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The Currency of Space Flight
Conservation of Energy
As bodies move through space they have both kinetic energy and potential energy.
Although these forms of energy may be interchanged, the total amount of
energy remains constant. This is a manifestation of the Law of Conservation of
Energy.
Kinetic Energy
Ke = ½ mv2
The kinetic energy of a body in orbit depends entirely upon its speed and its mass.
In order to reach a low altitude circular orbit a spacecraft must be given energy
in the form of kinetic energy.
A rocket, sitting on a launch pad, is nothing more (from a physics point of view)
than a stored energy source.
The total amount of energy available is determined by the amount of fuel in the
rocket. The job of the rocket designer and the rocket engineer is to create a
rocket that transfers the maximum possible amount of the chemical potential energy
stored in the rocket fuel into the kinetic energy of the payload.
Gravitational Binding Energy
Pe = -GMm/r
The gravitational potential energy of a body (with respect to a mass M) is
determined entirely by the mass of the object M and the body's distance from the
object having mass M.
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Energy Required for Elliptical (and Circular) Orbits
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If the amount of kinetic energy transferred to a satellite or space vehicle
during its launch provides it with less kinetic energy than is needed to reach
escape velocity, then the satellite will either fall back to Earth or attain
a closed elliptical (or circular) orbit.
In this case the total energy is less than zero.
Ke + Pe
< 0
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Energy Required for Parabolic Orbits
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Larger and more energetic rocket engines can transfer more energy to the
spacecraft. If the energy transferred to the spacecraft exactly equals the
gravitational potential energy of the spacecraft, then it will be launched on
a parabolic trajectory which will cause it to escape the Earth's gravitational
field..which extends to infinity.
Note that having enough energy to escape from the Earth's gravity does not mean
that the spacecraft can escape from the Sun's gravitational influence.
In this case the total energy is exactly zero.
Ec + Ep = 0
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Energy Required for Hyperbolic Orbits
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Gigantic multi-stage rockets can launch payloads with sufficient energy that
the energy they acquire exceeds the gravitational binding energy of the Earth.
In this case the payload will be launched on an hyperbolic orbit.
In this case the total energy is greater than zero.
Ke + Pe > 0
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Transparency Master
Conic Sections
| Total Energy |
Conic Section |
eccentricity |
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Total Energy is negative, i.e. E < 0
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circles and ellipses
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e < 1
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Total Energy is zero, i.e. E = 0
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parabola
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e = 1
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Total Energy is positive, i.e. E > 0
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hyperbola
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e > 1
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Student Activity
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Answer Key
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