1. Gravity and the Rise of Modern Astronomy
Chapter 3
Gravity and the Rise of Modern Astronomy

2. 3-1 Galileo Galilei and the Telescope
Galileo was the first to use a telescope to study the sky.
He observed:
Mountains and valleys on the Moon.
Sunspots—dark areas on the Sun.
More stars than can be observed with the naked eye.
Four moons of Jupiter.
The complete cycle of phases of the planet Venus.

3. Observing the Moon, the Sun, and the Stars
First three cast doubt on the geocentric model, but don't rule out either theory.
Earth-like features on the Moon and dark spots on the Sun did not fit with the idea of perfection.
What is the purpose of stars we can't see?
© Paschalis Bartzoudis/Dreamstime.com
Courtesy of SOHO (ESA & NASA).

4. Jupiter's Moons
Galileo observed four “stars” moving around the planet Jupiter.
He concluded they were satellites revolving around Jupiter.
This contradicted the Ptolemaic model, that if the Earth moved the Moon would be left behind.

5. The Phases of Venus
With his telescope Galileo saw Venus going through the same phases as the Moon: full, gibbous, and crescent.
Courtesy of Lowell Observatory Photograph.

6. The Phases of Venus
The Ptolemaic model placed Venus always between the Earth and Sun so that the sunlit side never faces the Earth.

7. The Phases of Venus
The phases can only be explained by the heliocentric model.
Galileo began the standard of relying on observation and experimention rather than authority in science.

8. 3-2 Isaac Newton's Grand Synthesis
Newton built on the work of Galileo and Kepler to make a new theory of motion, summarized in three laws.
First Law, (The Law of Inertia): Unless an object is acted upon by a net, outside force, the object will maintain a constant speed in a straight line (if it is initially moving) or remain at rest (if initially at rest).
Inertia: The tendency of an object to resist a change in its motion.

9. The second law extends the first, saying how much force is needed to produce a certain acceleration of an object.
The acceleration of an object is proportional to the force on it.
The property of an object that determines its inertia is its mass.
Mass: The quantifiable property of an object that is a measure of its inertia.

10. An Important Digression—Mass and Weight
Mass is an intrinsic property of an object. It is the same independent of where it is located in the universe.
Mass is not volume or weight. Weight is the measure of the force experienced due to gravity.
The international standard unit of mass is the kilogram.
A kilogram weighs about 2.2 pounds on the Earth but weighs about 0.3 pounds on the Moon.

11. Force = mass  acceleration or F = m a or a = F/m
Back to Newton's Second Law
Second Law: A net external force applied to an object causes it to accelerate at a rate that is proportional to the force and inversely proportional to its mass.
Force = mass  acceleration or F = m a or a = F/m
If the net force is zero, there is no acceleration, just as the first law states.

12. Newton's Third Law
Third Law: When object X exerts a force on object Y, object Y exerts an equal and opposite force back on X.
“For every action there is an equal and opposite reaction.”
Forces come in pairs.

13. 3-3 Motion in a Circle
Motion in a circle is an example of acceleration causing a change in direction but not speed. The acceleration is in the direction of the force, which is towards the center of the circle.
Centripetal force: The force directed toward the center of the curve along which the object is moving.
This is not a new force, but the label for a net force that causes an object to move in a curve.

14. The string provides the centripetal force
The string provides the centripetal force. In which direction will the rock go after the string breaks?

15. 3-4 The Law of Universal Gravitation
Newton applied the laws of motion to Moon: it circles around the Earth so there must be a centripetal force. He hypothesized that this was the same gravity that caused objects to fall on the Earth.
Law of Universal Gravitation: Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

16. Weight: The gravitational force between an object and the planetary/stellar body where the object is located.
If this object weighs 12 pounds on Earth it would weigh 2 pounds on the Moon, but its mass won‘t change.

17. Arriving at the Law of Universal Gravitation
It's easy to test that the force of gravity is proportional to mass. If you double an object's mass then its weight also doubles.
To find the dependence on distance, Newton compared the acceleration of objects falling on the Earth to the centripetal acceleration of the Moon. Both are caused by gravity.

