Gravity and Orbits   Newton’s Law of Gravitation   The attractive force of gravity between two particles   G = 6.67 x Nm 2 /kg 2 Why is this important? 12/8/2015APHY1011 m1m1 m2m2 r

Gravity and Orbits   Earth’s composition and g   The value of g = 9.8 m/s 2 is an average value for objects near the Earth’s surface   Variations are due to altitude, the shape of the Earth and its local density 12/8/2015APHY1012

Gravity and Orbits   Tides   Caused by differences in the force of gravity across an object 12/8/2015APHY1013

Gravity and Orbits   Tides   The Sun’s tidal effect is smaller than the Moon’s even though it has a larger gravitational pull on the Earth. 12/8/2015APHY1014

Gravity and Orbits   Newton’s Cannon   A thought experiment that related the motion of the Moon around the Earth and a falling object   How fast would you need to travel to orbit the Earth? v ~ 8000 m/s ~ 17,600 mi/h Why does this only happen when in outer space? 12/8/2015APHY1015

Gravity and Orbits   Circular Orbits   Satellites travel at a constant speed depending on their distance from the central body   The mass of the satellite does not affect its orbital speed 12/8/2015APHY1016

Gravity and Orbits   Kepler’s First Law   Planets orbit the Sun in elliptical paths Tycho Brahe – observations of Mars Johannus Kepler – mathematical explanation of orbits 12/8/2015APHY1017 Sun planet

Gravity and Orbits   More on ellipses and orbits   Semimajor axis (a) and eccentricity (e) define the shape of an orbit 12/8/2015APHY1018 Sun a d

Gravity and Orbits   Kepler’s Second Law   Planets sweep out equal areas in equal times 12/8/2015APHY1019 Sun

Gravity and Orbits   Kepler’s Third Law   Relationship between the orbital period and the semimajor axis: T 2 ~ a 3 Assumes that m 1 >> m 2 12/8/2015APHY10110