13.3 A2 Level

Gravitational field of a point mass

7 flashcards to master this topic

Definition Flip

State Newton's Law of Gravitation.

Answer Flip

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 their centers. Mathematically: F = Gm₁m₂ / r².

Key Concept Flip

Derive the formula for gravitational field strength (g) due to a point mass.

Answer Flip

Starting with Newton's Law of Gravitation (F = GMm/r²) and the definition of gravitational field strength (g = F/m), substitute F to get g = (GMm/r²)/m. Simplifying, g = GM/r².

Definition Flip

What is the equation for gravitational field strength (g) due to a point mass?

Answer Flip

g = GM/r², where G is the gravitational constant, M is the mass of the point mass, and r is the distance from the center of the point mass.

Calculation Flip

Calculate the gravitational field strength on the surface of a planet with mass M = 6 x 10^24 kg and radius r = 6.4 x 10^6 m. (G = 6.67 x 10^-11 Nm²/kg²)

Answer Flip

Using g = GM/r², g = (6.67 x 10^-11 Nm²/kg² * 6 x 10^24 kg) / (6.4 x 10^6 m)² = 9.77 N/kg (or m/s²).

Key Concept Flip

Explain why 'g' is approximately constant for small changes in height near the Earth's surface.

Answer Flip

Near the Earth's surface, small changes in height (Δr) result in negligible changes to the overall distance 'r' from the Earth's center. Since g is inversely proportional to r², g remains approximately constant (g ≈ GM/r²).

Key Concept Flip

Describe the relationship between gravitational field strength and distance from a point mass.

Answer Flip

Gravitational field strength (g) is inversely proportional to the square of the distance (r) from the point mass (g ∝ 1/r²). As distance increases, field strength decreases rapidly.

Key Concept Flip

If the distance from a planet's center doubles, how does the gravitational field strength change?

Answer Flip

If the distance doubles, the gravitational field strength is reduced to one-quarter of its original value. Since g ∝ 1/r², if r becomes 2r, then g becomes g/4.

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