Daily Science Pg.30 Write a formula for finding eccentricity. Assign each measurement a variable letter. If two focus points are 450 km away from one another and the major axis that runs through those two foci is 1200 km, what is that ellipses’ eccentricity value? The eccentricity for an elliptical orbit of a planet is The major axis that runs through the ellipse is 1890 km in length. What is the distance between the foci? What is the length of the major axis that runs through an ellipse that has an eccentricity value of 0.43 and the distance between foci is 89 cm?

PG. 31 Kepler’s laws

First law Each planet orbits the Sun in a shape called an ellipse.

Second Law An imaginary line between the Sun and a planet sweeps out equal amounts of area in equal amounts of time.

Third Law Derived a relationship between size of a planet’s ellipse and its orbital period. P 2 = a 3 P is a unit of time measured in Earth years and a is a unit of length measured in AU.

Gravity and Orbits Newton observed the moon’s motion, the orbits, and the acceleration of objects toward Earth to get a better understanding of gravity. Two bodies will attract each other with a force that depends on their masses and the distance between them. Bigger the mass, bigger the pull of gravity. Shorter the distance, greater pull of gravity.

Gravity Law of universal gravitation- every pair of bodies in the universe attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. F= G [(m 1 m 2 ) / r 2 ] F= force measured in Newtons G is the universal gravitational constant ( x m 3 /kg* s) m 1 and m 2 are the masses of the bodies in kg r is the distance between the two bodies in meters

Center of Mass Each planet orbits a point between it and the Sun called the center of mass. The balance point between two orbiting bodies. Center of mass is closer to the body with more mass Similar mass= center of mass in between the two.