1. Example problem:
Halley’s comet has an orbital period of 76 years and its furthest distance from the Sun is 35.3 AU.
How close does Halley’s comet come to the Sun?
How does this compare to the Earths distance from the Sun?
What is its eccentricity? .

2. Homework #3
An asteroids closest approach to the Sun (perihelion) is 2 AU, and farthest distance from the Sun (aphelion) is 4 AU.
What is the semi major axis of its orbit?
What is the period of its orbit?
What is it’s eccentricity?
Calculate the energy required to raise an electron in a Hydrogen atom to the 2nd excited state:

3. Depending on its initial velocity, the cannonball will either fall to Earth, continually free-fall (orbit), or escape the force of Earth’s gravity.

4. Newton’s Laws of Motion
A body at rest or in motion at a constant speed along a straight line remains in that state of rest or motion unless acted upon by an outside force.
# 1
# 2
The change in a body’s velocity due to an applied force is in the same direction as the force and proportional to it.
# 3
For every applied force, a force of equal size but opposite direction arises.

5. y Dx Dy b x
y= mx+b
where m=Dy/Dx

6. s= mt+constant where m=Ds/Dt i.e., speed
Now consider plotting distance (s) versus time (t). Then the slope is simply the speed. s Dt Ds t
s= mt+constant where m=Ds/Dt i.e., speed

7. What if the motion is more complicated than constant velocity?
Then we can get closer to the instantaneous speed by making Dt smaller and smaller… s * Dt Ds * Dt t

8. making Dt smaller and smaller is taking the limit
But that is just taking the derivative

9. Now the integrals or inverse derivatives can be computed so we can start with the sum of all the forces acting on a body and figure it backward until we get to the position and velocity as a function of time.

10. We get these equations for constant acceleration motion
All from adding up all the forces acting on a body!

11. h y q x
In most astronomical observations, the x or h lengths are large compared to the y size scale and in order to observe features of size y in an object the angular resolution (q) must be as small as possible.

12. The angle measured by going completely around a circle is 360o
But that is pretty arbitrary – why not tie it to something that is meaningful?

13. r s q r

14. If a function has continuous derivatives up to (n+1)th order, then this function can be expanded in the following fashion:
If the Rn term (remainder) converges to a value, this is the Taylor series expansion of the function f.

15. Angular Momentum
angular momentum – the momentum involved in spinning /circling = massnvelocitynradius
torque – anything that can cause a change in an object’s angular momentum (twisting force) massnaccelerationnradius

16. v m r
a = v2/r
F = m v2/r