Transcript Motion Along a Straight Line at Constant Acceleration

Book Reference : Pages 66-67
1.
To do some sums!
2.
To define what a satellite is
3.
To describe two popular types of orbit for
man-made satellites
4.
To connect Satellite motion with circular
motion
5.
To look at Kepler’s third law
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Radius/
1010 m
6
11
15
23
78
143
Orbit
Period/
107 s
0.8
1.95 3.2
5.9
37.4 93.0
r3 / T2
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Please calculate the missing figures
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Definition : an object with a small mass in orbit
around an object with a large mass
The objects can be either natural satellites... i.e.
Moons & planets or man-made satellites, space
craft and space stations.
a. The path of a celestial body or an
artificial satellite as it revolves around
another body.
b. One complete revolution of such a
body.
Discuss and make a list of some of the
common uses for man-made satellites
Communication
TV & Radio
Telephone (Relay of calls & “Sat phones”)
Weather
Spy
Sat Nav
Scientific monitoring (remote sensing)
Astronomy
Now classify each as to whether in terms of orbit
it needs to “stay put” or whether it needs to
“move”
When we need a Satellite to “stay still” in a
relative position we use a geostationary orbit
TV
Some Comms
When we need a Satellite to “move” and provide
coverage for a large proportion of the Earth’s
surface we use a polar orbit
Weather, spy,
remote
sensing etc
Some applications such as “Satnav” (GPS) require
a constellation of many satellites. A SatNav will
receive from several satellites at the same time
The force of gravitational attraction for a satellite
can be equated to a centripetal force acting upon
the satellite
Velocity v
Planetary
Motion
Force F
Sun mass M
Radius r
Planet of Mass m
The Gravitational force can be given by
F = G mM/r2
The centripetal force on the planet of mass m can
be given by
F = mv2/r
Hence we can equate the two and simplify
GM/r = v2
This gives us the speed of the satellite in orbit
GM/r = v2
Moreover since
Speed = circumference of orbit / Period of orbit
Speed = 2r / T
GM/r = 42r2 / T2
Which can be rearranged thus
GM/42 = r3 / T2
For a given set of planets e.g. Our solar system
where M is the mass of the sun, The left hand
side will be a constant
GM/42 =
But if the LHS is a constant, then the RHS must
also be a constant
= r3 / T2
Kepler’s third law!
Newton’s law of gravitation was developed as a
direct result of Kepler’s work
Calculate GM/42 where M is the mass of the
Sun. (2.0 x1030kg)
Where have we seen this figure today?
Show that the height of a geostationary satellite
is 35600km (note you are on the right lines if you
get 42000km)
Mass of Earth = 6.0x1024kg
Radius of Earth = 6400km