Satellites & “Weightlessness”

“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 centripetalacceleration keeps it in orbit!!

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

“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)

• 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 toreading on scale.

• ∑F = 0 = W - mg Scale reading is

W = mg

• 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)mgPerson is “heavier” also!Person experiences 1.5 g’s!

• 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)mgPerson is “lighter” also!Person experiences 0.5 g’s!

(½)mg

(down) +

• 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 3rd Law equal & opposite to scale reading. Scale reading (apparent weight)

W = mg -ma = mg - mg W = 0! Elevator & person areapparently “weightless”. Clearly,though, THE FORCE OF GRAVITY STILL ACTS!

• (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!

• 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(msME)/r2

This exists (& is NOT zero) even for HUGE distances r away from Earth!

F 0 only for r