# Tycho Brahe ( )

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1 Gravity

2 Tycho Brahe ( ) Tycho Brahe (without a telescope) made extremely accurate measurements of the posiaons of the stars and planets over the course of 20 years.

3 Tycho believed that the other planets orbit the Sun, and the Sun and those planets together orbit the Earth. He hoped that his measurements of the moaons of the planets would confirm this model of the solar system. Tycho Brahe ( )

4 Johannes Kepler ( ) Tycho hired a young mathemaacian, Johannes Kepler, to show that his measurements of the planets moaons could be reproduced by his preferred model for the solar system. Kepler tried to do this, but failed. AQer Tycho died, Kepler conanued to search for a model that would match the observed moaons of the planets. He eventually succeeded with a variaaon of Copernicus model in which all of the planets, including Earth, orbit the Sun.

5 Kepler s Laws 1) Planets move in ellipses with the Sun at one focus 2) Planets sweep out equal areas in equal Ames as they orbit (as a result, planets farther from the Sun move slower) 3) The period, P, of an orbit (in years) and its radius, a (in units of the Earth- Sun distance) are related by P 2 = a 3 These laws perfectly predicted the posiaons of the planets, but they were just math, and Kepler didn t have a physical understanding of why they were true. hwp://astro.unl.edu/naap/pos/animaaons/kepler.html

6 Galileo Galilei ( ) Galileo is considered the father of modern physics, and even modern science. He performed a variety of experiments, such as: Dropping balls to measure gravity Rolling balls to examine ineraa Observing the sky through a telescope

7 Galileo Galilei ( )

8 Isaac Newton ( ) Galileo found that bodies with different masses experienced the same acceleraaon when dropped to the ground. But he didn t know why. Kepler discovered that the moaons of the planets were perfectly reproduced by 3 mathemaacal relaaons. Like Galileo, Kepler didn t know why these relaaons worked. Isaac Newton was able to explain the results of Galileo and Kepler, and many other phenomena in nature, with a few general principles

9 Newton s Concepts 1) m (mass): the amount of mawer an object contains 2) v (velocity): a body s speed and direcaon 3) a (acceleraaon): the change in a body s velocity 4) F (force): what is needed to change a body s velocity

10 Newton s Laws of MoAon 1) A body s velocity will remain constant, unless acted upon by an outside force = ineraa

11 Newton s Laws of MoAon 1) A body s velocity will remain constant, unless acted upon by an outside force = ineraa 2) A body s acceleraaon depends on the force acang upon it, and will be in the direcaon of that force. Its resistance to acceleraaon depends on its mass. In equaaon form, this is F = m a 3) For every force, there is an equal and opposite force.

12 Newton s Law of Gravity Any two objects with mass experience an awracave force from gravity that tries to pull them towards each other. The strength of this force depends on the masses of the two bodies, and the distance between their centers (squared). The awracave force is greater for larger masses and smaller distances. Both objects feel the same force of gravity, even if they have different masses. F = G m 1 m 2 d 2

13 Explaining Galileo s Experiment m M = Earth s mass Newton s 2nd law: F = m a Newton s law of gravity: F = G m M / d 2 F = m a = G m M / d2 a = G M / d 2 An object s acceleraaon does not depend on its own mass. It depends on the mass of the other object (the Earth, in this case).

14 Explaining ProjecAle MoAon The moaon of a projecale can be separated into two components: horizontal & veracal. Due to Newton s 1 st Law, the horizontal moaon remains unchanged because there is no force acang on the ball in that direcaon (ignoring air resistance). The ball does experience a force in the veracal direcaon (gravity), so the veracal moaon undergoes acceleraaon downward (Newton s 2 nd law)

15 Explaining ProjecAle MoAon

16 Explaining Weight and Weightlessness You feel weight because of Newton s third law. Gravity is pulling you down, but the ground is not allowing you to fall. It must therefore be exerang a force on you to keep you from falling. That force is the weight that you feel. If you were allowed to fall, you would not feel any weight. So when you are in free- fall, you feel weightlessness.

17 Explaining Weight and Weightlessness As an example, a sky diver is in free fall towards the earth, and therefore feels weightlessness. gravity

18 Explaining Weight and Weightlessness If an addiaonal force is applied to the sky diver that is not in the direcaon of gravity, he will fall on a curved path because of ineraa (Newton s 1st law). ineraa gravity

19 Explaining Orbits If the size of the force is just right, the sky diver falls on a curved path that never reaches the ground and loops back on itself. This is an orbit. The sky diver (or astronaut) experiences weightlessness indefinitely. ineraa gravity

20 Explaining Orbits An orbit is a compromise between gravity and ineraa. Earth coalesced from gas and dust orbiang around the Sun, so it was born with the ineraa that maintains an orbit. If Earth had been born staaonary relaave to the Sun (no ineraa), it would have fallen immediately into the Sun.

21 Explaining Orbits Because planets are much less massive than the Sun, they induce very liwle acceleraaon in the Sun, so the Sun barely moves and has a very small orbit, while the planets are move a lot and have large orbits because of the strong acceleraaon induced by the Sun.

22 Explaining Orbits If the Sun was orbited by larger bodies, like other stars, it would move much more in its orbit. hwp://astro.unl.edu/naap/esp/animaaons/radialvelocitysimulator.html hwps://phet.colorado.edu/en/simulaaon/gravity- and- orbits

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