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Gravity Ancient Greece- Aristotelian Universe is Earth Centered (Geocentric system) Copernican Revolution – Nicolas Copernicus figures out that the Sun is the center of the Solar System (Heliocentric system) Galileo- discovered that all things fall at a constant rate regardless of mass. We call this local g (for the surface of the Earth g=9.80m/s2) Tycho Brahe-Made meticulous charts of the planets and their orbits Johannes Kepler- Used Brahe’s work to find 3 laws of Planetary Motion. 1st law- Planets orbits are ellipses with the sun at 1 focus. 2nd law-Planets sweep equal area in equal time. (the closer to the sun the faster they move) ra 3rd law-Law of Periods r b 3 Ta Tb 2 Isaac Newton- Finds that the same force that causes an apple to fall to the earth also caused the moon to constantly fall to the earth. Newton’s Universal law of Gravitation - FGrav Gm1m2 r2 The constant (G=6.67 x 10-11N∙m2/kg2) allowed Newton to turn a proportionality (α) into an equality (=) 1 The r 2 makes it so that if the distance between the objects is doubled the Force is one- fourth. ORBITS- Any orbiting object (Earth) is falling at the same rate the object being orbited (Sun) is curving away from it. Weightlessness- In Space Astronauts feel weightless because they are accelerating towards earth at the same rate as the space shuttle. Weighing the Earth- Cavendish used a torsion pendulum to find Big G. This can also be done using the orbital period of the moon and the equation r3 T 2 GM E . The orbital velocity can be found using v GM E r Einstein Theory of Gravity -Describes mass as causing curvature in space time. This is similar to a mass causing a curve in a rubber sheet. Local g Local g is the acceleration due to gravity on the surface of any planet or asteroid. - Just like on earth it does not depend on the mass of the object being dropped. - The weight of an object is found by multiplying mass x local g F ma GMm F 2 r So GMm ma 2 r GM a 2 r GM g 2 r M – the object being orbited r – the distance from the center of the object being orbited Ex 1: Find local g on the surface of the Earth. (ME=5.97 x 1024 kg, rE=6.37x106m.) Ex 2: Find local g on a satellite 6.3x106m above the surface of the earth. (ME=5.97 x 1024 kg, rE=6.37x106m.) Hint: r= rE + rabove Earth Newton’s Universal law of Gravitation GMm F r2 Ex 3: Find Mr. Eisenberg’s Weight on Jupiter if his Mass is 75.0kg and my average radius is 0.3 m. (mJ=1.90 x 1027 kg, rJ=6.98 x 107 m) Ex 4: Jupiter has a mass of 1.90 x 1027 kg and an average radius of 6.98 x 107 m. What is the Weight of Jupiter on Mr. Eisenberg? (mEis=75.0 kg , rEis=0.3 m) Ex 5: Find local g on Jupiter. (mJ=1.90 x 1027 kg, rJ=6.98 x 107 m)