1. Honors Physics Chapter 7
Gravitation

2. Honors Physics Turn in Chapter 6 Homework, Worksheet, and Lab Report
Lecture
Q&A

3. Kepler’s First Law of Planetary Motion
The paths of the planets are ellipses with the center of the sun at one focus.

4. Kepler’s Second Law of Planetary Motion
An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. Thus, planets move fastest when closest to the sun slowest when farthest away.
Animation

5. Kepler’s Third Law of Planetary Motion
The ratio of the squares of the periods of any two planets revolving about the sun is equal to the ratio of the cubes of their average distances from the sun. Thus, if TA and TB are their periods and rA and rB their average distances, then

6. Kepler’s Laws Observation
Valid for any objects (without own power) orbiting around a common object.
When using the average distance from the sun, we are taking the path as circular.

7. Example: Pg174-2: An asteroid revolves around the sun with a mean (average) orbital radius twice that of Earth’s. Predict the period of the asteroid in earth year.

8. Practice Pg174-4: The Moon has a period of 27
Practice Pg174-4: The Moon has a period of 27.3 days and a mean distance of 3.90  105 km from the center of Earth. a. Use Kepler’s laws to find the period of a satellite in orbit 6.70  103 km from the center of Earth. b. How far above Earth’s surface is this satellite?
a. TM = 27.3dy, rM = 3.90  105 km , rS = 6.70  103 km , TS = ? RE H r

9. Newton’s Law of Universal Gravitation
m1 and m2 are masses of the two objects
r = distance between m1 and m2, center to center
Gravitational force is always attractive, pointing from center to center.

10. Gravitational force between you and person next to you.
m1=50kg, m2 = 50 kg, r = 1m, F =?
Negligible for most purpose.

11. Practice: Pg178-8 What is the gravitational force between two 15-kg packages that are 35 cm apart? What fraction is this of the weight of one package?

12. Gravitational force and gravitational field
What is the gravitational force between you and Earth?
RE=6.4× 106 m, ME = 6.0 × 1024 kg, m = 50 kg, F = ?
What is the your weight?
Weight is gravitational force Earth pulling on you.
Gravitational field at distance r (r >= R) from object (M):
or acceleration due to gravity

13. Practice: Pg185-16 The mass of the Moon is 7
Practice: Pg The mass of the Moon is 7.2  1022 kg and its radius is 1785 km. What is the strength of the gravitational field on the surface of the Moon?

14. Newton and Kepler Objects of T and r revolving around M
Kepler’s Third Law

15. Using Universal Gravitation and Centripetal ForceM m r
Using Universal Gravitation and Centripetal Force
Speed of object in orbit (of r) revolving around M under gravity
From last slide:
Period of object in orbit (of r) revolving around M under gravity

16. Example: Pg Use the data in Table 7-1 on Pg 173 for Mercury to find the following. a. the speed of a satellite in orbit 260 km above the surface b. The period of the satellite.
Mercury:
Average radius: 2.43× 106 m
mass: 3.2× 1023 kg
Average distance to sun: 5.8× 1010 m • R H r

17. Practice: Pg178-6 Neptune orbits the Sun with an orbital radius of 4
Practice: Pg178-6 Neptune orbits the Sun with an orbital radius of  1012 m, which allows gases, such as methane, to condense and form an atmosphere, as shown in Figure If the mass of the Sun is 1.99  1030 kg, calculate the period of Neptune’s orbit.

18. Practice: Pg Use Newton’s thought experiment on the motion of satellites to solve the following. a. Calculate the speed that a satellite shot from a cannon must have to orbit Earth 150 km above its surface. b. How long, in seconds and minutes, would it take for the satellite to complete one orbit and return to the cannon?

19. Practice: Pg185-18 Two satellites are in circular orbits about Earth
Practice: Pg Two satellites are in circular orbits about Earth. One is 150 km above the surface, the other 160 km. a. Which satellite has the larger orbital period? b. Which one has the greater speed? a.
r: increases  T: __________.
increases 
160km has larger T. b.
r: increases  v: __________.
decreases 
150km has greater speed.