Apparent Weightlessness and Artificial Gravity
• In order to simulate weightlessness it is necessary to eliminate the
effect of air resistance.
• To accomplish this a plane it used to fly passengers first upwards at a
high acceleration. When the plane begins to maintain a steady arc at
the top, the normal force becomes zero giving the impression of
weightlessness.
• NASA Low g plane
Lecture 13
Neat Videos
• Drinking coffee in Low g
• Drinking water
• Water Balloons in Low g
Apparent Weightlessness and Artificial Gravity
• In space far from the earth
astronauts are in a perpetual
state of weightlessness.
• In order to make space-goers
more comfortable it is
possible to use the effects of
uniform circular motion to
simulate the effects of gravity.
• By constructing a space
station is the form of the
cylinder the floor would
provide the necessary
centripetal force necessary to
get objects going around in a
circle.
Lecture 13
4.7 The Gravitational Force
Newton’s Law of Universal Gravitation
Every particle in the universe exerts an attractive force on every
other particle. A particle is a piece of matter, small enough in size to be regarded as a mathematical point.
The force that each exerts on the other is directed along the line
joining the particles.
4.7 The Gravitational Force
For two particles that have masses m1 and m2 and are separated by a distance r, the force has a magnitude given by
F
G
m1m2
G 2
r
6.673 10
11
N m 2 kg 2
Three interesting examples:
a. Calculate the gravitational force between the earth and a 60 kg person
b. Calculate the gravitational force between two 60 kg people one meter apart
c. Calculate the gravitational force between the earth and moon
THESE NUMERICAL EXAMPLES ARE ONLY PRESENTED TO SHOW THE SIZE OF THE GRAITATINAL FORCE.YOU DON’T NEED TO BE ABLE TO DO THEM!
Example a:
Fg =
GM p M E
r2
=
6.67x10 11 * 60 * 6x10 24
(6.38 x10 ) 2
6
N = 588N
and W = mg = 60kg * 9.8m/s 2 = 588N (same answer!)
Formula for weight and universal law of gravity give the same answer. GM E
This is because in formula W=mg g=
r2
Example B: FORCE BETWEEN TWO 60 KG PEOPLE
Fg =
GM p M E
r2
=
6.67x10 11 * 60 * 60
(1) 2
N = .00000024 N
THE FORCE IS VERY SMALL!!
Example C: FORCE BETWEEN EARTH AND MOON
Fg =
GM p M E
r2
=
6.67x10 11 * 6x10 24 * 7.35x10 22
(3.85x10 8 )
2
N = 1.98X10 20 N
THIS FORCE IS VERY LARGE!
GRAVITY IS THE WEAKEST OF THE FOUR FUNDAMENTAL
FORCES BUT CAN BE LARGE WHEN THE MASSES INVOLVED ARE LARGE.
Satellite Motion A projectile launched from the center of the earth will fall back to earth until...
The speed of a satellite at a distance r
from the earth’s center is: GM Earth
VS =
r
Note that the mass of the satellite does not appear in the equation. This means that the speed of a satellite in orbit DOES NOT depend on the satellite mass so all objects in this orbit will move at the same speed irregardless of size.
How fast is this speed?
Example: International Space Station
r=6380km+340 km=6780km
MEarth=6x1024kg
GM
6.67x10 11 6x10 24
VS =
=
r Earth
6780x10 3
= 7683m/s = 27, 658 km/h!!
The ISS which is only 340km above the earth must travel at 27,658 km/h in order to stay in that orbit. THIS IS VERY FAST!!
Some Interesting stuff...
GLOBAL POSITIONING SYSTEM(GPS)
• The first GPS satellite was
launched in 1978.
• A full constellation of 24 satellites was achieved in 1994.
• Each satellite is built to last about 10 years. Replacements are constantly being built and launched into orbit.
• A GPS satellite weighs approximately 2,000
pounds and is about 17 feet across with the solar panels extended.
• Transmitter power is only 50 watts or less.
Global Positioning System
Global Positioning System
• The GPS system works by having the satellite send radio waves which
carry precise time measurements.
• When receivers on the earth detect the waves they can calculate the
radial distance they are from the satellite.
Global Positioning System
• Therefore the signal from one satellite allows people to determine
where they are located within a circle.
• When two other satellites are used, the receiver can determine a more
precise location.