Chapter 9 – Universal Gravitation

Caused by gravity… Things fall Moon orbits Earth Keeps people stuck to E Keeps Earth together Pulls other stuff toward E Planets in orbit around sun Tides Sun is “burning” Solar systems, galaxies, moons around planets Black holes Everything!!

Universal Law of Gravitation Inverse Square Law Weight & Weightlessness Ocean Tides

Isaac Newton Gravity extends through the universe Newton knew inertia, and that if something changed its speed or direction a force must be responsible Apple falling … apple changed its motion, so a force must be responsible-- Gravity Noticed the moon, and that it was traveling in circular motion This also requires a force ….same force was responsible for the Moon as was the apple

The Falling Moon- Satellite Motion Newton realized the moon must be falling or else it would travel away in a straight line So if it is falling, why is it never getting closer?? hypothesized that moon is just a projectile falling under the influence of gravity. And it never falls to Earth because of its speed….

Newton’s Law of Universal Gravitation Force of gravity acting between 2 objects is directly proportional to their mass and inversely proportional to the square of the distance between them m1 and m2 represents the masses of the two objects involved d - distance between the center of the two objects G- Universal Gravitation Constant, value of G = 6.67 x 10-11 Nm2/kg2 F - represents the Force of Gravity between any 2 objects Remember that Force of Gravity is the same thing as Weight

Examples What is the force of gravity between two 3 kg blocks that are placed 4 meters apart? How much is the force of gravity from the Earth acting on a 90 Kg man? (Mass of the Earth = 6.0 x 1024 Kg ; radius of the Earth = 6400 km)

What this law means Whatever factor the mass is increased by, Fg is increased by the same amount Ex. Triple the ‘m’, Fg is also tripled Whatever factor the ‘d’ between 2 objects is increased by, the force of gravity is multiplied by the inverse of the square of that number Ex. Triple the distance, force of gravity is 1/9th as much

Examples The force of gravity acting on you while on the surface of the Earth is 100 N. What would be the force of gravity acting on you if the Earth’s mass was doubled? Force Directly proportional to mass, So 200 N What would it be if your mass was doubled and the Earths stayed the same? What would the force of gravity acting on you be if you were twice as far from the center of the Earth as you are now? Force is Inversely proportional to the square of the distance, so distance is increased by 2, inverse square of 2 is 1/22 or 1/4th , so force of gravity would be 1/4th as much or 25 N.

More examples…. A spaceship with a weight of 10,000 N on the surface of the Earth moves to a distance that is 3 times further away from the center of the Earth, what is the force of gravity on it now? Distance increased by 3 x , so Fg decreases by the inverse square of this number so Fg goes down by 1/9th. 10,000/9 = 1111.1 N R Space ship weighs 1111.1N here Space ship weighs 10,000N here

Why this happens?? Inverse Square Law… Surface Area of a sphere

Gravity… In general “How masses communicate with each other” Force that exists between any two masses anywhere in the universe Causes tides, shape of planets, orbits, pressure necessary for stars to burn, falling objects, projectile motion, formation of solar systems, galaxies More mass…. More gravitational pull Closer to something… more gravitational pull Pulling force

Weight and Weightlessness Being weightless Can’t happen anywhere around the Earth Would mean there is no gravity acting on you Even astronauts are not weightless Feeling weightless Happens all the time Astronauts feel weightless Happens because of a lack of a support force

Weight and Weightlessness Astronauts in orbit are in a continuous free fall Nothing supporting them so the feel weightless Gravity still acting though, so not actually weightless

Any time you are not being supported by a force equal to your Weight… Any time you are not being supported by a force equal to your Weight…. You feel weightless BUT…. Gravity still acts… so not actually weightless

Gravitational Fields g= Gm d2 The ‘field’ is the area of space affected by an objects gravity The further an object is away… the weaker the field ‘g’ (acc of gravity) indicates the strength of a field The field strength on the surface of the Earth is about 9.8 m/s2 or about 10 m/s2 ‘g’ also changes by the inverse square rule If you are twice as far away from the center of the Earth ‘g’ = (9.8)/4 m/s2 =2.45 m/s2 g= Gm d2

Gravity field inside the Earth According to Newton, the closer you get to an object the stronger gravity is, but if you were travelling to the center of the Earth, all of the mass above you would start to cancel the gravity below you, so as you travel towards the center of earth gravity will become less and less strong Any tunnel through E will take 42 min to travel through!

