Unit 5 Gravitation. Newton s Law of Universal Gravitation Kepler s Laws of Planetary Motion

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1 Unit 5 Gravitation Newton s Law of Universal Gravitation Kepler s Laws of Planetary Motion

2 Into to Gravity Phet Simulation Today: Make sure to collect all data. Finished lab due tomorrow!!

3 Universal Law of Gravitation Developed by Isaac Newton All objects attract each other through gravitational force. Depends on the masses of the objects and the distance between them Gravity increases when mass increases Gravity decreases when distance increases Both objects will feel the same force

4 Universal Law of Gravitation: Relationships Gravity and distance: Inversed squared distance

5 Universal Law of Gravitation: Relationships Gravity and mass: Direct

6 Law of Gravitation Practice The gravitational force of attraction between two objects would be increased by: A. Doubling the mass of both objects only B. Doubling the distance between the objects only C. Doubling the mass of both objects and doubling the distance between the objects D. Doubling the mass of one object and doubling the distance between the objects Answer: A

7 Law of Gravitation Practice The gravitational force between two objects is 50N. If the distance between the objects is cut in half, what happens to the force? 200 N (quadruples) The gravitational force between two objects is 50N. If the mass of each object is tripled, what happens to the force? 450 N (50 x3 x3)

8 Law of Gravitation Practice Draw a graph that represents the gravitational force F that a rocket experiences as it travels a distance D away from the surface of the Earth.

9 Law of Gravitation Practice A 72 kg woman stands on top of a very tall ladder so she is one Earth radius above Earth's surface (double the distance she normally is) Step 1: Figure out her normal weight on the surface of the Earth: Step 2: Gravity and distance have an inverse squared relationship so if she is double the distance away the force of gravity is 1/4 th as strong. So divide her normal weight by 4.

Law of Gravitation Practice A rocket moves away from the surface of Earth. As the distance r from the center of the planet increases, what happens to the force of gravity on the rocket? A. The force increases directly proportional to r B.

10 Law of Gravitation Practice A rocket moves away from the surface of Earth. As the distance r from the center of the planet increases, what happens to the force of gravity on the rocket? A. The force increases directly proportional to r B.The force increases directly proportional to r2 C. The force doesn t change D. The force becomes zero after the rocket loses the contact with Earth E. The force decreases inversely proportional to 1r2

11 Universal Law of Gravitation Calculations The relationship between gravity, mass and distance can be calculated using the below equation: Where: F = gravitational force mb = mass of second object G = gravitational constant ma = mass of first object d = distance between the two objects

12 Law of Gravitation Practice Two spherical objects have masses of 200 kg and 500 kg. Their centers are separated by a distance of 25 m. Find the gravitational attraction between them.

13 Law of Gravitation Practice Two spherical objects have masses of 3.1 x 10 5 kg and 6.5 x 10 3 kg. The gravitational attraction between them is 65 N. How far apart are their centers?

14 Law of Gravitation Practice A 1 kg object is located at a distance of 6.4 x10 6 m from the center of a larger object whose mass is 6.0 x kg. What is the size of the force acting on the smaller object? 9.8N What is the size of the force acting on the larger object? Newton s Third Law the forces are equal so the answer is 9.8N

15 Law of Gravitation Formula Rearrangement If we know the gravitational force between two objects that have the same mass, how can we rearrange our equation to solve for those masses? need to solve for the masses: m a x m b = m 2 F = Gm 2 d 2 Fd 2 = Gm 2 m = Fd 2 G Fd 2 = m 2 G

16 What is gravity? What do you think gravity is? What do you think causes gravity? Is gravity a push/pull force?

17 Gravity: From Newton to Einstein

18 Relationships that affect Gravity More mass = greater gravity Same mass in smaller radius = greater gravity Why do you think that is?

19 General Relativity Why do more dense things create a stronger gravity? They create a deeper bend in the fabric of space-time Space tells masses how to move and masses tell space how to curve/bend

20 General Relativity Gravity is not a pulling force, but instead a warping of space-time which creates dimples that objects fall into Too much mass in too small an area, the warping causes a black hole!

21 General Relativity

22 Relationships that affect Gravity Mass & Gravity = Direct relationship

23 Gravitational Strength Relationships that affect Gravity Gravity & Radius = Inverse Squared Relationship Radius Size

24 Calculating Acceleration Due to Gravity Use the formula below to calculate the acceleration due to gravity created by any mass: d **where G is the same gravitational constant used before, m is the mass of the object and r is the radius of the object**

25 Calculating Gravity Practice Jupiter s mass is hundred s of times that of the Earth. Why is the acceleration due to gravity on that planet only 3x that of Earth? Jupiter is much bigger/less dense Compute g at a distance of 4.5 x 10 7 m from the center of a spherical object whose mass is 3.0 x kg. d

26 Kepler s Laws of Planetary Motion 1 st Law: Law of Ellipses 2 nd Law: Law of Equal Areas 3 rd Law: Law of Periods

27 Kepler s 1 st Law The orbits of the planets are elliptical (not circular) with the Sun at one focus of the ellipse.

28 Kepler s 1 st Law The further a planet is from the sun the more flattened the ellipse will be

29 Kepler s 2 nd Law Law of equal areas Planets move faster closer to the sun, slower further away, but over the same period of time, the area of the circle will be equal

30 Kepler s 3 rd Law Shows the relationship between the distance of planets from the Sun, and their orbital periods. Further away = longer time it takes to make one orbit around the sun

31 Kepler s 3 rd Law Relationships: Distance and Velocity: Direct Distance and Period: Inverse Squared

32 Keplers 3 rd Law: Part 1 The Law of Periods: The square of the period of any planet is proportional to the cube of the planets distance from the sun. T 2 r 3 T = Period of the object Period is the time it takes for the object to orbit the sun Measured in years r = distance to the sun Measured in au (astronomical units=distance from Earth to Sun=1.50 x m)

33 Kepler s 3 rd Law Practice An asteroid is found and its distance from the Sun is measured to be 4 A.U. What is the period of its orbit round the Sun? T in years and r in AU Since T = 4 A.U T 2 = r 3 T 2 =(4) 3 T 2 = 64 So T = 8 years.

34 Kepler s 3 rd Law: Part 1 If you plot the ratio of T 2 = r 3 values for objects in the solar system you get the below graph Straight slope indicates that the ratio of T 2 = r 3 is the same for all bodies in orbit.

35 Kepler s 3 rd Law: Part 1 What would happen if we drew in the moons orbiting different planets? Why?

36 Kepler s 3 rd Law: Part 2 In order to compare objects orbiting a different object than the sun, we must use a ratio: Doesn t matter what the units are as long as they match!

37 Kepler s 3 rd Law Practice Based on the below chart what is the orbital period of Phobos around Mars? Need to compare to another satellite of Mars Compare Phobos and Deimos (x/1.262) 2 = (9.38/23.46) 3

38 Kepler s 3 rd Law Practice Based on the below chart what is the orbital period of Janis around Saturn? Need to compare to another satellite of Saturn Compare Janis and Mimas (x/0.942) 2 = (151.47/185.54) 3

39 Kepler s Review Use the diagram below to explain how and why a planet s speed changes as it travels around its sun. Think about when a planet travels faster/slower in its orbit.

CHAPTER 7 GRAVITATION

Physics Approximate Timeline Students are expected to keep up with class work when absent. CHAPTER 7 GRAVITATION Day Plans for the day Assignments for the day 1 7.1 Planetary Motion & Gravitation Assignment