Transcript Universal Gravitation and Kepler`s Laws

Universal Gravitation and
Kepler’s Laws
Physics 12
Jokes of the day:
Clip of the day:
• Is the Earth round?
• http://www.youtube.com/watch?v=o_W280R_
Jt8
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
Circular Motion:
• Even though planets are moving in elliptical
orbits, the concepts of circular motion mostly
apply
Speed of Earth’s orbit:
• Determine the speed of the Earth’s orbit around the
sun using the following data using the universal
gravitation and centripetal force formulas
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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
Hints:
 Assume that centripetal force is equal to gravitational force
 Find Fg first then use the Fc formula!
 Don’t forget to convert km to m!
And the answer is……
• 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
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
Newton’s Universal Law of Gravitation
and Kepler’s Third Law:
Fg  Fc
Gms m p
r
2

mpv2
r
2r
v
T
2 2
Gms 4 r
 2
2
r
T r
Gms r 3
 2
2
4
T
This is called
Newton’s version of
Kepler’s Third Law
Note: use the mass of the object
at the centre of the orbit
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
Cavendish:
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http://www.youtube.com/watch?v=hKTNMNxW5tQ
Should we watch Newton and Galileo too?
http://www.youtube.com/watch?v=PZsdi7hISOM
http://www.youtube.com/watch?v=1d5ZAX_fj-I
Try it :
• Page 586
▫ Questions 9-14
• Page 597
▫ Question 30-32