Is Gravitation: Kepler's Laws part of the EAPCET Physics syllabus?

Yes. Gravitation: Kepler's Laws is taught in Intermediate first year Physics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.

How many Physics questions are there in EAPCET?

40 of the 160 questions in the Engineering paper are Physics, spread across 30 chapters.

What mistakes do students make in Gravitation: Kepler's Laws?

Using g′ ≈ g(1 − 2h/R) when h is comparable to R — use the exact form g R²/(R + h)² instead. Using h instead of the orbital radius r = R + h in v₀ = √(GM/r) and in Kepler’s law. Thinking escape velocity depends on the mass of the body or the launch direction — it depends only on the planet’s M and R. Treating the total energy of an orbiting satellite as positive — it is −GMm/2r; the kinetic energy is +GMm/2r.

EAPCET Physics · Intermediate first year

Gravitation: Kepler's Laws

Gravitation covers Newton’s law of gravitation, the variation of g, gravitational potential energy, escape and orbital velocity, satellites and Kepler’s laws.

Subject: Physics
Taught in: Intermediate first year
Physics in the paper: 40 of 160 questions

Key formulas and results

$F = \frac{Gm_{1}m_{2}}{r^{2}}$
$g = \frac{GM}{R^{2}}$ ; at height $h \ll R$ , $g' \approx g\left(1 - \frac{2h}{R}\right)$ ; at depth $d$ , $g' = g\left(1 - \frac{d}{R}\right)$
Escape velocity $v_{e} = \sqrt{2GM/R} = \sqrt{2gR} \approx 11.2\ \text{km/s}$ for the earth
Orbital velocity $v_{0} = \sqrt{GM/r}$
Kepler’s third law: $T^{2} \propto r^{3}$
$g$ at height $h$ (exact): $g' = \frac{g}{(1 + h/R)^{2}}$
Effect of the earth’s rotation at latitude $\lambda$ : $g' = g - R\omega^{2}\cos^{2}\lambda$
Field on the axis of a ring: $E = \frac{GMx}{(R^{2} + x^{2})^{3/2}}$ , zero at the centre and maximum at $x = R/\sqrt{2}$
Inside a solid sphere: $E = \frac{GMr}{R^{3}}$ and $V = -\frac{GM(3R^{2} - r^{2})}{2R^{3}}$ ; at the centre $V = -\frac{3GM}{2R}$
Inside a thin spherical shell: $E = 0$ and $V = -GM/R$ everywhere
Field of an infinite line mass of linear density $\lambda$ : $E = \frac{2G\lambda}{r}$
Satellite energies: $\text{KE} = \frac{GMm}{2r}$ , $\text{PE} = -\frac{GMm}{r}$ , total energy $E = -\frac{GMm}{2r}$
Satellite period: $T = \frac{2\pi r}{v_{0}} = 2\pi\sqrt{\frac{r^{3}}{GM}}$

What this chapter covers

Newton’s law of gravitation
Acceleration due to gravity and its variation
Gravitational potential energy
Escape and orbital velocity
Satellites
Kepler’s laws

How it is usually asked

Variation of g with height or depth
Escape and orbital velocity
Energy of a satellite
Kepler’s laws

Understanding Gravitation: Kepler's Laws

Newton’s law of gravitation says every two masses attract with a force proportional to the product of the masses and inversely proportional to the square of the distance between their centres. At the earth’s surface this gives g = GM/R². Going up, g falls because the distance from the centre grows; going down, g falls because less mass lies inside the radius, reaching zero at the centre.

Gravitational potential energy is −GMm/r, negative because the zero is taken at infinity. A satellite in a circular orbit of radius r moves at v₀ = √(GM/r), and its total energy is negative, meaning it is bound. Giving a body the escape velocity √(2GM/R) at the surface makes its total energy zero, so it can just reach infinity. Kepler’s third law, T² ∝ r³, follows directly from these ideas.

EAPCET usually tests the variation of g with height and depth, escape and orbital velocity, the kinetic, potential and total energy of satellites, and Kepler-law ratios. Most of these are ratio questions: write the formula, note which quantities stay fixed, and compare. For example, orbital speed scales as 1/√r and the period as r^(3/2), so doubling the orbit radius increases the period 2√2 times.

Worked example

EAPCET-style question

At what height above the earth’s surface does the acceleration due to gravity become one-fourth of its value at the surface? (Radius of the earth $R = 6400\ \text{km}$ )

(1)6400 km
(2)2400 km
(3)3200 km
(4)12800 km

Solution

At height $h$ , $g' = \frac{gR^{2}}{(R + h)^{2}}$ .
Set $g' = g/4$ : $(R + h)^{2} = 4R^{2}$ , so $R + h = 2R$ .
$h = R = 6400\ \text{km}$ .
The approximation $g' \approx g\left(1 - \frac{2h}{R}\right)$ would give 2400 km, but it is valid only for $h \ll R$ , which is not the case here.

Answer: 6400 km

Shortcuts and results to remember

Neutral point between masses $m_{1}$ and $m_{2}$ a distance $r$ apart lies at $x = \dfrac{r}{1 + \sqrt{m_{2}/m_{1}}}$ from $m_{1}$ .
For a satellite, $\text{KE} = -E$ and $\text{PE} = 2E$ , where $E$ is the total energy.
As the orbit radius increases, orbital speed and KE decrease while the period, PE and total energy increase.
Gravitational potential is greatest (zero) at infinity and negative everywhere else.
Kepler’s second law (equal areas in equal times) is conservation of angular momentum.

Common mistakes to avoid

Using g′ ≈ g(1 − 2h/R) when h is comparable to R — use the exact form g R²/(R + h)² instead.
Using h instead of the orbital radius r = R + h in v₀ = √(GM/r) and in Kepler’s law.
Thinking escape velocity depends on the mass of the body or the launch direction — it depends only on the planet’s M and R.
Treating the total energy of an orbiting satellite as positive — it is −GMm/2r; the kinetic energy is +GMm/2r.

How to prepare it

Escape velocity from the surface is √2 times the orbital velocity close to the surface — a quick check for many options.

Once the formulas feel familiar, test them the way the exam does: practise Gravitation: Kepler's Laws questions chapter-wise, then attempt a full previous year paper to see whether it holds up under a 3-hour timer.

Related Physics chapters

See every chapter in the EAPCET Physics syllabus.

Practise Gravitation: Kepler's Laws chapter-wise

Chapter-wise quizzes show exactly which topics in this chapter you still get wrong — before a full paper does.

Frequently asked questions

Is Gravitation: Kepler's Laws part of the EAPCET Physics syllabus?: Yes. Gravitation: Kepler's Laws is taught in Intermediate first year Physics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.
How should I prepare Gravitation: Kepler's Laws for EAPCET?: Escape velocity from the surface is √2 times the orbital velocity close to the surface — a quick check for many options.
How many Physics questions are there in EAPCET?: 40 of the 160 questions in the Engineering paper are Physics, spread across 30 chapters.
What mistakes do students make in Gravitation: Kepler's Laws?: Using g′ ≈ g(1 − 2h/R) when h is comparable to R — use the exact form g R²/(R + h)² instead. Using h instead of the orbital radius r = R + h in v₀ = √(GM/r) and in Kepler’s law. Thinking escape velocity depends on the mass of the body or the launch direction — it depends only on the planet’s M and R. Treating the total energy of an orbiting satellite as positive — it is −GMm/2r; the kinetic energy is +GMm/2r.