The Universal Law of Gravitation

1
Physics and Daily Life -

• The Universal Law of Gravitation

F.6B Au Mei Wa, Yeung Ka-Wing
2
Background

• There is a popular story that Newton was sitting
  under an apple tree, an apple fell on his head,
  and he suddenly thought of the Universal Law of
  Gravitation. As in all such legends, this is
  almost certainly not true in its details, but the
  story contains elements of what actually
  happened.

3
What really happened with the Apple?

• Probably the more correct version of the story is
  that Newton, upon observing an apple fall from a
  tree, began to think along the following lines

4
What really happened with the Apple?

• The apple is accelerated, since its velocity
  changes from zero as it is hanging on the tree
  and moves toward the ground. Thus, by Newton's
  2nd Law there must be a force that acts on the
  apple to cause this acceleration.

5
What really happened with the Apple?

• Let's call this force "gravity", and the
  associated acceleration the "acceleration due to
  gravity". Then imagine the apple tree is twice as
  high. Again, we expect the apple to be
  accelerated toward the ground, so this suggests
  that this force that we call gravity reaches to
  the top of the tallest apple tree.

6
Newton's Law of Gravitation

• It states that any two objects exert a
  gravitational force of attraction on each other.
  The direction of the force is along the line
  joining the objects.

7
Newton's Law of Gravitation

• The magnitude of the force is proportional to the
  product of the gravitational masses of the
  objects, and inversely proportional to the square
  of the distance between them.

8
Satellites

• Nowadays, there are many commercial satellites
  moving around the earth.
• They serve one or more functions
• Communications
• Navigation
• Weather
• Environmental monitoring
• Manned Platforms

9
Communications Satellites
10
Navigation Satellites
Where am I? Where do I want to go? How can I get
there?
11
Navigation Satellites

• These are questions we've all asked at one time
  or another. Satellites for navigation were
  developed in the late 1950's as a direct result
  of ships needing to know exactly where they were
  at any given time.

12
Orbital speed of a satellite

• Now consider satellites moving around the earth.
  As the satellites underground circular motion,
  the centripetal force is provided by the
  gravitational pull on the satellite by the earth.

mv2/r GMm/r2 V vGM/r
13
How are satellites launched?

• The trick when launching a satellite is to get it
  high enough to do its job without losing the
  capsule to outer space. It's a delicate balance
  of push and pull, accomplished by the inertia of
  the moving object and the Earth's gravity.

14
Escape Velocity

• It means the minimum velocity v0 that a rocket
  must have at the Earths surface to escape
  completely from the gravitational field.

v0 v2GM/R
15
Why does a satellite stay in orbit?

• Due to the balance of two factors
• velocity, or the speed at which it would travel
  in a straight line, and
• the gravitational pull between the Earth and the
  satellite.

16
Why does a satellite stay in orbit?
17
Satellites' Orbits

• Man-made satellites circle the Earth in many ways
  including polar and geostationary orbits.
• A satellite in a polar orbit travels over the
  North and South Poles. A polar orbit may be from
  several hundred miles to several thousand miles
  above Earth. This type of satellite circles the
  Earth approximately 14 times each day.

18
Satellites' Orbits
19
Satellites' Orbits

• A satellite in a high-altitude, geostationary
  orbit circles the earth once every 24 hours, the
  same amount of time it takes for the Earth to
  spin on its axis.

20
Satellites' Orbits

• The satellite turns eastward along the Equator.
  It stays above the same point on Earth all the
  time. To maintain the same rotational period as
  the Earth, a satellite in geostationary orbit
  must be 22,237 miles above the Earth. At this
  distance, the satellite can view a huge portion
  of the Earth's surface.

21
Parking Orbit

• Parking orbit is the orbit of satellites it which
  the period of revolution is the same as that of
  the Earth.
• The satellites in such orbits appear stationary
  relative to the observer on earth.
• The satellites in the parking orbits can be used
  for receiving radio signals from one place and
  transmitting them to another.

22
Space Stations

• What in the world are we doing in space? Why
  spend the time and resources to build a
  laboratory in space when we have plenty of them
  on Earth?

23
Space Stations

• The answer is a unique tool called microgravity.
  Microgravity (also called zero-g) opens a new
  universe of research possibilities. It unmasks
  phenomena that gravity on Earth can obscure.

24
Microgravity

• In a microgravity environment, the effects of
  gravity are very small and objects appear to
  weigh almost nothing. Astronauts and science
  experiments aboard the space station experience
  microgravity because they are in what is called
  "free fall."

25
END