Background Material

Answer the subjoined questions following reviewing the “Kepler's Laws and Planetary Motion” and “Newton and Planetary Motion” enhancement pages.

Question 1: Inhale a sequence connecting each law on the left after a opportunity a name of it on the exact.


planets progress faster when cease to the sun


planets revolution the sun in pregnant paths


planets after a opportunity abundant revolutions obtain?} a crave spell to entire an revolution

Question 2: When written as P2 = a3 Kepler's 3rd Law (after a opportunity P in years and a in AU) is ry to …

a) any aim revolutioning our sun.

b) any aim revolutioning any star.

c) any aim revolutioning any other aim.

Question 3: The ejection to the exact has an perturbation of encircling … a) 0.25

b) 0.5

c) 0.75

d) 0.9

Question 4: For a planet in an pregnant revolution to “range out resembling areas in resembling amounts of spell” it must …

a) progress slowest when neighboring the sun.

b) progress fastest when neighboring the sun.

c) progress at the similar urge at all spells.

d) accept a adequately spherical revolution.


Question 5: If a planet is twice as far from the sun at aphelion than at perihelion, then the sinew of the gravitational sinew at aphelion conciliate be as it is at perihelion.

a) impure spells as considerable

b) twice as considerable

c) the similar

d) one half as considerable

e) one region as considerable

Kepler’s 1st Law

If you accept not already produced so, expatiate the NAAP Planetary Revolution Simulator.



Tip: You can     fluctuate the esteem of a slider by     clicking on the slider bar or by entering a enumerebuke in the esteem box.

Open the Kepler’s 1st Law tab if it is not already (it’s understandn by lapse).

· Enable all 5 inhibit boxes.

· The stainhither dot is the “false planet”. One can click on it and pull it environing.

· Fluctuate the dimension of the revolution after a opportunity the semimajor axis slider. Voicelessness how the enhancement grid denotes fluctuate in lamina opportunity the displayed revolution dimension sediment the similar.

· Fluctuate the perturbation and voicelessness how it affects the cast of the revolution.

Be apprised that the ranges of distinct parameters are scant by serviceable issues that appear when creating a pretender rather than any gentleman substantial limitations. We accept scant the semi-major axis to 50 AU past that covers most of the aims in which we are careful in our light administration and accept scant perturbation to 0.7 past the ejections would be severe to fit on the shade for abundantr esteems. Voicelessness that the semi-major axis is aligned horizontally for all pregnant revolutions inventd in this pretender, where they are randomly aligned in our light administration.

· Animate the false planet. You may need to extension the liveliness rebuke for very abundant revolutions or curtail it for insignificant ones.

· The planetary presets set the false planet’s parameters to those approve our light administration’s planets. Explore these non-interferences.

Question 6: For what perturbation is the minor centre (which is usually emptiness) located at the sun? What is the cast of this revolution?   


Question 7: Invent an revolution after a opportunity a = 20 AU and e = 0. Pull the planet earliest to the far left of the ejection and then to the far exact. What are the esteems of r1 and r2 at these colonys?


r1 (AU)

r2 (AU)


Far Left


Far Right

Question 8: Invent an revolution after a opportunity a = 20 AU and e = 0.5. Pull the planet earliest to the far left of the ejection and then to the far exact. What are the esteems of r1 and r2 at these colonys?


r1   (AU)

r2   (AU)


Far Left


Far Right

Question 9: For the ejection after a opportunity a = 20 AU and e = 0.5, can you invent a subject-matter in the revolution where r1 and r2 are resembling? Sketch the ejection, the colony of this subject-matter, and r1 and r2 in the extension adown.

Question 10: What is the esteem of the sum of r1 and r2 and how does it tell to the ejection properties? Is this gentleman for all ejections?   



þÿQuestion 11: It is not-difficult to invent an ejection using a loop of string and two thumbtacks. The string is earliest natty balance the thumbtacks which act as foci. The string is then pulled firm using the pencil which can then investigate out the ejection.

Assume that you hope to inhale an ejection

after a opportunity a semi-major axis of a = 20 cm and e = 0.5. Using what you accept versed antecedent in this lab, what would be the alienate distances for a) the dissociation of the thumbtacks and b) the diffusiveness of the string? Please amply teach how you mention these esteems.