18. 3-5 Newton's Laws and Kepler's Laws
Newton used his laws of motion and gravity to prove and expand Kepler's laws:
First Law: An orbit will be an ellipse if the force varies inversely as the distance squared. Orbits can also be circles, parabolas, or hyperbolas.
Second Law: That orbits sweep out equal areas in equal times also comes from the law of gravity. The Sun's force of gravity changes the speed and direction of the object orbiting.

19. Third Law: The relationship between period and size of the orbit can also be derived from the law of gravity.
If one mass is the Sun and the other is much smaller, such as a planet, then the right side is nearly equal to 1 as Kepler found.
This equation can be applied to any binary system in which two objects orbit each other due to their mutual gravitational attraction.

20. 3-6 Orbits and the Center of Mass
Center of mass: The average location of the various masses in a system, weighted according to how far each is from that point.
The center of mass of the Earth-Moon system is 4800 km from the center of the Earth.

21. It is the center of mass of the Earth-Moon system that orbits the Sun in an elliptical path.

22. 3-7 Beyond Newton
Newton succeeded in describing planetary motion with a few basic ideas of motion and gravity. These ideas were also used to:
Explain tides
Explain the Earth's precession
Predict the existence of the planet Neptune
Predict the return of Halley's comet
and more
By the 20th century we found Newton's laws cannot be applied to all situations. Einstein's theories and quantum mechanics were needed.

23. 3-8 General Theory of Relativity
Mass was defined as a measure of the inertia of an object.
The same mass is used in the law of universal gravity.
Why is the same quantity needed for two seemingly different physical properties?
Explaining this apparent coincidence led Einstein to his general theory of relativity.

24. Principle of equivalence: The effects of acceleration are indistinguishable from gravitational effects.
If the spaceship accelerates at the same rate that falling objects accelerate on the Earth, the woman will see the book fall in exactly the same way in both situations.

25. Einstein explained this equivalence as a curvature of space.
Matter causes space to curve, and the curvature of space tells matter how to move.
A flat 2-D surface can be used as an analogy to our 3-D space.

26. 3-9 Gravitation and Einstein
Newton's law of gravity says that objects attract each other across the empty space between them.
Einstein's explanation says the masses cause space to curve and that curvature affects the motion of objects.
Many tests have shown that Einstein provided a better explanation of gravity than Newton.

27. Test 1: The Gravitational Bending of Light
Relativity predicts light will curve around a massive object.
This is observed during a solar eclipse when light from stars behind the Sun is bent, causing them to appear to shift position.
Newton's law of gravity doesn't explain the observed effect.

28. Test 2: The Orbit of Mercury
Mercury's orbit precesses by 574 arcseconds per century. This is the change in the orientation of the major axis of the orbit ellipse. (Exaggerated in figure.)
Newton's theory explains 531 arcseconds due to the gravity from other planets.
Remaining 43 arcseconds can be explained by Einstein's theory.

29. Additional Tests
According to relativity, massive objects also warp time, causing it to slow near them. This was first tested and confirmed in 1960.
Relativity predicts gravitational waves, ripples in the curvature of space produced by changes in the distribution of matter. Indirect evidence for these comes from observations of double star systems.
Newton's theory does not include these effects.

30. Correspondence Principle: Predictions of a new theory must agree with the theory it replaces in cases where the previous theory was been found to be correct.
Galileo's observations supported the heliocentric model.
Newton's work expanded on Galileo's and Kepler's results.
Einstein's theory has replaced Newton's.
Will Einstein's theory be supplanted by a new one?

31. Advancing the Model: The Special Theory of Relativity
Einstein's Special Theory of Relativity is based on two principles:
All laws of physics are the same for all non-accelerating observers, no matter what the speed of those observers.
The speed of light is the same for all non-accelerating observers, no matter what their motion relative to the source of light.

32. Special relativity predicts that if observing a moving object:
Its length along the line of motion becomes less than its length when measured at rest.
The observed passage of time becomes slower for the moving object.
Its observed inertia becomes greater than its inertia when at rest.
Energy and mass are related: E = m c 2