What if….

Earth Shrunk but you stayed same location…?? Force of gravity would be unchanged

Earth Shrunk and you stayed on its surface… Force of gravity would increase

Ocean Tides From the Moon Side of the Earth closest to the moon, has a high tide As well as the side of earth furthest from the moon This happens because… Water flows There is a large difference in gravitational strength from the moon on either side of the Earth… because of difference in distance from the moon Gravity from the moon tugs on Earth just a bit Gravity from moon is of course stronger when moon is close And weaker when far away Earth Earth

http://www.youtube.com/watch?feature=fvwp& NR=1&v=u3LtEF9WPt4 http://www.youtube.com/watch?v=RXK4BIpRx- k&feature=related - 2:30 Inuit People – Mussel Gathering

The Sun also causes Tides The Sun, like the Moon pulls on Earth, so the side of Earth closest to Sun, receives a high tide from Sun Tides from the Sun are weaker than from the moon Why is this? Sun actually has a lot stronger pull on Earth than the moon does, so why aren’t solar tides larger?? Not that big of a difference in how far the sun is from sunny side compared to dark side So difference in gravity strength is small City analogy

Tidal Effects… spring tides, Neap Tides

Neap Tide – Solar & Lunar tides subtract from each other Neap Tide – Weak Tide Spring Tide - Solar & Lunar tides combine Spring Tide - “Super” Tide

Gravity is a mutual tug of war Earth and moon orbit a common point in space Point is center of gravity of Earth Moon system

Perturbations Small irregularities in the orbit of a planet caused by a close proximity to another planet Gravity of one planet slightly tugging on another This is how Neptune was discovered http://csep10.phys.utk.edu/astr161/lect/histor y/perturbations.html

Earth Tides and Atmosphere Tides Tides don’t just happen with water Occur w/ the ground Earth is really just a thin solid crust on top of molten (liquid) rock Ground rises and lowers small amount depending on moon’s location and with the atmosphere Atmosphere has much larger tides than oceans do

Einstein’s Theory of Gravitation & Black Holes Next Chapter

Chapter 10 Projectile & Satellite Motion

But the ground also curves (Earth is not flat) Launched projectiles will follow a curved path (see below) until they hit the ground But the ground also curves (Earth is not flat) Most projectiles have a curve that are much steeper than the curve of the Earth BUT, if you throw a projectile fast enough, then curved path of the projectile will match the curve of the Earth Then, the projectile will never reach the surface and forever be in an orbit Projectile must also be above the Earth’s atmosphere, so that air resistance does not slow it down

Projectile being thrown a different speeds, from the top of a mountain above the atmosphere If you could throw something as fast as you wanted and there was no air resistance could you make something orbit?/

Satellite Motion Satellite - any object that orbits around another object… includes, planets, moons, man-made satellites, etc. As discussed before, satellites are just projectiles that fall at the exact same rate that Earth (or another planet) curves away from it… and never reaches the surface

The Motion of Planets… For a long time,most scientists thought all satellites travel in perfectly circular orbits NOT TRUE Could not make accurate predictions of their motion Planets, moons, etc. were not where they were supposed to be! Planets did not follow these predicted paths Then…… along came Johannes Kepler

Kepler’s 3 Laws of planetary motion First Law 1) The paths of the planets are ellipses, with the sun at one focus (the other focus is just a point in space) http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Kepler/kepler.html

Keppler’s 2nd Law An Imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. This means planets move faster when they are closer to the sun and slower when they are further away http://www.phy.syr.edu/courses/java/mc_html/kepler_frame.html

