GravitationClass 10 Science Part 1 Chapter 1 Notes – Maharashtra Board

Summary: Gravitation

Every object in the universe pulls every other object towards itself. Newton realised this when he wondered why apples always drop straight down. He guessed that the same pull of the earth that brings an apple down also keeps the moon moving around us. This pull is called gravitation, and it is the main idea of this chapter.

Anything moving in a circle needs a force pointing to the centre, called the centripetal force. Kepler had already found three rules for how planets move around the Sun by studying careful records of their positions. Newton used these rules, especially the third one, to show that the force on a planet must fall off as the square of its distance from the Sun.

This led to Newton's universal law of gravitation: the force between two masses is proportional to the product of the masses and inversely proportional to the square of the distance between them. The constant G is tiny, so the pull between two people is too small to notice, but the huge mass of the earth makes its pull strong.

The earth's pull gives every falling object the same acceleration, g, about 9.8 m/s² near the surface. g is a little more at the poles than at the equator, and it becomes smaller as we go up or deep down. Mass stays the same everywhere, but weight (mg) changes from place to place, which is why we would weigh much less on the moon.

An object moving only under gravity is in free fall, and we can use the equations of motion with a = g. Throw something fast enough, about 11.2 km/s from the earth, and it never comes back. That speed is the escape velocity, and rockets going to the moon or Mars must cross it.

Key points to remember

• Gravitation is a universal force of attraction that acts between any two objects in the universe.
• An object moving in a circle needs a centripetal force directed towards the centre; its magnitude is mv²/r.
• If the centripetal force stops, the object flies off along the tangent to the circle.
• Kepler's laws: orbits are ellipses with the Sun at one focus; equal areas are swept in equal times; T² is proportional to r³.
• Newton's law: F = G m₁m₂/d². Doubling one mass doubles F; doubling the distance makes F one-fourth.
• G = 6.67 × 10^-11 N m² kg^-2; it was first measured by Henry Cavendish and is the same everywhere in the universe.
• Acceleration due to gravity on the earth's surface is g = GM/R² ≈ 9.8 m/s²; it does not depend on the mass of the falling object.
• g is highest at the poles (9.832 m/s²) and lowest at the equator (9.78 m/s²); it decreases with height and with depth, and is zero at the earth's centre.
• Mass is a scalar measured in kg and stays constant everywhere; weight W = mg is a vector force measured in newton and changes with g.
• On the moon g is about 1/6 of the earth's value, so weight there is about 1/6 of the weight on the earth.
• Free fall means motion under gravity alone: v = gt, s = ½gt², v² = 2gs. True free fall is possible only in vacuum.
• Gravitational potential energy at height h is −GMm/(R + h); it is taken as zero at infinite distance.
• Escape velocity v_esc = √(2GM/R) = √(2gR); for the earth it is about 11.2 km/s.
• Astronauts feel weightless because they and their spacecraft are in free fall together, not because g is zero there.

Gravitation – Notes

1. Gravitation: Newton's big idea

• Newton noticed that apples always drop straight down, never sideways. He concluded that the earth pulls them towards its centre.
• The line from the apple to the earth's centre is the vertical, so a falling object moves vertically downward.
• He then asked: if the earth pulls apples at the top of a tree, does the pull also reach the moon, the planets and the Sun? The answer turned out to be yes.
• So gravitation is a universal force. It acts between a mango and the earth, between the earth and the moon, and between the Sun and every planet.
• Recall: a force can change the speed of an object, its direction of motion, or both.
• Newton explained Kepler's laws mathematically and also invented calculus and built the first reflecting telescope.

2. Circular motion and centripetal force

• Whirl a stone tied to a string. Your hand keeps pulling the stone towards the centre of the circle through the string.
• This centre-directed force needed for circular motion is called the centripetal force. Centripetal means centre-seeking.
• If you let go of the string, the force vanishes and the stone shoots off along the tangent, because that was the direction of its velocity at that instant.
• A coin on a spinning plate flies off along the tangent for the same reason.
• The moon's direction keeps changing as it goes round the earth, so a force must act on it all the time. This force is the earth's gravitational pull towards its centre.
• In the same way, the Sun's gravitational pull acts as the centripetal force that keeps the planets in their orbits.

