Newton's Law of Gravitation: Earth and Moon
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Study Notes

Newton's Law of Gravitation

  • The force of attraction between two particles is directly proportional to the product of the masses and inversely proportional to the square of the distance of separation.
  • The mathematical formula for Newton's law of gravitation is: F = Gm₁m₂/r²
  • The value of G is 6.67 × 10⁻¹¹ Nm²/kg²

Earth and Moon

  • The mass of the earth is approximately 6.0 × 10²⁴ kg.
  • The mass of the moon is approximately 7.3 × 10²² kg.
  • The distance between the earth and the moon is approximately 4.0 × 10⁸ m.
  • The force of attraction between the earth and the moon is approximately 1.75 × 10²⁰ N.

Orbital Motion

  • When the earth is in orbit around the sun, the centripetal force equals gravitational force.
  • The velocity of the earth in orbit can be calculated using the formula: v = √(GM/R)
  • The period of the earth's orbit can be calculated using the formula: T² = 4π²R³/GM

The Earth's Characteristics

  • The earth is considered spherical in shape.
  • The mass of the earth is concentrated at its center.
  • g is considered constant at all points on the earth.
  • The earth is considered a fixed stationary.
  • The weight of the body acts along a line joining the centers of the earth and the body.

Gravitational Field

  • A gravitational field is the region in which a mass will experience gravitational force of attraction.
  • The gravitational field strength, or intensity (g) of the earth is defined as the gravitational force acting on a unit mass placed in the field.
  • Mathematically, g = F/m

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Description

Apply Newton's law of gravitation to calculate the force of attraction between the earth and the moon. Learn about the gravitational force and its relationship with mass and distance.

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