Earth Satellites - Weightlessness in a Satellite

The concept of weightlessness in a satellite is best understood by first examining apparent weight within a moving elevator. Our sensation of weight is due to the normal reaction force (N) exerted by the floor, not just gravity itself. By analyzing the net forces acting on a passenger inside a lift under various acceleration conditions, we can see how the apparent weight changes. The state of weightlessness occurs when this normal reaction force becomes zero, a condition known as free fall.

The feeling of weightlessness is the state where "there will not be any feeling of weight," and the weighing machine will record zero.

According to Newton's second law of motion:

Where:

• F is the net force acting on an object.
• m is the mass of the object.
• a is the acceleration of the object.

For a passenger in a lift, the net force in the downward direction is:

Where:

• F is the net force.
• m is the mass of the passenger.
• g is the gravitational acceleration (gravitational force is mg).
• N is the normal reaction force exerted by the floor (this is the experienced/apparent weight).

The source material discusses the following cases affecting apparent weight (the magnitude of the Normal Reaction Force, N):

• Normal Weight (N = mg): Occurs when the lift's acceleration is zero (at rest or moving at constant velocity).
• Heavier Apparent Weight (N > mg): Occurs with a net upward acceleration (a_u).
• Lighter Apparent Weight (N < mg): Occurs with a net downward acceleration (a_d).
• Total Weightlessness (N = 0): Occurs during free fall, where downward acceleration (a_d) equals gravitational acceleration (g).

The sensation of weight we feel is actually the normal reaction force (N) exerted by the floor against us. This is the reading recorded by a weighing machine. The net force (F) acting on a passenger in a lift is the difference between the gravitational force (mg) and the normal force (N), or vice versa, depending on the direction of net acceleration (a).

Analysis of Forces in a Lift (Elevator)

Case I: Zero Acceleration (a = 0)

• Condition: Lift at rest or moving with constant velocity (up or down).
• Equation: F = 0 = mg - N
• Result: N = mg
• Sensation: The passenger feels their normal weight.

Case II: Net Upward Acceleration (a_u)

• Condition: Lift starts moving up, or stops while moving down.
• Equation: F = ma_u = N - mg
• Result: N = mg + ma_u
• Sensation: N > mg, the passenger feels heavier (apparent weight increases).

Case III (a): Net Downward Acceleration (a_d)

• Condition: Lift starts moving down, or stops while moving up.
• Equation: F = ma_d = mg - N
• Result: N = mg - ma_d
• Sensation: N < mg, the passenger feels lighter (apparent weight decreases).

Case III (b): State of Free Fall (Weightlessness)

• Condition: The lift's cables are cut, causing the downward acceleration a_d to be equal to g.
• Equation: N = mg - m a_d ⇒ N = mg - mg = 0
• Result: N = 0
• Sensation: The passenger experiences total weightlessness; the weighing machine records zero.

A revolving satellite, along with the astronauts inside, is continuously in a state of free fall.

• The required centripetal acceleration for its circular motion is provided by the gravitational acceleration (g) at that height.
• This means the satellite and everything inside are constantly accelerating towards the Earth at g (i.e., a_d = g).
• Since the astronaut and the satellite floor are falling together at the same rate, the normal reaction force (N) between them is zero, resulting in an apparent weight of zero and the feeling of total weightlessness.
• Why doesn't the satellite fall to Earth? It has a tangential velocity that is sufficient to keep it moving in a circular orbit at that height, despite the continuous free fall towards the Earth.

1. Roller Coasters: You feel lighter at the top of a hill — your weight feels less than usual.
2. High Dive / Bungee Jump: Just before the cord pulls or parachute opens, you’re in near free fall, feeling almost weightless.
3. Vomit Comet (Zero-G Plane): In a special parabolic flight, you feel weightless for a short time — used for astronaut training.