Gravitational Fields

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Beryl Jones
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1 Gravitational Fields

2 although Earth and the Moon do not touch, they still exert forces on each other Michael Faraday developed the idea of a field to explain action at a distance

3 a field is defined as a sphere of influence where one object can exert a force on another without direct contact all masses are surrounded by a gravitational field the field exerts a force on any other mass placed in the field

4 direction of the field is always to the centre of the object causing the field field direction is indicated by the use of field lines the field lines indicate the direction of the force acting on another mass placed in the field Field lines that are far apart mean the field is weaker here

5 The field is radially inward

6 near the surface of Earth, the field lines appear to be at right angles to the surface The parallel field lines means the direction is the same Equal spaces between the field lines means the magnitude is the same

7 gravitational fields are vector fields (magnitude and direction) the field extends to infinity

8 The gravitational field vector at any location in space is found by placing a test mass m at that point and measuring the force acting on it. g

9 Gravitational field strength Units N/kg (same as m/s 2 ) g F g m gravitational force acting on mass in field Mass in gravity field ( test mass )

10 Magnitude of gravitational field strength g = field strength N/kg at a point in space G= Universal Gravitational Constant g Gm r 2 m = mass of object causing field r = distance from centre of object causing the field

11 the value of g depends on the distance from the centre of the planet and geology (value of g is higher close to dense rock such as metal ore deposits)

12 Astronauts repair the Hubble move than 300 km above the coast of Australia

13 Yellow and red are regions of high g values Chicxulub gravity map

16 Example Determine the magnitude of the gravitational field strength on the surface of Mars (mass = 6.37 x kg, r = 3.43 x 10 6 m).

17 g Gm r 2 Solution 2 11 m N kg 2 g kg m 2 g = 3.61 N/kg

18 Example Determine the acceleration of gravity 900 km above the surface of Earth.

19 g g Solution Gm r m N kg kg m90010 g = 7.53 N/kg m

20 When many masses are present, each mass contributes its own field to each point in space. To find the net field strength, use vector algebra to find the value and direction.

21 Example Two 6.9 x 10 3 kg objects are arranged as shown. Determine the net gravitational field at point P. A B

22 Solution find the field caused by each mass g Gm r m N kg Ignore mass B, the g field caused by A 130m2 will not be N / kg left influenced by mass B. A 3 kg

23 Ignore mass Gm g A, find the 2 B r field caused 2 3 by mass B m N g kg m N / kg left Net g = 2.1 x N/kg left kg

24 Tides Tides rise and fall because the moon's gravity pulls the water into a tidal bulge which the earth rotates under.

25 On the side of the Earth nearest to the moon, the pull from the Moon is the strongest. It's clearly stronger than the pull from the Moon at locations on Earth further away from the Moon

26 Because the gravitational pull from the Moon is less at the farthest-from-the-moon point than it is at other locations on the surface of the Earth, the water at this point is literally left behind.

27 The sun and the moon can make tides much larger than usual, depending on their position

29 Inertial & Gravitational Mass Inertial mass measures the inertial resistance to acceleration of the body when responding to all types of force. a = F net m

30 Inertial & Gravitational Mass Gravitational mass is determined by the strength of the gravitational force experienced by an object when in the gravitational field g. F g = mg Inertial mass and gravitational mass are equal

31 AP Example A plant s radius is measured from orbit to be 7.01 x 10 6 m. An away team lands and measures the gravitational field strength to be 10.4 N/kg. A) determine the mass of the planet

32 B) Determine the average density of the planet. m 4 V r 3 V 3

33 C) If the density of the surface material is 2.7, what conclusions can you make about the planet?

34 Practice P 219: 1, 2 P 220: 1, 2, 3

PHYSICS 12 NAME: Gravitation

PHYSICS 12 NAME: Gravitation NAME: Gravitation 1. The gravitational force of attraction between the Sun and an asteroid travelling in an orbit of radius 4.14x10 11 m is 4.62 x 10 17 N. What is the mass of the asteroid? 2. A certain