1. Aim: How do we compute Eccentricity?

2. Kepler, Newton, and Orbits

3. Kepler’s 1st Law
The orbit of a planet/comet about the Sun is an ellipse, with the Sun as one focus.
This is the equation for an ellipse:
Eccentricity = Distance between foci
Length of major axis

4. SHAPE OF ELLIPSES
Eccentricity = circle
Eccentricity = line

5. Kepler’s 2nd Law:
A line joining a planet/comet and the Sun sweeps out equal areas in equal intervals of time
                             

6. 2. An imaginary line connecting the Sun to any planet sweeps out equal areas in equal time..

7. Aphelion and Perihelion
1.Perihelion -- the point on its orbit when the Earth is closest to the sun
2.Aphelion -- the point on its orbit when the Earth is farthest from the sun

8. Ellipse
91,5000,000
94,5000,000
Not to scale

9. Angular (Apparent) Diameter
The apparent diameter of a celestial object is the diameter measured by an observer at a specific distance from the object. The smaller the distance between the observer and object, the greater the apparent diameter. Apparent diameters are often expressed as angular diameters.

10. Kepler Law 3
The further a planet is away from the sun the slower the orbit:

11. Retrograde Motion
Retrograde motion is the apparent motion backwards in the sky as viewed from the Earth.

12. Newton’s Law of Gravity
Every object in the universe has a gravitational force and will pull all other objects with a certain gravitational force.

13. Newtons laws of inertia
I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
2. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma.