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Chapter 21 Gravitational Fields (21.1 (Free Fall (Weight= force of gravity…
Chapter 21
Gravitational Fields
21.1
Gravitational field
- region surrounding an object in which it exerts a gravitational force on any other object
Field line or line of force
- its direction indicates the direction of the force and represents the path an object
at rest affected by the force field would take
Gravitational field strength (g)
- force per unit mass on a small test mass placed in the field
g=F/m
(must be small so other object doesn't change position) units are
Nkg-1
Free Fall
Weight= force of gravity on object
Mass of m W=mg so
acceleration= g
Object falls freely with acceleration g
Weightlessness is due to there being no support force
Field patterns
1)
Radial Field
Field lines are like spokes of a wheel
Always directed toward centre
Usually arise from spherical or point like objects
Get stronger as you get closer
2)
Uniform field
Where gravitational strength is the same throughout the field
Parallel and equally spaced
Surface of planet they are uniform (zoomed in)
Density
- higher density= stronger field
21.2
Gravitational potential energy
- energy of an object due to its position in a gravitational field- change in Ep
Gravitational potential
- work done per unit mass to move a small object from infinity to that point
unit= Jkg-1
Gravitational potential at infinity is zero- usually negative
Potential Gradients
Equipotentials
Surfaces where potential is constant
No work done to move along
Perpendicular to force line
Start and end on the same equipotential line no net change in gravitational potential energy
Start and end on different change in potential energy and work is done
Potential gradient
Rate at which potentials change with distance (spacing of equipotentials)
At earth's surface increase in 1m = change in potential of 9.8Jkg-1 so negative potential gradient= gravitational field strength
Negative because as potential increase field strength decreases
Closer together equipotential= greater potential gradient and stronger the field is
Equal change in spacing= equal potential gradient
If you double distance away from planet you half the potential
21.3
Kepler's third law
- r^3/T^2 = constant
Inverse square law
- intensity is inversely proportional to the square of the distance from the source
Newton's law of gravitation
3 assumptions- Gravitational force between 2 point masses is...
1)
Always attractive
2)
Proportional to the mass of each objects
3)
Proportional to 1/r2
21.5
Satellites
Geostationary
Orbit over same point of surface of earth
Must orbit over equator
Time period of 24hrs
Height of geostationary satellite above earth's surface is 36000km
Geosynchronous
24hr time period
Inclined to equator
Same point over earth at same time each day
Uses
Communications
Satellite can continuously monitor same part of the earth's surface without needing to change orbit
Weather
Ground antenna don't need to change direction they're pointing
Set at a direction in space
Orbital Energy
-
Total= negative of its KE
EP is negative and double magnitude KE
EP double total
All proportional to 1/r
21.4
Variation of g
From surface outwards
Follows behaviour of equation
remove constants, g drops by 1/r^2 (gives 1/r^2 graph)
From surface inwards
Inner shell and outer shell
Outer shell contributes nothing- no overall pull, they cancel
Inner sphere
where m=mass of inner sphere
Sub in M=pv (density) and V=4πr3/3
Gives equation g=
Remove constants, g is proportional to r
Escape Velocity
- minimum velocity an object must be given to escape from the planet when projected vertically from the surface
Variation of V
Forms -ve 1/r curve
i.e.
at 2r distance potential is half that of r