3. Kepler's laws of planetary motion

• Johannes Kepler studied the planetary positions recorded by Tycho Brahe and found three rules that planets follow.
• An ellipse is a stretched circle with two focal points. For any point on it, the sum of its distances from the two foci is constant.
• First law: The orbit of a planet is an ellipse with the Sun at one of the foci.
• Second law: The line joining the planet and the Sun sweeps equal areas in equal intervals of time. So a planet moves faster when it is closer to the Sun and slower when it is farther away.
• Third law: The square of a planet's period of revolution is directly proportional to the cube of its mean distance from the Sun, T² ∝ r³, or T²/r³ = K (constant).
• Kepler only described how planets move. He could not explain why. Newton later used the third law to discover the inverse square law.

4. Newton's universal law of gravitation

• Law: Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
• G is the universal gravitational constant. Its value is the force between two 1 kg masses kept 1 m apart, 6.67 × 10^-11 N m² kg^-2.
• For spheres, the force acts along the line joining their centres and d is the distance between the centres. For irregular bodies, we use their centres of mass.
• Centre of mass is the point where the whole mass of a body can be imagined to be concentrated. For a uniform sphere it is the geometric centre.
• Why inverse square? For a planet in a circular orbit, F = mv²/r and v = 2πr/T, so F = 4π²mr/T². Using T² = Kr³ gives F = (4π²m/K) × 1/r², so F ∝ 1/r².
• Gravity is the weakest force in nature, but planets and stars have enormous masses, so gravity controls the motion of the whole universe.
• You and your friend on the next bench also attract each other, but the force is so small that friction easily cancels it.
• Tides: the moon's pull raises the sea water facing it, giving high tide there. Places at 90° from it get low tide. Each coastal place, like Mumbai, sees two high and two low tides a day.

5. Earth's gravitational force and acceleration due to gravity (g)

• The earth's centre of mass is at its centre, so its pull on every nearby object points towards the centre, that is, vertically downward.
• A stone thrown up slows down because this pull acts opposite to its motion. Its speed becomes zero at the top, and then it falls back.
• By Newton's second law, the earth's pull produces an acceleration called the acceleration due to gravity, g. It is a vector pointing towards the earth's centre.
• Equating mg = GMm/r² gives g = GM/r². On the surface, r = R, so g = GM/R².
• With M = 6 × 10²⁴ kg and R = 6.4 × 10⁶ m, g works out to about 9.77 m/s², usually taken as 9.8 m/s².
• g depends only on the mass and radius of the earth, not on the falling object. So a cricket ball and a brick have the same g at a place.
• An apple pulls the earth with an equal force, but the earth's mass is so huge that its acceleration is negligible.
• The moon and satellites are pulled by the earth too, but their sideways orbital speed keeps them going round instead of falling in.

6. Variation in the value of g

• Along the surface: the earth bulges at the equator and is flatter at the poles because of its rotation. R is largest at the equator, so g is least there (9.78 m/s²) and greatest at the poles (9.832 m/s²).
• With height: r increases, so g decreases. For an aeroplane 10 km up, the change is negligible, but at satellite heights it is large (about 8.7 m/s² at 400 km and only 0.225 m/s² at 35,700 km).
• With depth: r decreases, but the mass of the earth below you that pulls you also decreases. The overall effect is that g decreases as we go deeper.
• At the centre of the earth, mass pulls equally from all sides, so g becomes zero.
• Different planets and moons have different M and R, so their g values differ. On the moon g is about 1/6 of the earth's value.
• So, with the same push, you could jump about 6 times higher on the moon.

