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ISCI 2002 – Independent Notes
Gravity – Chapter 5
I. Gravity
(1). Newton’s Universal Law of Gravitation
 Newton discovered that every mass pulls on another mass
 The force involved is proportional or Force ~ mass 1 x mass 2
 The force is however inversely proportional to the square of the distance separating them or F ~ d 2
 This can be expressed as a formula: F ~ m1 x m2 / d2
 The closer the masses are together, the greater the attraction or force of gravity (vise a versa)
 Greater the masses the greater the force of gravity between them (vise a versa)
(2). Inverse Square Law and Gravity
 As objects move farther away, the gravitational attraction between them weakens
 Can be explained in terms of light: As light spreads out its brightness decreases. Light which shines on a
object 1 meter away covers the object (square). When it moves to two meters away it now covers an area
that is twice as tall and twice as wide. If moves to an area 3 meters away, it now fills a space three times as
large and 3 times as wide.
 In other words, 2 meters wide the light is 1/4th less bright. 3 meters away it is 1/9th times as bright. This is
at the core of the Inverse Square Law. As distance increases between objects gravitational force decreases
(inverse relationship).
 So gravitation force is: Gravitation Force is ~ 1/d 2
(3). Can gravitational attraction be or reach zero?
 The answer is no. No matter how far apart there is still gravitational attraction.
 It may be small, but never reaches zero.
(4). The Gravitational Constant
 When using the formula in number 1, to make it a true equation you must add what is called the
gravitational constant or ‘G’
 ‘G’ or the constant equals the gravitational attraction between two 1.0-kg masses (6.67 x 10-11 N – m2 / kg2
 To add this to the equation: F ~ (G ) (m1 x m2 )/ d2
 This constant or G is consistent throughout the universe
According to the law of universal gravitation, the attractive force (F) between two bodies is
proportional to the product of their masses (m1 and m2), and inversely proportional to the square
of the distance (r) between them:
The constant of proportionality, G, is the gravitational constant
The gravitational constant G is a key element in Newton's law of universal gravitation.
The gravitational constant is perhaps the most difficult physical constant to measure. [2] In SI
units, the 2006 CODATA recommended value of the gravitational constant is: [3]
(5). Your center of Gravity
 A person’s center of gravity is the point located at the object’s average position of weight.
 Center of gravity of a person is usually located at the heavier end.
 CG is relative to its base of support: This determines stability. If the CG of an object is above the area of
support, the object will remain upright; but if the CG is below the support base, the object will topple. If
something does not extend beyond its base, it will remain upright.
II. Weightlessness
(1). Weight is defined as a force of gravity on a mass
 Your weight has the value of mg if you are NOT accelerating
 So the weight of something is the force that is exerted onto something. A bathroom scale for example.
 What happens if you are in tall building and the floor falls out from underneath you. Will you have
weight? Maybe, but you have lost your supporting force that gives you weight. If an elevator is in free fall
your weight would actually be 0.
 Why do astronauts achieve weightlessness? When they are in space that have no supporting force. They
and the shuttle are in a situation called free fall. They are falling back to Earth at tremendous speeds. The
supporting force is lost, so they are weightless.
 However if the shuttle undergoes acceleration, the astronauts will again achieve weightlessness.
III. Centripetal Force
(1). What is CF?
 Any force that that causes an object to follow a circular path.
 This is the force that keeps the Moon in the Earth’s orbit.
 This is the gravitational force acting across space that keeps objects in orbit.
III. Types of Motion
(1). Projectile
 An object set into motion and continues that motion by its own inertia.
 A simple projectile is a falling stone we studied previously. It falls at a rate of 10 m/s. The distance of the
fall keeps increasing and can be calculated by using the formula: d = ½ gt 2
 When you throw a stone off of a cliff, gravity begins to act on it. It is thrown with a horizontal initial
velocity (x direction) and gravity begins to act on it (y direction).
 The stone takes a curved path or a curved path called a parabola.
 So there are two forces involved when throwing an object. Number 1 is the force of gravity in the Ydirection and the initial horizontal force in the X-direction. See figures 5.23 and 5.25
 These components are called vectors. And the direction of the stone at any one moment in time is called
the resultant (direction and velocity)
 When looking at figures 5.23 and 5.24, you see that at each second of the fall the distance of the of the
dropped stone and the thrown stone are equal. Why? Because the force of gravity and the horizontal force
are independent of each other. Gravity acts on the thrown stone as well as the dropped stone in the same
manner.
(2). Projectile Altitude and Range
 In section 5.9 you see different paths of projectiles (absence of drag).
 Projectiles reach different altitudes above the ground.
 They travel different horizontal distances or have different ranges.
 When adding the altitude of two different ranges they have the same ranges.
 For example, projectile with a 75 degree altitude, and one launched at 15 degrees will land in the same
place.
 When an object is launched straight up into the air, without air drag, speed lost while going up equals speed
gained while going down. Figure 5.30
(3). Projectiles and Drag
 When drag occurs both altitude and range are affected. Figures 5.32 and 5.33
(4). Calculating velocity for projectiles
 Look at figure 5.31
 The boy throws the ball 20m. He throws it from a height of 5m. What is the velocity of the ball?
 The velocity of an object can be calculated by using the formula v = d/t as you know. We know the
distance but what about the time? If an object falls 5 m you already know it only takes 1 second due to the
downward force of gravity. So the time is 1 second. V = 20 m / 1 s = 20 m/s!
IV. Fast Moving Projectiles and Objects
(1). Satellites and Long Range Projectiles
 If an object is launched with a great enough velocity, its path may very well be able to fall around the Earth
or fall to match the curvature of the Earth.
 To become a satellite, an objects horizontal velocity must be great enough for its falling distance to match
Earth’s curvature.
 The Earth drops a vertical distance of 5 meters for every 8000 meters. See the tangent figure 5.34
 If a projectile can achieve a speed fast enough to match this it can stay in orbit around the Earth and never
reach ground.
 To do this satellites or space vehicles must achieve a speed of 8 km / s or 29,000 km/hr
 If they stay within the atmosphere, they will burn up. So they launch these vehicles to an altitude of 150
km above the Earth to avoid this from happening.
 One thing to remember. The vehicle is still subject to gravity at this height. So the vehicle continues to
free fall towards the Earth, but if it maintains its velocity it will continue to match the curvature and stay in
orbit.
(2). Escape Speed
 For an object to leave the Earth’s gravitational pull, it must achieve what is called escape speed.
 This is 11.2 km/s
 For a vehicle such as the shuttle it must consider its payload or mass before it can get to escape speed.
 As the vehicle gets farther away from the Earth, gravitational effects diminish (Inverse Square Law)
 The force of gravity on the payload would be the greatest near Earth. The change of PE of a 1 kg body
moved from the surface of the Earth to infinite distance is 62 million joules. So if the payload is far from
the surface requires at least 62 mega joules of energy per kilogram of load. 62 mJ of energy corresponds to
a speed of 11.2 km/s whatever the total mass involved.
(3). Elliptical Orbits
 Planets orbit the sun, not in a circle, but in the shape of an ellipse.
 Read page 91.