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Leaving the Earth

Going Up:

GPE Change in a Uniform Field
Close to surface of the earth the gravitational field is almost completely uniform
o Meaning g is a constant value of 9.81 N kg-1
Meaning the work done in lifting an object through a distance h will be given…

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Equipotential Surfaces
GPE of an object at a particular height depends on
o The mass of the object
o The mass of the earth
Gravitational field strength
o Useful to think of the space around the earth as having a property which
depends only on the mass of the earth…

Page 3

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Escape from the Earth:

Escape Velocity
In order to escape from the earth's gravitational field the object needs to have
enough initial kinetic energy
o When added to the negative potential energy would need to make a total
energy of at least zero
In order to escape the total energy…

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o Mass increases
o Or Radius decreases
The escape velocity need to increase too
If a planet or star is sufficiently massive the escape velocity matches the speed of
light, such an object would not emit or reflect electromagnetic radiation
And would therefore appear black
It is not possible to…

Page 5

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Conservation of Energy
In any closed system the total energy remains constant although it may change form
and internal work may also be done when one body interacts with another


momentum = mass ×velocity

Momentum is conserved providing no external forces act on the system before and
after the…

Page 6

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Rocket Science:
Forces on a Rocket

Thrust opposes weight on a rocket when rocket is close
enough to the earth for gravity to be significant
Lift is used to stabilise the rocket
Forces vary throughout the flight
o Weight reduces as the fuel is used up
o Thrust changes as…

Page 7

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No external force acts so momentum must stay at zero
As exhaust is ejected the gases have momentum in one direction and
the rocket must have an equal momentum in the opposite direction
Meaning the rocket will move

Loss of Mass
o Assuming the rocket can ejects its mass at…

Page 8

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Most efficient at the moment
Meaning a lot depends on the mass ratio
o Mass Ratio
Lighter materials can be used to improve the payload: fuel ratio by
making the payload lighter or eliminating some structure
The ratio is hard to improve as carrying more fuel means a bigger

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Combustion of the fuel in a chemical rocket produces a high pressure gas which
ejected through the rocket nozzle
o Accelerated exhaust gas is called the working fluid
Turbine engines and propeller powered aircraft used air from the
atmosphere as the working fluid, however, no atmosphere/air means
they won't work…

Page 10

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Pressure is defined as force per unit area

p= A

o This is rearranged to F=pA, meaning the work done by a gas expanding at a
constant pressure will be given by
W = pAs

If area is constant, As = V , the increase in volume. This means…


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