Gravitation | General Awareness for SSC CGL PDF Download

Introduction

Gravitation is the phenomenon where every massive body attracts every other massive body due to their masses.

Newton’s Law of Gravitation

• The gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
   The universal gravitational constant, G, has a value of 6.67×10⁻¹¹ N m²kg⁻².  
• force is both central and conservative.

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:

1. 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.

2. 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.

3. Effect of Altitude: The value of g at height h from the earth’s surface is given by
   Therefore, g decreases with altitude.

4. 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:

• Gravitational Field: The region around a mass where its gravitational force can be felt.
• Gravitational Potential: The work done to bring a unit mass from infinity to a specific point in the field.
• Gravitational Potential Energy: The work done to assemble a system of masses from infinity to their current configuration.

Mass and Weight

• The mass of an object is the amount of stuff inside it. It is a basic quantity and is measured in kilograms.
• Mass is gauged using a simple balance scale.
• Mass doesn't change wherever you go; it stays the same.
• An object's weight is the pull it feels toward the center of the Earth. Weight (w) = mass x gravity.
• The center of gravity is where an object's entire weight seems to be concentrated.
• This center can be within or outside the object's material. For regularly shaped objects, the center of gravity is at the middle.
• Weight is a directional amount measured in newtons. It's found using a spring scale.
• An object's weight varies in different places.

Weight in a Lift:

• At Rest or Uniform Motion: The spring balance shows the true weight, w=mg.
• Accelerating Upward: The spring balance reads more than the true weight, w′=m(g+a).
• Accelerating Downward: The spring balance reads less than the true weight, w′=m(g−a).
• Free Fall: The body experiences weightlessness as the spring balance reads zero, w′=m(g−g).
• When lift is falling freely under gravity The apparent weight of the body w′ = m (g − g ) (∵a = g ) w ′ = 0
  Therefore, body will experiences weightlessness.

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.

Planets

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:

1. Mercury
2. Venus
3. Earth
4. Mars
5. Jupiter
6. Saturn
7. Uranus
8. Neptune

Kepler’s Laws of Planetary Motion

Kepler’s Three Laws are:

1. Elliptical Orbits: All planets orbit the Sun in elliptical paths with the Sun at one focus.
2. Equal Areal Speed: A planet sweeps out equal areas in equal times, meaning its areal speed is constant.
3. Harmonic Law: The square of a planet's orbital period (T) is directly proportional to the cube of the semi-major axis (a) of its orbit, expressed as T² ∝ a³.

Satellites

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:

• Orbit: These satellites orbit Earth in the equatorial plane, at a height of about 36,000 km.
• Period: They have an orbital period of 24 hours, matching Earth's rotational period.
• Use: They appear stationary relative to Earth and are used for communication, weather forecasting, atmospheric studies, and mapping.

Polar Satellites:

• Orbit: These orbit Earth in a polar trajectory, approximately 800 km above the surface.
• Period: They complete an orbit roughly every 84 minutes.
• Use: They are employed for weather monitoring, which involves gathering data on atmospheric conditions, and live broadcasts such as sports events through communication satellites.

Time Period of a Satellite

The time period of a satellite is the duration it takes to complete one full revolution around Earth.

Escape Velocity

The 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 (v_e)

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) v_e = √2 v₀ 
Therefore, when orbital speed of a satellite is increased by √2 times (41%), then it will escape from its orbit.

Plant Responses to Gravity

Geotropism: The response of plants to gravity. Plants exhibit two primary effects due to gravity:

1. Roots: Grow downward.
2. Stems (or Shoots): Grow upward.

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.