Kepler’s First Law n The orbit of a planet about the Sun is an ellipse with the Sun at one focus.
Kepler’s Second Law n A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.
Kepler’s Third Law n The square of a planet's orbital period is proportional to the cube of the length of its orbit's semimajor axis. n Or simply… T 2 = R 3 if T is measured in years and R is measured in astronomical units.
An Astronomical Unit... n …is the average distance of the Earth from the Sun. n 1 AU = 93,000,000 miles = 8.3 lightminutes
Kepler’s Laws n These are three laws of physics that relate to planetary orbits. n These were empirical laws. n Kepler could not explain them.
Kepler’s Laws...Simply (See page 192.) n Law 1: Elliptical orbits… n Law 2: Equal areas in equal times… n Law 3: T 2 = R 3
Newton’s Law of Universal Gravitation n From Kepler's 3rd Law, Newton deduced inverse square law of attraction. G=6.67 10-11 N m 2 /kg 2 G=6.67 10-11 N m 2 /kg 2
Gravity Questions n Did the Moon exert a gravitational force on the Apollo astronauts? n What kind of objects can exert a gravitational force on other objects? n The constant G is a rather small number. What kind of objects can exert strong gravitational forces?
Gravity Questions n If the distance between two objects in space is doubled, then what happens to the gravitational force between them? n What is the distance is tripled? n …is quadrupled? n What if the mass of one of the object is doubled? n …tripled? n …quadrupled?
Weight and Weightlessness n Weight »the force due to gravity on an object »Weight = Mass Acceleration of Gravity »W = m g n Weightlessness - a conditions wherein gravitational pull appears to be lacking –Examples: »Astronauts »Falling in an Elevator »Skydiving »Underwater
Ocean Tides n The Moon is primarily responsible for ocean tides on Earth. n The Sun contributes to tides also. n What are spring tides and neap tides?