1. Universal Gravitation and Kepler’s Laws
Physics 12

2. Newton’s Universal Law of Gravitation and Kepler’s First Law
Newton had shown in his original article De Motu and later in Principia that the inverse square nature of gravity would lead to elliptical not circular orbits

3. Newton’s Universal Law of Gravitation and Kepler’s Second Law
Even though planets are moving in elliptical orbits, the concepts of circular motion mostly apply
Determine the speed of the Earth using the following data and assume that centripetal force is equal to gravitational force:
Sun’s Mass – 1.99x1030kg
Earth’s Mass – 5.98x1024kg
Distance Earth to Sun (aphelion) – 152,171,522 km
Distance Earth to Sun (perihelion) – 147,166,462 km

4. Newton’s Universal Law of Gravitation and Kepler’s Second Law
Earth’s speed:
Aphelion – 2.95x104m/s
Perihelion – 3.00x104m/s
This would indicate that Kepler’s Second Law is also supported by Newton’s Universal Law of Gravitation

5. Newton’s Universal Law of Gravitation and Kepler’s Third Law
Since Kepler’s Third Law is a ratio of the orbtial radius cubed to the orbital period squared, we should be able to apply Newton’s Universal Law of Gravitation to the planetary motion to determine the value of the constant
Set the centripetal force equation equal to Newton’s Universal Law of Gravitation
Replace the velocity expression using orbital radius and orbital period

6. Newton’s Universal Law of Gravitation and Kepler’s Third Law
This is called Newton’s version of Kepler’s Third Law

7. Mass of the Sun and Planets
Henry Cavendish developed a torsion balance to determine the value of the Universal Gravitation Constant (approximately 70 years after Newton’s death)
Using his apparatus, he was able to determine a value of G = 6.75x10-11Nm2/kg2 which is within 1% of the currently accepted answer
Using G, he was then able to determine the mass of the Sun and other planets

8. Practice Problems
Page 586
Questions 9-14