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Name: Eve
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Question:
Why does the speed of the orbit slow down the further away you go from the source of the gravity?



Replies:
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


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


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


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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