From: Ronald Wong (ronwong@inreach.com)
Date: Mon Nov 10 2003 - 22:44:56 PST
Message-Id: <l03102800bbd4f05f0aba@[209.209.18.93]> Date: Mon, 10 Nov 2003 22:44:56 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: re: two questions
Mike asked:
> ... What prevents the speed of an object moving in a gravitational
> field from getting above escape velocity?
In a sense, nothing.
It's all a matter of energy.
If object A is x-meters from object B, then there is a gravitational force
acting on object A pulling it towards object B.
To escape object B's influence requires energy. This energy can come from
many sources but ultimately it is object A's kinetic energy (KE) that will
determine whether it escapes the influence of object B or not.
If object A has no KE, then it will soon acquire it as the gravitational
force acting on it draws it towards object B, converting it's potential
energy at x-meters from object B into KE as it accelerates towards and
later crashes into object B.
If object A has the right amount of KE, then, under the right initial
conditions, it can orbit object B forever at an average distance of
x-meters from object B.
To escape the influence of object B, object A's KE must equal the amount of
work done overcoming the attractive force of object B as object A is moved
from it's original position, x-meters from object B, to a position an
infinite distance away.
Surprisingly enough, this work can be determined mathematically and, from
it's value, one can compute the speed needed to escape the gravitational
influence of object B. When you add the direction that object A must
travel, you have it's "escape velocity".
--------------------
There are a number of ways "...an object moving in a gravitational
field..." can get "...above the escape velocity".
1. First of all, as it enters the gravitational field, it's speed may already
be greater than the escape velocity so, assuming it isn't heading for the
object that is responsible for the gravitational field, it escapes.
2. Of course, if the object is orbiting a body, it's speed is less than that
of the escape velocity and an external force will be necessary in order to
bring it's speed up to the escape velocity.
A. A collision with another body can bring this about. This was not
uncommon during the early stages of planetary formation and it can
happen even now since a good size asteroid traveling at the right
speed could collide with our own plant and send sizeable chunks of
the earth sailing right out of our solar system.
B. If the object is a man-made spacecraft, then just firing up and
running the propulsion system for the right length of time with the
object pointing in the proper direction can accelerate it up to the
prescribed escape velocity.
3. When Pioneer 10 was launched from the earth in 1972, it's launch speed was
15 km/s. This exceeded the escape velocity for the earth (an example of
2B) - around 11 km/s - but not the escape velocity for the sun at the
earth's distance from the sun - around 43 km/s. To acquire the necessary
speed to escape from the sun's influence, Pioneer 10 was sent along a
predetermined path towards the planet Jupiter. As it approached the giant
planet, it came under it's gravitational influence and accelerated to a
speed that was not only great enough to escape the gravitational influence
of Jupiter but, at that distance, the sun's as well.
As it headed out into the great unknown, it continued
to move further away from the sun and, in 1984, it's
distance from the sun exceeded that of the planet Pluto.
It's science mission ended in 1997 but it continued to
send telemetry data until early last year (30 years
after it was launched). Until February of this year,
the small, 9 ft-diameter spacecraft was still responding
to ground control signals but, in February, the signal
from it's little 8 watt transmitter finally dropped below
the threshold of detection. At that point it was almost
8 billion miles away.
Amazing!
If you have nothing better to do, step outside and look at the night sky
late in the evening. During this time of year, you can see where Pioneer
10 is heading. It's the star Aldebaran in the constellation Taurus (it's
the blood-red eye of the bull) - not far from the beautiful group of
stars known as the Pleiades (or, as they are known in Japan, Subaru).
Cheers.
ron
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