Does the Earth move when an apple falls?

Well, it does! Let's break it down. According to Newton, for every action, there's an equal and opposite reaction. So, when the apple falls, it pulls the Earth toward it.

First, let's find out how long it takes for the apple to hit the ground. Using this equation, we get about 4.5 seconds. The force of gravity on the apple is 5 Newtons, and Newton says the Earth feels the same force in the opposite direction. Now, let's see how much does the Earth accelerates towards the apple. It's an incredibly tiny value: 8 x 10⁻²⁵ m/s². Finally, how much does the Earth move during this time? Just 8 x 10⁻²⁴ meters! Super small, right? So, when that apple falls, the Earth does move, but just a teeny-tiny bit. and that's the magic of physics!

Detailed Calculations for Movement of Earth:

• Let the height from which the apple falls be h = 100 meters.
• Assume the mass of the apple m = 0.5 kg.
• The Earth has a mass of approximately M = 6 × 10²⁴ kg.

1. Time of Impact:

• • The equation of motion for the apple's descent is given by ½gt² = h.
  • Solving for t yields t² = 2h/g ⇒ t ≈ 4.5 seconds.

1. Forces in Action:

• • The gravitational force exerted by the Earth on the apple is F = mg = 0.5 × 10 = 5 Newtons (assuming g = 10 m/s² for simplicity).
  • By Newton's third law, the Earth experiences an equal and opposite force of 5 Newtons towards the apple.

1. Earth's Reaction

• • The acceleration of the Earth towards the apple is found using F = Ma.
  • Solving for a gives a = F/M = 5/(6 × 10²⁴) ≈ 8 × 10⁻²⁵ m/s².

1. Earth's Displacement

• • The distance the Earth moves towards the apple in the 4.5 seconds is given by d = ½at².
  • Substituting the values, we get d = ½ × 8 × 10⁻²⁵ × (4.5)² ≈ 8 × 10⁻²⁴ meters.