Gravitational Field (Copy)

Definition of Gravitational Field

• A gravitational field is a region in space where a mass experiences a gravitational force due to another mass.
• It is a type of field of force, which means:
  • The force acts at a distance, with no physical contact.
• All objects with mass produce gravitational fields.
• Gravitational fields are vector fields:
  • They have both magnitude and direction.
  • The direction is always towards the mass that produces the field.
• The gravitational field strength (g) at a point is defined as the force per unit mass experienced by a small test mass placed at that point.
• Formula:
  • g = F / m
    • g = gravitational field strength (N/kg)
    • F = gravitational force (N)
    • m = mass of the object experiencing the force (kg)

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Units of Gravitational Field Strength

• From the definition: g = F / m
  • Force (F) is measured in newtons (N)
  • Mass (m) is measured in kilograms (kg)
• Therefore, g is measured in newtons per kilogram (N/kg)
• Since F = ma, and a has units of m/s², it follows that:
  • 1 N/kg = 1 m/s²

Characteristics of Gravitational Fields

• Always attractive: Gravity always pulls objects towards the source mass.
• Acts at a distance: There is no need for physical contact between interacting masses.
• Infinite range: The field never truly disappears but becomes weaker with distance.
• Superposition applies: The total gravitational field at a point is the vector sum of the fields from all masses.
• Independent of test mass: The field strength depends only on the source mass and the distance from it, not on the test object used to measure it.

Gravitational Field Lines

• Field lines represent the direction and strength of the gravitational field.
• Properties of field lines:
  • They point towards the mass creating the field (gravity is always attractive).
  • They never cross.
  • The closer together the lines, the stronger the field.
  • Around a point mass or spherical mass, lines are radially inward.
  • In a uniform field (like near Earth’s surface), field lines are parallel and equally spaced.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Uniform vs Non-Uniform Fields

• In a uniform field: g = constant
• In a radial field: g decreases with increasing distance (g ∝ 1/r²)

Gravitational Field Strength Due to a Point Mass

• The gravitational field strength at a distance r from a point mass M is given by:

  g = GM / r²

  where:

  • G = universal gravitational constant = 6.674 × 10⁻¹¹ Nm²/kg²
  • M = source mass (kg)
  • r = distance from the centre of the mass (m)
  • g = gravitational field strength (N/kg)
• This formula assumes:
  • The mass M is a point or spherical symmetric object.
  • The field is being measured outside the mass.
• Direction of g is always towards the mass M.

Newton’s Law of Universal Gravitation

• The force between two point masses M and m separated by distance r is:

  F = GMm / r²

  where:

  • F = gravitational force (N)
  • G = gravitational constant = 6.674 × 10⁻¹¹ Nm²/kg²
  • M = first mass (kg)
  • m = second mass (kg)
  • r = distance between centres of mass (m)
• Substituting into g = F / m gives:

  g = GM / r²

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Worked Examples

Example 1:
Find the gravitational field strength at a point 1.0 × 10⁷ m from a planet of mass 5.0 × 10²⁴ kg.

g = (6.674 × 10⁻¹¹ × 5.0 × 10²⁴) / (1.0 × 10⁷)²
g = (3.337 × 10¹⁴) / (1.0 × 10¹⁴)
g = 3.34 N/kg

Example 2:
A 10 kg mass is placed in a gravitational field of strength 9.81 N/kg. What is the force acting on it?

F = mg = 10 × 9.81 = 98.1 N

Example 3:
The gravitational field on the Moon’s surface is 1.62 N/kg. What is the weight of a 75 kg astronaut?

F = mg = 75 × 1.62 = 121.5 N

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

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