1. Satellites and “Weightlessness”

2. Example: Geosynchronous Satellite
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. 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.

3. International Space Station

4. Its speed or it’s centripetal acceleration keeps it in orbit!!
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!!
Figure Caption: A satellite, the International Space Station, circling the Earth.
Figure Caption: Artificial satellites launched at different speeds.
So, a satellite is kept in orbit by its speed:
It continually “falls”, but Earth curves from underneath it.

5. 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!
Figure Caption: A moving satellite “falls” out of a straight-line path toward the Earth.

6. Free-Fall Acceleration
Have you heard this claim?
“Astronauts are weightless in space,
therefore there is no gravity in space.”

7. 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!

8. 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!!

9. 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-fall around the Earth, just as you would be in the elevator. They don’t fall to Earth, only because of their very high tangential speed.

10. “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.

11. W is equal & opposite to the reading on the scale.
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 reading is W = mg

12. W is equal & opposite to the reading on the scale.
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 or W - 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 !
For a = (½)g, W = (3/2)mg
Person is “heavier” also!
Person experiences 1.5 g’s!

13. W is equal & opposite to the reading on the scale.
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 or W - 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!
(½)mg 
(down)

14. Newton’s 3rd Law, W is equal & opposite to the reading
Case 4
The elevator cable breaks! It free falls down with acceleration a = g!
 ∑F = ma or W - 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!

15. F = G(msME)/r2 = (msv2)/r ∑F = ma = - (mv2)/r W - mg = - (mv2)/r
(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!

16. F = G(msME)/r2 F  0 ONLY for r  
LESSON!!! TV reporters are just plain WRONG (!!) 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 (& is NOT zero) even for HUGE distances r away from Earth!
F  0 ONLY for r  

17. Examples are shown in these figures.
Effective Weightlessness obviously 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.
Figure Caption: Experiencing “weightlessness” on Earth.

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