1 Previous Classes: Angular Momentum Newton’s Laws This Class GravityPhys 1830: Lecture 14 The Vela Cloud Today: Office Hours so come take up your test starting at 3pm. Appointment otherwise e.g. 2:45 pm Wednesday. J. English Astroclub Wed 5:30pm Allen 330 Previous Classes: Angular Momentum Newton’s Laws This Class Gravity Tides Coming up: General Relativity Workshop is probably the Monday after Reading Week. Do not hand in greyscale images. ALL MATERIAL COPYRIGHT JAYANNE ENGLISH AND ORIGINAL PRODUCERS OF MATERIAL. This is a group of interacting galaxies. Note the distortions. The HI is in red and overlaid on colourized and combined Digitized Sky Survey optical images. Note the cloud – it has the mass of a normal galaxy but we haven’t detected stars yet.
2 Equal and opposite reactionMotion: Angular Momentum Newton’s Laws Inertia Acceleration Equal and opposite reaction
3 Gravity Newton Tidal Forces Interacting Galaxies Einstein Gravitational Lensing
4 Newton’s Law of Gravity Einstein’s General Theory of Relativity Remember that “laws” are not absolute but general rules that describe how nature works. Einstein’s theory has been very good at describing how nature works, and should be called a law too, but it has retained the original name. Gravity is a force that causes motion in the universe e.g. orbits, tides Newton’s Law of Gravity Einstein’s General Theory of Relativity In both descriptions, gravity depends on mass.
5 Question about the role of gravity:If the Sun (and hence its mass) were suddenly to disappear the Earth would Continue in its current orbit. Suddenly change its orbital speed. Fly off into space. Stop spinning. What is your intuition here. Think of the example with the ball on the string – the tension on the string can represent the force of gravity.
6 2.7 Newton’s Laws Gravity For two massive objects, gravitational force is proportional to the product of their masses divided by the square of the distance between them. Newtonian Gravity is always attractive. When an object is in orbit, the radius “r” of the orbit is the distance between the 2 objects. In Newton’s description gravity is always a force of attraction. Caption: Gravitational Force. (a) The gravitational force between two bodies is proportional to the mass of each and is inversely proportional to the square of the distance between them (b). Inverse-square forces rapidly weaken with distance from their source. The strength of the Sun’s gravitational force decreases with the square of the distance from the Sun, but never quite reaches zero, no matter how far away from the Sun.
7 2.7 Newton’s Laws m F 2 * m1 2 * F 3 * m1 3 * FGravity The constant G is called the gravitational constant; it is measured experimentally and found to be: G = 6.67 x m3/s2/kg If we keep the distance the same (r = constant) m F 2 * m * F 3 * m * F Increasing the mass, increases the force between the objects. Substitute in examples of masses and you will see that the F on one object is equal to the F on the other. The force felt on m1 due to m2 is equal to the force felt by m2 due to m1.
8 Question 14 1) increases with distance. 2) depends upon the state of matter (solid, liquid, or gas). 3) can be attractive or repulsive. 4) increases with mass. Newton’s Law of Gravity states that the force between two objects
9 Question 14 1) increases with distance. 2) depends upon the state of matter (solid, liquid, or gas). 3) can be attractive or repulsive. 4) increases with mass. Newton’s Law of Gravity states that the force between two objects The attractive force of gravity INCREASES with greater mass, and DECREASES QUICKLY with greater distance. The force doesn’t depend on the kind of matter.
10 The mass of the Earth is a few millionths that of the Sun. Therefore Question: The mass of the Earth is a few millionths that of the Sun. Therefore The gravitational force of the earth on the sun will be roughly 1/1,000,000 that of the gravitational force of the sun on the earth. The gravitational force of the earth on the sun will be equal to the gravitational force of the sun on the earth.
11 Gravity is inversely proportional to DISTANCEGravity is inversely proportional to DISTANCE! The closer the objects the stronger the gravitational force. r F 1 1 2 ¼ 3 1/9 etc.
