1Chapter 9Gravity22The Law of Universal Gravity• Newton speculated that the same force that made an apple fall to the Earth caused the moon to orbit the Earth• The moon falls around the EarthThe three animations at the bottom of this slide illustrate that is one was to throw a ball harder and harder, that the balls trajectory would curve at the same rate as the Earth and would be in orbit.33The Law of Universal Gravity• Two masses attract each other• The greater the distance between them, the less the attraction• The force between two masses is the same regardless of their relative weights221~dmmFRemember, equal and opposite forces! So two masses will exert the exact same gravitational force on each other even though one may weigh MUCH more.44The Gravitational Constant• The law of universal gravitation can be expressed as an exact equation:• G is the measure of the force of gravity between two 1 kg masses 1 m apart2211221kgNm1067.6−×==GdmmGFG can also be written as 0.0000000000667 (Nm2/kg2). That’s a VERY SMALL number!55Gravity Over a Distance•Every time you double the distance between two objects, you quarter the gravitational force between them66Problem Solving: Universal Gravitation• Using the law of universal gravitation, g and the radius of the Earth, determine the mass of the EarthkgkgNmmmGgrGmmgrGmFrmEarthEarthEarthEarthEarth24221162221096.51067.6)107m/s/s)(6.38.9(×=××====−Note that the m’s cancel out. This is a direct consequence of the fact that gravity makes all objects fall at the same rate regardless of their masses.Make a note that it does not matter what the distribution of mass is (we consider the Sun to be located at its center of mass – if it shrunk to half its size and stayed the same mass, our orbit would not be effected).77Weight and Weightlessness• Before, we defined weight as mg, when the object is not accelerating…• Refine: the weight of something is the force it exerts against a supporting floor or weighing scale88Even though you may be weightless, the force of gravity may still be large.99Tides• Tides are caused by the differences in gravitational pull on different sides of the Earth caused by the moon (and to a lesser extent, the Sun)– There are 2 high tides and 2 low tides every day• Spring tides – occurs when the sun, Earth and moon are lined up– High tides are extra high, low tides are extra low– The moon is in the new or full phase• Neap tides – occurs when the Earth is at the apex of a corner formed by the sun and moon– High tides are not as high and low tides are not as low– The moon is in its first quarter or ¾ phaseRemember, the tides are cause of a difference in gravitational force from one side of the Earth to the other.1010Problem Solving: Tides• The force on the Earth by the sun is 180 times greater than the force of the moon on the Earth. Why does the moon have more effect on the tides than the sun?–The sun is so far away, the difference in gravitational force between the sides of the Earth is much smaller than the difference caused by the moon.1111Gravitational Fields• Since you do not need to touch something to exert a gravitational force on it, gravity is called an action at a distance• Gravity can also be seen as a field: gravity affects the space around it so that an object at a point in space feels a force proportional the the strength of the field– Gravitational fields effect all space, even inside an object1212Drawing Gravitational Field Lines• Field lines are represented by arrows• The arrows always point in the direction an object will fall• The closer the field lines, the stronger the field• The more field lines, the stringer the field1313Einstein’s Gravity• Picture a bed sheet pulled tight with a heavy ball in the middle. The heavy ball makes an indentation in the sheet. A marble that is rolled on the sheet will be deflected in a straight line much like a planet is deflected around the sun by gravity.• Einstein proposed space-time (the sheet) is warped by mass (the heavy ball). Gravity is caused by this warping.• Black holes (enormous mass compressed into an infinitesimal volume) could deform space-time so much that even light could not escape1414The Warping of Space-time from a Black HoleThe BH will be in the center of the dip. The steeper the dip, the greater the force of gravity. Planets and other objects will follow the same curved paths that a marble would if rolled across a sheet with this dip in it.1515Universal Gravitation• Everything in the universe attract everything else– This is why the Earth (and nearly every other celestial body) is round• The Earth is pulled by not only the sun, but also the other planets in our solar system as well as every other star in the universeRemember, you exert a gravitational force on everything in the universe (small though that force may be)… That is why we call this universal