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**Newton’s Law of Universal Gravitation**

Nicolaus Copernicus- Polish astronomer who said that the Earth revolves around the sun, not the other way around! Johannes Kepler- German astronomer who discovered 3 basic laws of planetary motion. Kepler said there was a “holy spirit” force that kept the planets revolving around the sun.

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Isaac Newton- The force of attraction between two objects of mass depends on the two masses, the inverse-square of the distance between them, and a universal constant. FG = G m M/ R G = 6.67 E -11 Nm2/kg2 Mass of the Earth = 5.98 E 24 kg Radius of the Earth = 6.38 E 6 m

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**Newton realized that all objects fall in curved paths.**

Objects in orbit travel in curved paths around another object. Ex: Earth around the sun, or moon around the earth. We say these objects are “falling around” the bigger object. The same gravity that pulls an apple off of a tree is pulling the moon around the earth!

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**Inverse-square law F ~ 1/R2**

If you double the distance, force is reduced to ¼, If you cut the distance in half, force increases 4 times!

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**Gravity affects the ocean tides**

Gravity affects the ocean tides. When the moon is in line with an ocean, that ocean will have a high tide. When the moon is at a 900 angle to the ocean, it experiences low tide. The tidal pattern is every 6 hours. Example: Florida’s coast may experience high tide at midnight, low tide at 6 am, high tide at noon, low tide at 6 pm.

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**Gravitational field strength – g**

g = G M/ R M= mass of planet, R = radius of planet g is the free fall acceleration for that planet.

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**Kepler- Three laws of planetary motion.**

Each planet travels in an elliptical orbit around the sun, and the sun is at one of the focal points. An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals. The square of the orbital period is proportional to the cube of the average distance between planet and sun. T2~R3

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**Period of a satellite in circular orbit**

T = 2p(r3/GM)1/2 r = distance between centers of mass, M= mass of planet Speed of a satellite in circular orbit vt = (GM/r)1/2 M= mass of planet, r = distance between centers of mass

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