Gravitation

Define Gravitational Field

It’s a Field Force acting per unit Mass

Represent Gravitational Field lines

What’s the Point Mass of a sphere from an outside perspective?

Mass of a perfect Sphere can be considered to be located in the Center of Volume

State Newton’s Law of Gravitation

Gravitational Field Force directly ∝ Product of Masses

Gravitational Field Force inversely ∝ Square of Seperation

F ∝ (m₁m₂)/r²

F = GMm/R²

Derive Gravitational Field Strength due to a Point Mass

F = mg → g = F/m

g = (GMm/R²)/m

g = GM/R²

Why is g ~ constant close to Earth surface?

g = GM/R²

R = Radius + height above Surface

For heights ≤ 10⁴m, R ~ Radius ONLY
∴ g ~ 9.81

Define Gravitational Potential (ϕ)

Work Done per unit Mass in bringing a Test Mass from ∞ to point

Demonstrate the Conversion of ϕ to E_GP

ϕ = Jkg^-1

^E_GP = J

E_GP = (-)ϕm

Plot the relationship of r (height from surface) with E_GP , ϕ , F , g