Orbital Velocity and Radius

name         Eve
status       other
grade        4-6
location     N/A

Question -   Why does the speed of the orbit slow down the
further away you go from the source of the gravity?
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Hello Eve,

Thank you for your question.  The reason that planets move slower when
they are far away from the sun is very similar to what happens when you
throw a rock up in the sky.


If you toss and object up, it may start off moving very fast, but as it
climbs higher it will move slower and slower.  Eventually it begins
moving back down.  And the closer it gets to the ground, the faster it
is going.
This is very similar to how planets behave as they orbit the sun.

The reason for all this is that, so far as we know, the energy of the
universe is conserved.  Or put in other words, the total amount of
energy is constant.  Now, what does this mean regarding your question?

Well, A planet orbiting a star has energy stored in two places:

Kinetic Energy, which is the energy associated with how fast it moves
and massive the planet is.

Gravitational Potential Energy, which is the energy associated with the
gravitational attraction of the two objects.  The greater the separation
between the objects, then the greater the potential energy will be.


Now, because of the conservation of energy we expect that the sum of

Kinetic Energy + Potential Energy  = a constant value.

When the planet is close to the sun, the potential energy is small,
therefore the kinetic energy is large and the planet moves fast.  When
the planet is far from the sun, the potential energy is large and so the
kinetic energy must be small to compensate (therefore the velocity is
less!).

Likewise, when you first throw a rock upwards, it is close to the
ground.  So the potential energy will be small, but the kinetic energy
will be large (and it moves fast).  When it is high up in the air, the
potential energy will be very large and the kinetic energy will be small
(and it moves slow).   Right before it hits the ground, the kinetic
energy will be large again (and it will be moving fast) and the
potential energy will be small.


Now, in nature, there are many, many different types of energy, not just
Kinetic Energy and Gravitational Potential Energy.  There is energy
associated with temperature, chemical reactions, sound waves, friction
and many more things.  But if you account for all the forms of energy in
a particular system that you study, then they must all add up to a
constant amount.

In fact, the conservation energy (the same reason that planets travel
slower when they are further from the sun) is such a strong principle,
that whenever scientists find that they cannot account for all the
energy in a system, then they know that they have discovered something new!

---------------------------
Michael S. Pierce
Materials Science Division
Argonne National Laboratory
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Dear Eve,

The speed of an object circling a much more massive object, such as 
a communications satellite circling the earth, decreases as it gets 
further from the earth for a very simple reason: the gravitational 
pull on the satellite decreases as it gets further from the earth.

This is a consequence of the "inverse square law" of gravity.  If 
the satellite is moved to an orbit with twice the radius, the force 
of the gravitational pull on it is reduced by a factor of 4 (since 
2*2 = 4 or (1/2)^2 = 1/4.)

The centripetal acceleration of a satellite moving in a circle of 
radius R with a speed v is v^2/R and the force needed to produce 
that acceleration is F = mv^2/R.  Notice that it you double R, the 
needed force decreases only by a factor of two whereas the 
gravitational force decreases by a factor of 4. Therefore the speed 
of the satellite must also decrease (by a factor of the square root 
of 2) so the needed force matches the gravitational force.

Similar factors work for any change in the radius of the orbit.

Best, Dick Plano, Professor of Physics emeritus, Rutgers University
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Eve,

This is a tough concept for someone in grades 4-6!

There is a constant involved here called angular momentum.  This can 
be explained in that, for something to orbit some other object, it 
has to travel 360 degrees around that object.  Halfway around the 
object would sweep 180 degrees.

Because the orbits of the planets around the Sun are elliptical, the 
number of degrees traveled, though also 360 degrees, runs into a bit 
of a problem, because, as you mentioned, in an elliptical shape, the 
revolving object is sometimes closer to and sometimes farther from 
the object around which it is revolving.

Here is where the conservation of angular momentum comes in.....over 
the same period of time, there is a constant angular momentum, 
meaning that say, in one hour, or 24 hours, or 60 days, or what ever 
time period you want, an equivalent number of degrees are swept by 
the revolving object with respect to the object around which it is 
revolving.  For an object with a totally circular orbit, the 
velocity of the revolving object could remain the same constantly 
because the distance of the object from what it is revolving around 
is constant.  For something with an elliptical orbit, the velocity 
changes to preserve the conservation of angular momentum.  The 
number of degrees traveled stays the same, but the actual distance 
traveled, per unit of time, differs depending on the radius of the 
distance between the two objects.

As I said, any explanation of this requires knowledge of some 
difficult terms and concepts.....revolution, angular momentum, 
velocity, ellipse, etc..  That you asked the question indicates you 
do at least have some understanding of them.

You might try checking your science book or books for your grade, or 
a junior high/middle school text which could provide an explanation 
using other terms with which you are also already familiar.  I know 
this is an interesting topic, but it is a bit surprising...I can 
remember the wonder I faced the first time I heard about it, but it 
does make total sense once you grasp what is actually happening 
during the time any object with any orbit circles another object.

Thanks for using NEWTON!

Ric Rupnik
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Eve,
For an object to be in orbit around a planet, the planet must pull with
gravity to make the object move in a circle.  If the planet cannot pull hard
enough, the object will fly away.  If the planet pulls too hard, the object
will fall from the sky.

The greater the orbit's radius (i.e. the further the object is from the
planet), the weaker the pull of the planet on the object.  The weak pull at
a large radius is not strong enough to turn a very fast object.  For a
distant object to orbit a planet, it must move slow so that it doesn't fly
away.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
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