7. Mass and weight

• Mass is the amount of matter in a body. It is a scalar, measured in kg, and it is the measure of inertia. It is the same on the earth, the moon or Mars.
• Weight is the force with which the earth (or a planet) attracts a body. W = mg. Being a force, it is a vector measured in newton and directed towards the centre.
• Since g changes from place to place, weight changes, but mass does not.
• In daily life we say 'my weight is 50 kg'. Scientifically that is the mass; the weight is 50 × 9.8 = 490 N.
• A 1 kg mass weighs 9.8 N on the earth.
• A two-pan balance at a kirana shop compares two weights at the same place, so it effectively compares masses.

8. Free fall

• When you hold a stone, your hand balances its weight. When you let it go, gravity is the only force acting, so it falls freely.
• Free fall: motion of an object under the influence of gravity alone.
• In air, friction and buoyant force also act, so true free fall happens only in vacuum.
• For free fall from rest, use u = 0 and a = g in the equations of motion. For an object thrown up, take a = −g because gravity opposes the motion.
• Since g is the same for all objects at a place, a heavy and a light ball dropped together from the same height land together. Galileo is said to have shown this from the tower of Pisa.
• A feather falls slowly in air only because air resistance and buoyancy matter more for it. In vacuum it lands with a stone.
• The time to rise to the top equals the time to fall back from it.
• The moon, satellites and the space station are in free fall around the earth. That is why astronauts and objects inside float, i.e. feel weightless.

9. Gravitational potential energy and escape velocity

• Near the ground, potential energy is mgh, taking the ground as zero. This works only when h is small compared with R.
• For large heights g changes, so we take potential energy as zero at infinite distance, where the earth's pull is zero. Then the potential energy at any finite distance is negative.
• At height h above the earth's surface, potential energy = −GMm/(R + h).
• A ball thrown up with speed u rises to a maximum height u²/2g. More speed means more height.
• Escape velocity is the minimum initial speed with which an object must be projected upward so that it escapes the earth's gravity and never returns.
• Energy conservation: ½mv_esc² − GMm/R = 0 (total energy at infinity). So v_esc = √(2GM/R) = √(2gR).
• For the earth, v_esc = √(2 × 9.8 × 6.4 × 10⁶) ≈ 11.2 km/s. Spacecraft like Chandrayaan must exceed it to leave the earth.
• Escape velocity does not depend on the mass of the object being launched.

Formulas at a glance

Key terms

Gravitation – Flashcards

Read the question, answer it in your head, then tap the card to check. 20 cards.

Gravitation – MCQ Quiz

15 questions. Tap an option — you will see at once if it is right and why.

How to study Gravitation

⏱ About 4 hours over 3 days

1. Day 1 — Ideas and laws (80 min)
   Read the notes on gravitation, centripetal force and Kepler's laws. Write the three Kepler laws and Newton's law in exact words in your notebook. Draw the ellipse and the equal-area orbit figure. Then derive F ∝ 1/r² from F = mv²/r and T² ∝ r³ step by step without looking.
2. Day 2 — g, mass and weight (80 min)
   Derive g = GM/R² and calculate 9.77 m/s² yourself. Make a 3-row table on how g changes with latitude, height and depth with a reason for each. Write a 5-point mass vs weight comparison. Solve the solved examples here without looking at the steps.
3. Day 3 — Free fall and escape velocity (80 min)
   Practise 6–8 free fall numericals using v = gt, s = ½gt², v² = 2gs and a = −g for upward motion. Derive v_esc = √(2gR) using energy conservation. Finish with our 20 flashcards and the 15-question quiz; revise every topic where you went wrong.

✍️ Diagrams to practise

• Stone whirled on a string, showing centripetal force towards the centre and the tangent along which it flies off
• An ellipse with foci F₁ and F₂
• Elliptical orbit of a planet with the Sun at one focus, showing equal areas swept in equal times (Kepler's second law)
• Two masses m₁ and m₂ separated by distance d (Newton's law)
• High and low tides caused by the moon