1. Satellites & “Weightlessness”

2. “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!!

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 DOES NOT MEAN 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 3 rd 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 3 rd 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. Case 3: Elevator moves down with acceleration a.  ∑F = ma or W - mg = -ma W = upward force on m. Newton’s 3 rd 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! (½)mg (down) + 

8. Case 4: Elevator cable breaks! Free falls down with acceleration a = g!  ∑F = ma or W - mg = -ma, W = upward force on m. Newton’s 3 rd 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 m s ) free “falls” continually! Just so gravitational force = centripetal force. F = G(m s M E )/r 2 = m s v 2 /r Consider scale in satellite: ∑F = ma = -mv 2 /r (towards Earth center!) W - mg = -mv 2 /r Or, W = mg -mv 2 /r << mg!

10. LESSON!!!: TV reporters are just plain WRONG (!!) 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(m s M E )/r 2 This exists (& is NOT zero) even for HUGE distances r away from Earth! F  0 only for r  