1. Universal Law of Gravitation

2. “If gravity attracts an apple toward the Earth, perhaps it also attracts the Moon, and the moon is falling , or accelerating toward the Earth, under the influence of gravity”

3. Newton Quantizes Gravity
Derived a relationship between mass and distance m2
F12
F21 m1 r
Universal Gravitational Constant

4. Acceleration Due to Gravity
g = 9.8 m/s2

5. ma= 8 kg
mc= 6 kg
mb= 4 kg
F1= ?
F2= ?
r1= 5 m
r2= 3 m

6. How fast is the Earth traveling right now?Fg r
Ms=1.99 x 1030 kg
r = 1.5 x 1011 m

7. What is the total gravitational force on the moon by the sun and Earth during a lunar eclipse?
ms= 1.99 x 1030 kg
mE= 5.98 x 1024 kg
mm = 7.36 x 1022 kg
rsE= 1.5 x 1011 m
rEm= 3.84 x 108 m
Toward the sun

8. What is the total gravitational force felt by the moon by the sun and Earth during a solar eclipse?
ms= 1.99 x 1030 kg
mm = 7.36 x 1022 kg
mE= 5.98 x 1024 kg
rEm= 3.84 x 108 m
rsm= x 1011 m
rsE= 1.5 x 1011 m
Toward the sun

9. At what altitude are geosynchronous satellites?
Known:
Need to find r

10. Nick timed himself and found out that if he wore a bright white outfit he ran 20 miles in 80 minutes, but when he wore a dark outfit, he ran 20 miles in one hour and twenty minutes. What does this mean for his next race?

11. Kepler’s Laws 1st Law 2nd Law
The orbit of each planet is an ellipse with the sun at one focus.
2nd Law
The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse
Planets speed up as they get closer to the sun, slow down as they get further from sun

12. Kepler’s Laws 3rd Law Kepler’s Constant
The square of the orbital period of a planet is directly proportional to the cube of the average distance from the sun
Kepler’s Constant

13. Kepler’s Constant Unique to the body being orbited
Exp: K for the solar orbits (case of Earth orbiting the sun):
Same for any body orbiting the sun

14. Kepler’s Constant Estimate the mass of the sun:
Determine K for objects orbiting Earth
Estimate the mass of the Earth:
Mass of the sun
T = 27.3 days
r = 3.87 x 108 m