(Ta/Tb)2 =(ra/rb)3 Keppler’s Third Law The square of the ratio of the periods of any two planets revolving about the sun is equal to the cube of the ratio of their average distances from the sun. Thus, if Ta and Tb are the planets periods, and ra and rb are their average distances from the sun we get (Ta/Tb)2 =(ra/rb)3

Elliptical paths & Kepler Kepler came up with Three Laws of Satellite Motion These laws explained that planets & other satellites travel in ellipses (ovals), not circles When tested Kepler’s laws almost perfectly predicted paths of planets and moons This means planets are closer to the Sun at some points in their orbit, and farther from the Sun at other points

Orbits Earth’s orbitVery nearly circular, but elliptical like all other planets Elliptical path of Earth does not affect weather at all Other planets, like Mercury, have more exaggerated elliptical orbits

Conservation of Energy and Satellite motion Based on the fact that KE + PE always stays constant….. Planets travel faster when they are closer to the Sun, and slower when they are further away Slow Fast

Escape Speed Speed that something needs to travel in order to permanently escape an objects gravitational pull without getting pulled back Escape speed for the Earth is roughly 7 miles per sec.

Einstein & Gravity Kepler’s predictions of where objects should be were very close but still somewhat off Albert Einstein actually defined exactly how gravity works and his Theory of General Relativity predicted perfectly the orbits of all planets General Relativity stated mass warped Space-Time and this warping is what we feel as gravity Has been tested many times over the past 100 years, and all tests confirm Einstein’s predictions

General Relativity Many consider to be the greatest scientific discovery OF ALL TIME Will be discussed more next chapter In short, Gravity is not a force at all and is instead the curvature of space- time around a large mass

http://www.zamandayolculuk.com/cetinbal/H TMLdosya1/RelativityFile.htm

Black Holes Consequence of General Relativity Again more on this next Chapter What they are? Remnants of a collapsed star Shrunk to such a small size, that its gravity became infinitely strong…. So strong its escape velocity is faster than the speed of light One of the most interesting objects in the Universe Nothing can escape a black hole Creates an infinitely deep hole in Space-Time,

Gravitational Interactions Chapter 13 Gravitational Interactions

Gravity differences on Earth?? -Universal Law of Gravitation tells us if we are closer or further from Center of the Earth gravity will change -gravity slightly weaker at the top of a tall mountain… ie you weigh less -other inconsistencies….. Big Earthquakes change mass distribution of Earth… 2004 Indonesia Earthquake was so big the rate at which the Earth orbits slightly changed http://www.uwgb.edu/dutchs/platetec/rotationqk2004.htm http://www.sciencefriday.com/news/051407/news0514071.html

Mass of sun = 1.98 x 1030 kg Radius of the Sun = 695,500 km Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Radius (Earth=1) 0.382 0.949 1 0.532 11.209 9.44 4.007 3.883 Radius (km) 2,438 6,052 6,378 3,397 71,400 60,000 25,559 24,764 mass (Earth=1 =5.97 x 1024 kg) 0.055 0.815 0.107 318 95 15 17 mean distance from Sun (AU) 0.39 0.72 1.52 5.20 9.54 19.18 30.06 orbital period (Earth years) 0.24 0.62 1.88 11.86 29.46 84.01 164.8 orbital eccentricity 0.2056 0.0068 0.0167 0.0934 0.0483 0.0560 0.0461 0.0097 mean orbital velocity (km/sec) 47.89 35.03 29.79 24.13 13.06 9.64 6.81 5.43 rotation period (in Earth days) 58.65 -243* 1.03 0.41 0.44 -0.72* mean temperature at surface (C) -180 to 430 465 -89 to 58 -82 to 0 -150 -170 -200 -210 gravity at equator (Earth=1) 0.38 0.9 2.64 0.93 0.89 1.12 escape velocity (km/sec) 4.25 10.36 11.18 5.02 59.54 35.49 21.29 23.71 mean density (water=1) 5.25 5.52 3.93 1.33 0.71 1.24 1.67 number of moons 2 63 62 27 13 rings? no yes Mass of sun = 1.98 x 1030 kg Radius of the Sun = 695,500 km