gm1m3/r13 – Gm2m3/r23

Potential Gravitational (V):- V(r) =  -GM/r

On the surface of the earth,

Vs=  -GM/R

Here R is the radius of the earth.

Escape velocity (ve):-

It is described as the least velocity with which a body has to be be projected vertically upward so that it may just escape the gravitational pull of the earth.

ve = √2GM/R

or, ve = √2gR = √gD

Here R is the radius and D is the diameter of the earth

Scape velocity (ve) in terms of earth’s density:- ve = R√8πGρ/3

Orbital velocity (v0):-

v0 = √GM/r

If a satellite  of mass m revolves in a circular orbit around the earth of radius R and h be the height of the satellite above the surface of the earth, then,

r = R+h

So, v0 = √MG/R+h = R√g/R+h

In the case of a satellite, orbiting very close to the surface of the earth, then orbital velocity will be,

v0 = √g

• Relation between escape velocity ve and orbital velocity v0:- v0= ve/√2  (if h<<R)

• Time period of Satellite:- Time period of a satellite is the time taken by the satellite to complete one revolution around the earth.

T = 2π√(R+h)3/GM = (2π/R)√(R+h)3/g

If h<<R, T = 2π√R/g

Height of satellite:- h = [gR2T2/4π2]1/3 – R

Energy of satellite:-

Kinetic energy, K = ½ mv02 = ½ (GMm/r)

Potential energy, U = - GMm/r

Total energy, E = K+U

= ½ (GMm/r) + (- GMm/r)

= -½ (GMm/r)

Gravitational force in terms of potential energy:- F = – (dU/dR)

Acceleration on moon:-

gm = GMm/Rm2 = 1/6 gearth 

Here Mm is the mass of the moon and Rm is the radius of the moon. 

Some Simple Tips to Prepare for JEE Main

• Start with finding out the latest syllabus. Bifurcate them subject-wise and class-wise. Check the exam pattern and weightage of every chapter in each subject. Although you need to give equal importance to every topic, write down the percentage weightage and the number of questions that tend to appear from those topics besides the list of chapters in the syllabus.

• Your books, especially NCERT books, should be your primary source of study. Study the chapters in and out. Make small notes of the important laws, definitions, and formulae so that you can take a quick glance when you desire.

• Once you think you have studied and understood the chapters well, solve questions from previous years and sample papers. Time yourself while solving the questions to keep track of your speed and accuracy.

• Take as many mock tests as you can so that you can assess your level of preparedness and discover the areas you need to focus on more. Learn from your mistakes and revise the topics again and again.

• Keep sufficient time for revision! This does not just apply to your preparation but also while you are taking the actual JEE Main exam. Revision is a vital time when you can rectify silly errors and save a lot of marks.

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