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Satellites & “Weightlessness”

Satellites & “Weightlessness”. “Weightlessness”. What keeps a satellite in orbit? The centripetal acceleration is CAUSED by the Gravitational Force! F = (mv 2 )/r = G(mM E )/r 2 Its speed or centripetal acceleration keeps it in orbit!!.

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Satellites & “Weightlessness”

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  1. Satellites & “Weightlessness”

  2. “Weightlessness” • What keeps a satellite in orbit? The centripetal acceleration is CAUSED by the Gravitational Force! F = (mv2)/r = G(mME)/r2 Its speed or centripetal acceleration keeps it in orbit!!

  3. Newton’s 1st Law: If no there were (gravitational) force, the satellite would move in a straight line!

  4. “Weightlessness” • Objects in a satellite, including people, experience “EFFECTIVE weightlessness”. What causes this? • NOTE:THIS DOESNOTMEAN THAT THE GRAVITATIONAL FORCE ON THEM IS ZERO! • To understand this, first, look at a simpler problem: A person in an elevator. (4 cases)

  5. Case 1: Person in elevator. Mass m attached to scale. No acceleration. (no motion) (a = 0)  ∑F = ma = 0 • W = weight = upward force on mass m. By Newton’s 3rd Law, equal & opposite to reading on scale. • ∑F = 0 = W - mg Scale reading is W = mg

  6. Case 2: Elevator moves up with acceleration a.  ∑F = ma or W - mg = ma • W = upward force on m. Newton’s 3rd Law equal & opposite to the scale reading. Scale reading (apparent weight) W = mg + ma > mg ! For a = (½)g, W = (3/2)mg Person is “heavier” also! Person experiences 1.5 g’s!

  7. (½)mg • Case 3: Elevator moves down with acceleration a.  ∑F = ma or W - mg = -ma • W = upward force on m. Newton’s 3rd Law equal & opposite to scale reading. Scale reading (apparent weight) W = mg - ma < mg ! For a = (½)g, W = (½)mg Person is “lighter” also! Person experiences 0.5 g’s! + (down) 

  8. Case 4: Elevator cable breaks! Free falls downwith acceleration a = g! ∑F = ma or W - mg = -ma, W = upward force on m. Newton’s 3rd Law equal & opposite to scale reading. Scale reading(apparent weight) W = mg -ma = mg - mg W = 0!Elevator & person are apparently “weightless”. Clearly, though, THE FORCE OF GRAVITY STILL ACTS!

  9. (Apparent) “weightlessness” in satellite orbit? • With gravity, satellite (mass ms) free “falls” continually! Just so gravitational force = centripetal force. F = G(msME)/r2 = msv2/r • Consider scale in satellite: ∑F = ma = -mv2/r (towards Earth center!) W - mg = -mv2/r Or, W = mg -mv2/r << mg!

  10. LESSON!!!:TV reporters are just plainWRONG (!!)when they say things like: “The space shuttle has escaped the Earth’s gravity”. Or “has reached a point outside the Earth’s gravitational pull”. • Why? Because the gravitational force is F = G(msME)/r2 This exists (& isNOTzero) even for HUGE distances r away from Earth! F  0only forr  

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