Kepler’s 2nd Law

· Use the “clear non-interferenceal features” nonentity to reprogress the 1st Law features.

· Known the Kepler's 2nd Law tab.

· Press the “start rangeing” nonentity. Adjust the semimajor axis and liveliness rebuke so that the planet progresss at a steady urge.

· Adjust the dimension of the range using the “adjust dimension” slider.

· Click and pull the range section environing. Voicelessness how the cast of the range section fluctuates, but the area does not.

· Add over ranges. Erase all ranges after a opportunity the “erase ranges” nonentity.

· The “range unintermittently” inhibit box conciliate account ranges to be inventd unintermittently when rangeing. Test this non-interference.

Question 12: Erase all ranges and invent an ejection after a opportunity a = 1 AU and e = 0. Set the fractional range dimension to one-twelfth of the epoch. Pull the range section environing. Does its dimension or cast fluctuate?    



Question 13: Leave the semi-major axis at a = 1 AU and fluctuate the perturbation to e =

0.5. Pull the range section environing and voicelessness that its dimension and cast fluctuate. Where is the range section the “skinniest”? Where is it the “fattest”? Where is the planet when it is rangeing out each of these sections? (What names do astronomers use for these positions?)   


Question 14: What perturbation in the pretender gives the highest alteration of range section cast?   


Question 15: Halley’s comet has a semimajor axis of encircling 18.5 AU, a epoch of 76 years, and an perturbation of encircling 0.97 (so Halley’s revolution cannot be pompn in this pretender.) The revolution of Halley’s Comet, the Earth’s Orbit, and the Sun are pompn in the diagram adown (not correspondently to lamina). Based upon what you understand encircling Kepler’s 2nd Law, teach why we can barely see the comet for encircling 6 months total revolution (76 years)?



Kepler’s 3rd Law

· Use the “clear non-interferenceal features” nonentity to reprogress the 2nd Law features.

· Known the Kepler's 3rd Law tab.

Question 16: Use the pretender to entire the board adown.



P (years)

a (AU)


















Question 17: As the dimension of a planet’s revolution extensions, what happens to its epoch?  


Question 18: Start after a opportunity the Earth’s revolution and fluctuate the  perturbation to  0.6. Does changing the perturbation fluctuate the epoch of the planet?  


Newtonian Features

· Important: Use the “clear non-interferenceal features” nonentity to reprogress other features.

· Known the Newtonian features tab.

· Click twain pomp vector boxes to pomp twain the quickness and the succor of the planet. Observe the command and diffusiveness of the arrows. The diffusiveness is proportional to the esteems of the vector in the conspire.

Question 19: The succor vector is constantly subject-mattering towards what aim in the pretender?   


Question 20: Invent an ejection after a opportunity a = 5 AU and e = 0.5. For each notable colony on the conspire adown denote a) whether the quickness is increasing or decreasing at the subject-matter in


the revolution (by circling the alienate arrow) and b) the bearing θ between the quickness and

succor vectors. Voicelessness that one is entired for you.


Question 21: Where do the utmost and incompleteness esteems of quickness appear in the revolution?


Question 22: Can you illustrate a open administration which identifies where in the revolution quickness is increasing and where it is decreasing? What is the bearing between the quickness and succor vectors at these spells?    



Astronomers connect to planets in their revolutions as “forever escheatment into the sun”. There is an interesting gravitational sinew between the sun and a planet. By Newton’s 3rd law it is resembling in lump for twain aims. However, beaccount the planet is so considerable hither solid than the sun, the resulting succor (from Newton’s 2nd law) is considerable abundantr.

Acceleration is defined as the fluctuate in quickness – twain of which are vector quantities. Thus, succor perpetually fluctuates the lump and command of quickness. As crave as the bearing between succor and quickness is hither than 90°, the lump of quickness conciliate extension. Opportunity Kepler’s laws are abundantly illustrative of what planet’s do, Newton’s laws authorize us to illustrate the essence of an revolution in essential substantial laws!