Trajectories in an Attractive Central Potentialby Jason Janesky, Corinne Manogue & Kerry BrowneCopyright 2010 Corinne ManogueThis worksheet calculates the trajectories of a mass 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 under the influence of a CENTRAL force numerically.The main example of a central force which we've been studying in class is an attractive inverse square: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Note: You should feel free to change aspects of this worksheet to explore the properties of motion in central potentials. While many of the values can be changed, the worksheet will not function if you change others. To help guide you, the titles for the values you should feel comfortable changing are indicated in Bold Underline.
Setup the Problem
Choose values for the parameters below: Set the values of the masses of each of the particles and the reduced 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
Set values for the initial radial distance (r0), the initial angular position (phi0), the initial radial velocity (rdot0), and the initial angular velocity (phidot0), the central potential and the coupling constant k.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From these values, the angular momentum (el), the total energy (E), the effective potential (Veff) and and estimate for the orbital period (period0) are calculated. 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Set the minimum and maximum values of potential and the maximum value of r to display on the effective potential plot.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
What type of orbit would you guess for these parameters? What do you think 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 and 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 , the minimum and maxumum radial distances, will be?
Calculating the Orbit
First find the force in terms of 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define the system of differential equations: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
Input values for the approximate number of orbits (numorbits) and the number of frames to display per orbit (numframesperorbit). You may need to increase or decrease numorbits to get plots that make sense. In particular, if your plots don't make sense or you receive an error that the values cannot be calculated, it may help to reduce numorbits, possibly to a very small value. 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MCwwXUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0ZDRitGYW9GNkZkby8lK2V4ZWN1dGFibGVHRjhGQ0YrRmFvRjZGZG9Gam9GQ0YrRmFvRjZGZG9Gam9GQw==
The next set of commands tell Maple to solve the system of differential equations numerically and plot the result. The Maple details are unimportant, unless you are 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The next set of calculations generate an animation of the motion of the orbit in two dimensions and against the effective potential plot. To activate the animation, click on the plots that appear below the following commands and use the controls in the animation toolbar that appears at the top of the 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JSFHNote: Once you have gone through the worksheet step by step one time, you can speed up execution of the worksheet by selecting [Execute>>Worksheet] from the right click menu.
Bonus: Try some other potentials:1) Harmonic Oscillator 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First order General Relativistic correction to Newton 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for 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 very small.
3) Spiral orbits 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try setting phidot0 to values of 1.413 and 1.420 (with numorbits=3)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=