GRAVITATION
Science
Gravitation is a natural phenomenon by which all objects having mass attract each other.
It is a universal force acting between any two bodies in the universe.
Gravitation governs the motion of planets, satellites, stars, galaxies and even falling of objects on Earth.
2. UNIVERSAL LAW OF GRAVITATION
Proposed by Sir Isaac Newton in 1687.
Statement:
Every object in the universe attracts every other object with a force which is:
• Directly proportional to the product of their masses
• Inversely proportional to the square of the distance between their centres
Mathematical Expression:
F ∝ (m1 × m2)
F ∝ 1 / r²
Combining:
F = G × (m1 × m2) / r²
Where:
F = gravitational force
m1, m2 = masses of two objects
r = distance between their centres
G = universal gravitational constant
Value of G:
G = 6.67 × 10⁻¹¹ N m² kg⁻²
3. IMPORTANCE OF UNIVERSAL LAW OF GRAVITATION
Explains:
• Motion of planets around the Sun
• Motion of the Moon around the Earth
• Falling of objects towards the Earth
• Tides due to Moon and Sun
• Binding force of atmosphere to Earth
4. FREE FALL
When an object falls towards the Earth only under the influence of gravity, it is said to be in free fall.
In free fall, acceleration of the object is constant and equal to acceleration due to gravity (g).
5. ACCELERATION DUE TO GRAVITY (g)
Acceleration acquired by an object due to Earth’s gravitational pull.
Value:
g = 9.8 m/s² on Earth (average)
Characteristics:
• Same for all objects irrespective of mass
• Directed towards the centre of Earth
• Decreases with altitude and depth
• Maximum at poles and minimum at equator
6. DIFFERENCE BETWEEN MASS AND WEIGHT
Mass:
• Amount of matter in a body
• Constant everywhere
• SI unit: kilogram (kg)
• Scalar quantity
• Measured using beam balance
Weight:
• Gravitational force acting on a body
• Changes with location
• SI unit: Newton (N)
• Vector quantity
• Measured using spring balance
Relation:
Weight (W) = m × g
7. MOTION OF OBJECTS UNDER GRAVITY
Equations of motion under gravity (for downward motion):
v = u + gt
s = ut + ½ gt²
v² = u² + 2gs
Where:
u = initial velocity
v = final velocity
t = time
s = displacement
g = acceleration due to gravity
For upward motion, g is taken as negative.
8. GRAVITATIONAL POTENTIAL ENERGY
Energy possessed by an object due to its position in a gravitational field.
Near Earth’s surface:
PE = mgh
Where:
m = mass
g = acceleration due to gravity
h = height above ground
9. GRAVITATIONAL POTENTIAL AND FIELD
Gravitational Field:
Region around a mass where another mass experiences gravitational force.
Gravitational Potential:
Work done in bringing a unit mass from infinity to a point in a gravitational field.
10. ESCAPE VELOCITY
Minimum velocity required by an object to escape Earth’s gravitational pull without further propulsion.
Formula:
Escape velocity (ve) = √(2GM / R)
For Earth:
ve ≈ 11.2 km/s
Where:
G = gravitational constant
M = mass of Earth
R = radius of Earth
11. ORBITAL VELOCITY
Velocity required by a satellite to revolve around Earth in a circular orbit.
Formula:
vo = √(GM / R)
For Earth:
vo ≈ 7.9 km/s
12. SATELLITES
A satellite is an object that revolves around a planet.
Types:
• Natural satellite – Moon
• Artificial satellites – INSAT, IRS, GPS, NAVIC
Uses of Artificial Satellites:
• Communication
• Weather forecasting
• Navigation
• Remote sensing
• Defence and surveillance
13. GEOSTATIONARY SATELLITE
A satellite which appears stationary relative to Earth.
Characteristics:
• Orbits in equatorial plane
• Time period = 24 hours
• Height ≈ 36,000 km above Earth
• Used for communication and weather monitoring
14. POLAR SATELLITE
• Orbits from pole to pole
• Low altitude
• Covers entire Earth due to Earth’s rotation
• Used for remote sensing and mapping
15. THRUST AND PRESSURE
Thrust:
Force acting perpendicular to a surface.
Pressure:
Force per unit area.
Formula:
Pressure = Force / Area
SI unit: Pascal (Pa)
16. BUOYANCY
Upward force exerted by a fluid on an object immersed in it.
Causes:
• Pressure difference between upper and lower surfaces of object
17. ARCHIMEDES’ PRINCIPLE
Statement:
When a body is immersed fully or partially in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by it.
Applications:
• Floating of ships
• Submarines
• Lactometers
• Hydrometers
18. CONDITIONS FOR FLOATING AND SINKING
• If density of object < density of fluid → floats
• If density of object > density of fluid → sinks
• If densities are equal → remains suspended
19. RELATIVE DENSITY
Ratio of density of a substance to density of water.
Relative Density = Density of substance / Density of water
No unit.
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Subject: Science
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