Table of contents | |
Introduction | |
Mass and Weight | |
Planets | |
Satellites |
Gravitation is the phenomenon where every massive body attracts every other massive body due to their masses.
Newton’s Law of Gravitation
Acceleration Due to Gravity:
The uniform acceleration a freely falling body experiences due to Earth's gravitational pull is given by g = GM/R2, where M is Earth's mass and R is its radius. The value of g near Earth's surface is approximately 9.8 m/s2, though it varies slightly with location. Gravity is the weakest force in nature, approximately 1036 times weaker than electrostatic force and 1038 times weaker than nuclear force.
Factors Affecting Acceleration Due to Gravity:
Shape of Earth: Earth is not a perfect sphere; its equatorial radius is about 42 km greater than at the poles. Consequently, gravity is strongest at the poles and weakest at the equator, with a difference of 3.4 cm/s2.
Rotation of Earth: The rotation affects gravity. If ω is Earth's angular velocity, the adjusted acceleration due to gravity at a location is g′ = g − Rω2 cos2λ, where λ is the latitude. At the poles (λ = 90∘), there's no effect, while at the equator (λ = 0∘), the effect is maximum.
Effect of Altitude: The value of g at height h from the earth’s surface is given by
Therefore, g decreases with altitude.
Effect of Depth: The value of g at depth from the earth’s surface is given by
Therefore, g decreases with depth and becomes zero at centre of the earth.
Gravitational Field and Potential:
Weight in a Lift:
Weight on the Moon: Due to the Moon's smaller mass and radius compared to Earth, the gravitational force on the Moon's surface is weaker, approximately g/6.
Definition: Planets are celestial bodies that orbit the Sun. Our solar system has eight recognized planets, following the reclassification of Pluto as a dwarf planet. The planets, listed in order of increasing distance from the Sun, are:
Kepler’s Three Laws are:
Definition: A satellite is a celestial body that orbits a planet. For example, the Moon is a natural satellite of Earth. Satellites can also be artificial:
Geostationary Satellites:
Polar Satellites:
The time period of a satellite is the duration it takes to complete one full revolution around Earth.
Escape VelocityThe minimum velocity with which when an object is thrown vertically upwards from the earth’s surface just crosses the earth’s gravitational field and never returns. Escape velocity (ve)
Its value on earth’s surface is 11.2 km/s.
Escape velocity = √2 (orbital speed of a satellite when it is near the earth’s surface) ve = √2 v0
Therefore, when orbital speed of a satellite is increased by √2 times (41%), then it will escape from its orbit.
Geotropism: The response of plants to gravity. Plants exhibit two primary effects due to gravity:
Seasonal Variation in Day and Night: The change in the length of daytime and nighttime across seasons is a result of Earth's axial tilt and its orbit around the Sun.
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1. What is the difference between mass and weight? |
2. How does gravity affect the planets in our solar system? |
3. How do satellites stay in orbit around a planet? |
4. How does the concept of gravitation impact the movement of objects in space? |
5. How does the mass of a planet affect its gravitational pull? |
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