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Satellites and “Weightlessness”. A geosynchronous satellite is one that stays above the same point on the Earth, which is possible only if it is above a point on the equator. Such satellites are used for TV & radio transmission, for weather forecasting, as communication relays.
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A geosynchronous satelliteis • one that stays above the same point • on the Earth, which is possible only • if it is above a point on the equator. • Such satellites are used for TV & • radio transmission, for weather • forecasting, as communication relays. Example: Geosynchronous Satellite r m Earth, mass ME Calculate: a. The height above the Earth’s surface such a satellite must orbit. b. The satellite’s speed. c. Compare that to the speed of a satellite orbiting r = 200 km above Earth’s surface.
Satellites are routinely put into orbit around the Earth. • The tangential speed must be high enough so that the • satellite does not return to Earth, but not so high that • it “escapes” Earth’s gravity altogether. • What keeps a satellite in orbit? • The centripetal acceleration • is CAUSED by the • Gravitational Force! • F = (mv2)/r = G(mME)/r2 • Its speed or it’s centripetal • acceleration keeps it in orbit!! • So, a satellite is kept in orbit by its speed: • It continually “falls”, but Earth curves from underneath it.
A satellite is kept in orbit by its speed. • it is continually falling,(in Free Fall!) • but Earth curves • from underneath it. “Falls” in a circle! • Newton’s 1st Law: • Tells us that if there • were no (gravity) • force, the satellite • would move in a • straight line!
Free-Fall Acceleration • Have you heard this claim? “Astronauts are weightless in space, therefore there is no gravity in space.”
Free-Fall Acceleration • Have you heard this claim? “Astronauts are weightless in space, therefore there is no gravity in space.” • It’s true that if an astronaut on the International Space Station (ISS) steps on a scale, he/she will “weigh” nothing!
Free-Fall Acceleration • Have you heard this claim? “Astronauts are weightless in space, therefore there is no gravity in space.” • It’s true that if an astronaut on the International Space Station (ISS) steps on a scale, he/she will “weigh” nothing! • It may seem reasonable to think that if weight = mg, since weight = 0, g = 0, but this is NOT true!!
Free-Fall Acceleration • As we’ve already discussed, if you stand on a scale in an elevator & the cables are cut, you’ll also “weigh” nothing F = ma = N – mg but in free-fall, a = g, so normal force N = 0!. This does not mean that g = 0! • Astronauts in orbit are in free-fallaround the Earth, just as you would be in the elevator. They don’t fall to Earth, only because of their very high tangential speed.
“Effective Weightlessness”- More Details • As just mentioned, objects in a satellite, including people, experience “Effective Weightlessness”. What causes this? • As also already mentioned, This does NOT Mean that the gravitational force on them is zero! • They still have a gravitational force acting on them! • As already mentioned, the satellite & all of its contents are in “free fall”, so for people inside, There is no normal force FN. • This is what leads to the experience of “weightlessness”. • More properly, this effect should be called apparent or effective weightlessness, because the gravitational force still exists. • This can be experienced on Earth also, but only briefly.
To understand Effective Weightlessness, lets look at a simpler • problem: A person riding in an elevator in 4 different cases Case 1 • A person in an elevator. Mass m is attached to a scale. No acceleration. (no motion).(a = 0).N’s 2nd Law: ∑F = ma = 0 • W = “weight” = upward force on mass m. By N’s 3rd Law, W is equal & opposite to the reading on the scale. ∑F = 0 = W – mg Scale readingisW = mg
Case 2 • A person in an elevator. Mass m is attached to a scale. Elevator moves up with acceleration a. N’s 2nd Law: ∑F = ma orW - mg = ma • W = “weight” = upward force on mass m. By N’s 3rd Law, W is equal & opposite to the reading on the scale. Scale reading(Effective Weight) is W = mg + ma > mg ! Fora = (½)g, W = (3/2)mg • Person is “heavier” also! • Person experiences 1.5 g’s!
(½)mg Case 3 • A person in an elevator. Mass m attached to a scale. Elevator moves down with acceleration a. N’s 2nd Law: ∑F = ma orW - mg = -ma • W = “weight” = upward force on mass m. By N’s 3rd Law, W is equal & opposite to the reading on the scale. Scale reading(Effective weight) is W = mg - ma < mg ! a = (½)g, W = (½)mg • Person is “lighter” also! • Person experiences 0.5 g’s! (down)
Case 4 • The elevator cable breaks! It free fallsdownwith acceleration a = g! ∑F = ma orW - mg = -ma, • W = upward force on m. By Newton’s 3rd Law, W is equal & opposite to the reading on the scale. Scale reading (apparent weight) • The elevator & person are apparently “weightless”. Clearly, though, The Force of Gravity Still Acts!
(Apparent) “weightlessness” in the satellite orbit? • With gravity, the satellite (mass ms) free “falls” continually! Just so the gravitational force = the centripetal force. F = G(msME)/r2 = (msv2)/r • Consider a scale in the satellite: ∑F = ma = - (mv2)/r (towards the Earth’s center) W - mg = - (mv2)/r Or, W = mg - (mv2)/r << mg! “Falls” in a circle!
LESSON!!!TV reporters are just plainWRONG (!!)when they say things like: “The space shuttle has escaped the Earth’s gravity”. Or “The shuttle 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 HUGEdistances r away from Earth! F 0ONLY forr
Effective Weightlessnessobviously doesn’t mean that gravity • isn’t there, the gravitational force obviously still exists. • Other than in a falling elevator (discussed next), this effect • can be experienced in other ways on Earth, but only briefly. • Examples are shown in these figures.
