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Home , Artificial gravity, Weightlessness

Apparent and Artificial

• 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 . 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 Balloons in Low g Apparent Weightlessness and

• In space far from the earth are in a perpetual state of weightlessness. • In order to make space-goers more comfortable it is possible to use the effects of uniform to simulate the effects of gravity. • By constructing a is the form of the cylinder the floor would provide the necessary 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 m1 and m2 and are separated by a distance r, the force has a magnitude given by m m F G 1 2 r 2 G 6.673 10 11 N m2 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: 11 24 GM pM E 6.67x10 * 60 * 6x10 Fg = = N = 588N r2 (6.38x10 6 )2 2 and W = mg = 60kg * 9.8m/s = 588N (same answer!)

Formula for and universal law of gravity give the same answer. GM This is because in formula W=mg g = E r2

Example B: FORCE BETWEEN TWO 60 KG PEOPLE

11 GM pM E 6.67x10 * 60 * 60 Fg = = N = .00000024N r2 (1)2 THE FORCE IS VERY SMALL!!

Example C: FORCE BETWEEN EARTH AND MOON

11 24 22 GM pM E 6.67x10 * 6x10 * 7.35x10 20 Fg = = N = 1.98X10 N 2 8 2 r (3.85x10 ) 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 of a at a distance r from the earth’s center is: GM V = Earth S r

Note that the of the satellite does not appear in the equation. This means that the speed of a satellite in 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 24 MEarth=6x10 kg 11 24 GM 6.67x10 6x10 VS = = r Earth 6780x103 = 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 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.