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Ratacitori. Activitate: Forta universala de graviatie. Sumar:. In acasta activitate vom studia (a) orbitele eliptice si legile lui Kepler, (b) Legea gravitatie universale a lui Newton (c) greutatea aparenta pe orbita. Orbitele eliptice si legile lui Kepler.
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Ratacitori Activitate:Forta universala de graviatie
Sumar: • In acasta activitate vom studia • (a) orbitele eliptice si legile lui Kepler,(b) Legea gravitatie universale a lui Newton(c) greutatea aparenta pe orbita
Orbitele eliptice si legile lui Kepler • Unele orbite din sistemul solar nu pot fi aproximate cercuri - Un bun exemplu este Pluton la care distanta fata de Soare poate varia cu 50% Conform primei legi a lui Kepler, traiectoriile planetelor sunt elipse, avand Soarele intr-unul din focare.
F’ F Cand planeta se misca, Soarele este intr-unul din focare (F or F’) al elipsei. r C
F’ F Punctul cel mai apropriat de Soare este periheliul As a planet moves in an elliptical orbit, the Sun is at one focus (F or F’) of the ellipse perihelion v r C
F’ F … iar punctul cel mai departat este afeliul As a planet moves in an elliptical orbit, the Sun is at one focus (F or F’) of the ellipse perihelion Dreapta se numeste xa mare a elipsei v r C aphelion
F’ F a a Semiaxa mare a elipsei este foarte importanta pentru ca determina perioada orbitei Semiaxa mare este jumatate din axa mare si se noteaza cu a v r C
Pentru orbite circulare, perioada miscarii de revolutie, o rotatie completa in jurul Soarelui depinde doar de raza cercului r - a 3-a lege a lui Kepler’s M Pentru corpuri cu orbite aprox circulare r r m v Patratul perioadei orbitale este proportional cu cubul razei orbitei
F’ F a a a a Sa vedem ce determina perioada unei orbite eliptice Pentru orbite eliptice perioada depinde de semiaxa mare a. v r C
a a a a r = a r r r (Un cerc este un caz particular de elipsa, unde r=a)
Daca aplicam legea lui Kepler la elipse inlocuim raza cu semiaxa mare Pentru obiecte care se rotesc in jurul Soarelui Patratul perioadei orbitale este proportional cu cubul semiaxei mari a orbitei
a a a a Deci toate orbitele de mai jos vor avea aceiasi perioada
a a Pentru ca au aceiasi semiaxa mare a:
a a
a a
a a
a a a a
Deci daca fiecare din orbite este in jurul unui obiect masiv ca Soarele, Si daca toate au aceiasi semiaxa mare a,
Deci daca fiecare din orbite este in jurul unui obiect masiv ca Soarele, Si daca toate au aceiasi semiaxa mare a, Atunci conform legii a 3-a a lui Keplervor avea aceiasi perioada orbitala
Poti sa vezi o simulare a legii apasa aici (/essmovs/h7.htm)
P2perioadala patrat a3 semiaxa la cub Reprezentata grafic legea arata astfel • Deci asa cum se poate vedea din simulare corpurile • semiaxa mari vor avea si perioade orbitale foaret mari
Nu am discutat inca despre legea a 2-a a lui Kepler Pentru ca este de importanta numai daca orbitele sunt eliptice, de excentricitate mare Daca analizam de exemplu orbita unei comete cum este cometa Halley
Cometa Halley Neptune Sun
Un obiect cu traiectorie eliptica se misca incet cand este departe de Soare … dar accelereaza cand se apropie de Soare
Conform legii a doua a lui Kepler … linia care leaga obiectulsi Soarele
Aceasta este legea a 2-a a lui Kepler Linia care leaga planeta si Soarele, matura arii egale in intervale de timp egale
Legea gravitatiei universale a lui Newton • Forta care tine Luna pe orbita in jurul Pamantului se numeste gravitatie Sir Isaac Newton’s conceptual leap in understandingof the effects of gravity largely involved his realizationthat the same force governs the motion of a falling objecton Earth - for example, an apple - and the motion of the Moon in its orbit around the Earth.
Isaac Newton discovered that two bodies share a gravitational attraction, where the force of attraction depends on boththeir masses:
Both bodies feel the same force, but in opposite directions.
This is worth thinking about - for example, drop a pen to the floor. Newton’s laws say that the force with which the pen is attracting the Earth is equal and oppositeto the force with which the Earth is attracting the pen, even though the pen is much lighter than the Earth!
Newton also worked out that if you keep the masses of the two bodies constant, the force of gravitational attraction depends on the distance between their centres: mutual force of attraction
magnitude of the gravitational force between 2 fixed masses distance between the masses increasing • For any two particular masses, the gravitational force between them depends on their separation as: as the separation between the masses is increased, the gravitational force of attractionbetween them decreases quickly.
Your pen dropping to the floor and a satellite in orbit around the Earth have something in common - they are both in freefall. To see this, remember Newton’s thought experiment from the Activity on Solar System Orbits:
On all these trajectories,the projectile is in free fall under gravity.(If it were not, it would travel in a straight line - that’s Newton’sFirst Law of Motion.)
If the ball is not given enough “sideways” velocity, its trajectory intercepts the Earth ... that is, it falls to Earth eventually.
On the trajectories which make complete orbits, the projectile is travelling “sideways” fast enough ... On all these trajectories, the projectile is in free fall. On all these trajectories, the projectile is in free fall.
… that as it falls, the Earth curves away underneathit, and the projectile completes entire orbits without ever hitting the Earth. On all these trajectories, the projectile is in free fall.
Apparent Weightlessness in Orbit This astronaut on a space walk is alsoin free fall. The astronaut’s “sideways” velocityis sufficient to keephim or her in orbitaround the Earth.
Let’s take a little time to answer the following question: • Why do astronauts in the Space Shuttle in Earth orbit feel weightless?
Some common misconceptions which become apparent in answers to this question are: (a) there is no gravity in space, (b) there is no gravity outside the Earth’s atmosphere, or (c) at the Shuttle’s altitude, the force of gravity is very small. Click on each alternative to see why we claim that it’s a misconception! Then see if you agree with our explanation ...
In spacecraft (like the Shuttle) in Earth orbit, astronauts are in free fall, at the same rate as their spaceships. On all these trajectories, the projectile is in free fall. That is why they experience weightlessness: just as a platform diver feels while diving down towards a pool, or a sky diver feels while in free fall.
In the next Activity we’ll look at one Solar Systemorbit in particular - that of the Moon around the Earth. On all these trajectories, the projectile is in free fall.
Image Credits • NASA: View of Australia • http://nssdc.gsfc.nasa.gov/image/planetary/earth/gal_australia.jpg • NASA: Halley in 1910 • http://pds.jpl.nasa.gov/planets/gif/smb/hal1910.gif • NASA: Space Shuttle • http://shuttle.nasa.gov/shuttle/index.html
(a) There is no gravity in space? • At face value, this statement doesn’t bear too much examination, because Newton’s Law of Gravitation has been applied right from its inception to the motion of the Moon and planets - and they are in space. When people make this assumption, perhaps what theyare really saying is that the sort of gravity which makesus feel heavy only exists on planetary surfaces - but Newton developed the Law in the first place by realizing that gravity as it acts on Earth (e.g. on an apple)is the same force as that which acts on the Moon and planets.
