1. Chapter 10: Projectile and Satellite Motion
Brandon Hartfiel
Homework due 3/21
exercises
problems

2. Theory of Universal Gravitation
Review
Theory of Universal Gravitation
Near the earth’s surface
g=9.8 ~ 10
Vertical motion due to gravity
near the earth’s surface
example fall off cliff

3. Projectile Motion What happens if we throw an object sideways?
We can calculate the vertical and horizontal
components separately
Vertical motion
Horizontal motion
There is no acceleration in the horizontal direction
figure 10.4, run off cliff

4. What happens if we turn gravity off?
Gravity on
Gravity off
this is the only
difference
So we can just draw what would
have happened without gravity,
then subtract 5t2 from the height.
see fig 10.8

5. Interesting things about projectiles launched from the ground
time up = time down
speeds are equal at points of equal height
shape is a parabola y=ax2+b
maximum horizontal distance is obtained at 45 degrees
complementary angles (a+b=90) give same distance
figure 10.11

6. Planetary Motion Ptolemy (90-168) – earth centered universe
and now for something completely different …
Planetary Motion
Ptolemy (90-168) – earth centered universe
all motion circular
epicycles used to explain retrograde motion
retrograde motion

7. Copernicus (1473-1543) – Earth is in the
center – no epicycles.
Galileo ( ) – Used telescope to
observe the phases of Venus.
Phases of the inner planets

8. Johannes Kepler ( )
Noticed circles didn’t work for Mars orbit.
After trying about 40 other shapes, he found that the orbit was an ellipse and that the sun was at one of the foci. (Kepler’s first law)
equation for
an ellipse
If a=b, you have a circle with radius
a and both foci are in the middle. So
perfectly circular orbits are possible too

9. He also found that the line between the sun and a planet sweeps out equal areas in equal intervals of time. Kepler's Laws So planets move faster when they are closer to the sun.
This is what we expect from conservation of energy (invented after Kepler)
Close to the sun – high kinetic energy
low gravitational potential energy
Far from the sun – low kinetic energy
high gravitational energy

10. P2=kr3 where k is some constant.
By looking at the other planets, Kepler found that the period, P, of a planet’s orbit (length of a year) is related to its “average”* distance from the sun, r, in the following way
P2=kr where k is some constant.
Solar System Viewer
* actually it’s the length of the ellipse’s semi major axis

11. Isaac Newton (1643-1727) start with Kepler’s third law
Period=circumference of orbit/velocity = P=2pd/v
plug in v2 from the centripetal force equation
F=mv2/r (pg. 144)
cancel extra factors of r
rearrange
Force is proportional
to 1/r2
1/r2

12. Maybe gravity is responsible for the planets’ orbits and the motion of projectiles on earth
But why do planets move in ellipses and projectiles in parabolas?
When we calculate a projectile’s path near the surface of the earth, we use g=9.8 , but because g is inversely proportional to the distance from the center of the earth squared, the real value is
over short distances, there isn’t much difference, but if we
calculate the exact path of a projectile it is an ellipse too.
draw ellipse and parabola on the board, draw 5m vs 8k, figure 10.33