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**Universal Gravitation**

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**Key Ideas By the end of this unit you should know and understand:**

Kepler’s 3 Laws of planetary motion Newtonian Gravitation Gravitational Force Free Fall Gravitational Field Intensity Geosynchronous Orbits Newtonian Gravity as evidence of Dark Matter

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**Isaac Newton (1642-1727) The ultimate “nerd”**

Able to explain Kepler’s laws The Three Laws of Motion 3

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**Newton – Science in Reverse**

Newton used his ideas on motion (Three Laws) along with the data that was already available from Brahe and Kepler to come up with …

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**Universal Gravitation**

Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

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**Relating it to Newton’s Laws of Motion**

The force that mass 1 exerts on mass 2 is equal and opposite to the force mass 2 exerts on mass 1 The forces form a Newton’s third law action-reaction Gravitational forces are exerted from an object’s centre of mass (think back to torque and balance).

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**Fg = force of gravity (N) **

G = universal gravitational constant (Nm2/kg2) = 6.67 x 10-11 m1, m2 = masses (kg) R = distance between the centres of masses (m) 7

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**What about the equation for weight?**

How are these two things related???

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**How does this relate to Newton’s Laws of Motion?**

3rd Law: Equal and opposite reaction forces.

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Question - If an apple weighs 1N at distance 1d, as in the diagram at left, what will be its weight at a distance of 4d? Inverse square relationship: Answer: 1/d2 = 1/(4d)2 = 1/16 N 1/16 N

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Example 1 A 65.0 kg astronaut is walking on the surface of the Moon, which has a mass of 7.35 x 1022 kg and a mean radius of 1.74 x 103 km. What is the weight of the astronaut? 105 N

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Page 580 Questions 1 to 8 7 and 8 are more challenging

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Some Hints… The “r” value is sometimes given as d or distance of separation between two objects. If the altitude is given, you must add the altitude to the radius of the planet (etc) to get the actual orbital radius.

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Satellites All satellites orbit in circular motion. (Still follows Kepler’s First Law of Planetary Motion as circles are special cases of ellipses).

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Example 2 Find the mass of the Sun using Earth’s orbital radius (on formula sheet: x 1011 m) and period of revolution (on formula sheet: days). HINT: Remember to use correct units! 1.97 x 1030 kg

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