Modern Galileo Drop, Newton’s Gravitation & Derivation of g

Dropped a heavy object and a light object simultaneously.
Observation (in air): lighter objects like feathers appear slower because of air resistance.
Hypothesis: Remove air → reveal true gravitational behaviour.

Result: In vacuum, bowling ball and feathers hit the floor simultaneously—visually striking.
Confirms Galileo’s contention that mass does not influence gravitational acceleration in absence of air resistance.

Gravity force accelerates all masses by the same amount
Both objects accelerate because Earth exerts a gravitational force on them.
- Acceleration due to gravity designated g in honour of Galileo’s work.
Measured average near Earth’s surface: $g\approx9.8\,\text{m\,s}^{-2}$ .
- Value varies slightly with latitude, altitude, and local geology.

“For every action, there is an equal and opposite reaction.”
If Earth pulls mass $m$ downward with force $F$ , the mass pulls Earth upward with equal magnitude, opposite direction $F$ .
Diagrammatically:

Empirically formulated to quantify $F$ : F = G (m₁m₂)/(r²)
Variables:
- $F$ = gravitational force (N).
- m₁ and m₂ = interacting masses (kg).
- r = center-to-center separation (m).
- G = universal gravitational constant (6.6743 × 10^-11 m³kg^-1s^-2)

Earth is the round sphere
m = the test mass which is close to the surface of the earth
F = G (m₁m₂)/(r²)
Let m1 be the mass of the earth
m2 be the mass of the subject (this is m - the test mass)
r is the distance between the two masses (r is the distance between the centres of the masses) can approximate by the radius of the earth
Identify F = mg (Newton’s 2nd law):
Inputs used in the video:
- G = 6×6743 × 10^-11
- r_E = 6.378135 × 10⁶
- m_E = 5.9722 × 10²⁴
g = G (m_E/r_E²)
Plugging values ⇒ g =(approx) 9.8ms^-2 (excellent agreement with experiment).

Constants defined in SI units.
Single command evaluates $g$ via formula above.
Output displayed a number “very close to 9.8”, validating Newton’s universal law as well as experimental measurement