12 Tides: An example of the effect of gravityThe moon produces tides on Earth using the force of gravity.
13 No iclicker: Make note of your prediction. Tides No iclicker: Make note of your prediction. There is a difference in the gravitational force on each side of an object. Splitting the object into 3 parts, which is going to feel the most force? The red (closest) ball? The blue (middle) ball? The yellow (furthest) ball? Make note of your prediction.
14 No iclicker: Make note of your prediction. Which ball moves the least? Tides No iclicker: Make note of your prediction. Which ball moves the least? The red (closest) ball? The blue (middle) ball? The yellow (furthest) ball? Make note of your prediction.
15 Movie about the motion of the balls. Tides: Did it match your predictions? Movie about the motion of the balls. Note the perspective from someone sitting on the centre ball
16 Tides There is a difference in the gravitational force on each side of an object.
17 Objects are close together (e.g. Earth and Moon) Tides To the centre ball it looks like the other 2 balls have moved in opposite directions. These 2 opposing forces are referred to as tidal forces. Tidal forces cause the distortion of an object by the gravitational pull of another object. Can occur when Objects are close together (e.g. Earth and Moon) An object is very massive (e.g. Jupiter and Io; the Sun and the Earth.)
18 Tides The gravitational force between objects acts on both objects. Therefore the moon also distorts the earth. The water on the side of the earth that is closet to the moon is like the red ball and the water on the far side is like the yellow ball. Thus we get the same effect as with the example of the balls. Draw the Earth with a uniform layer of water and no moon, ignoring all other objects in the solar system for the moment. Draw the Moon. Draw the Earth. Draw the point of the ocean that is closest to the moon -- it has moved a larger distance towards the moon. Draw the ocean on the far side of the moon – it has moved toward the moon less than the Earth has. Now draw the layer of the ocean including these points. You will see there are 2 tides. The moon also pulls on the Earth and the tides effect the water more that the land.
19 Note that there are 2 tidal bulges at one time!Tides Note that there are 2 tidal bulges at one time!
20 Note that there are 2 tidal bulges at one time!Tides Two tides are also counter-intuitive. Note that there are 2 tidal bulges at one time!
21 Tidal Force Examples: The Asteroid Belt – the tidal force of Jupiter prevented planetesimals from coalescing into a planet.
22 The tidal force of Jupiter (and Europa) cause Tidal Force Examples: The tidal force of Jupiter (and Europa) cause - deformation of the interior of Io. -> heat volcanism Galileo Project, NASA Note the volcanic plume in the upper left.
23 Tidal Force Examples: Jupiter’s gravity attracts comets and other planetesimals. The tidal force can split comets into fragments. E.g. Comet Shoemaker –Levy NASA
24 Note the bruises made on Jupiter as each fragment hits and Jupiter rotates. Each is about the diameter of the earth. NASA
25 Tidal Force Examples: Interacting GalaxiesNote the distortions in these galaxies. They are due to tidal forces. Image credit: J. English and colleagues.
26 Tidal Force Examples: Interacting GalaxiesInteracting galaxies eventually merge together. Minor Merger: 2 galaxies One’s mass is smaller than the other. Galaxies that pass near each other can feel the gravitational pull between them interaction. They begin to travel around each other in tighter and tigher orbits, spiralling toward a common centre. Eventually (after ½ to 2 gigayear (10**9 yr) they will merge together.
27 Tidal Force Examples: Interacting GalaxiesHubble Heritage Minor Merger: Note the distortion of the smaller galaxy. It is extended on either side of the centre.
28 Tidal Force Examples: Interacting GalaxiesMajor merger: 2 galaxies They are approximately the same mass Bridge between galaxies and a long tidal tail left behind. Remember that there are 2 tidal “bulges” on earth. In the case a galaxy, the material experiencing the stronger gravitational force is pulled towards the partner galaxy. This forms a bridge between galaxies. Meanwhile the material that feels the weakest force is left behind as the galaxies orbit each other. This forms a tidal tail.
29 Tidal Force Examples: Interacting GalaxiesB. Whitmore (STScI) HST on right There is so much space between the stars that they pass by each other. The gas between stars however collides. This causes stars to form out of the gas. Antennae Galaxy. Hot, young stars (blue) in the disks. Long curved tails.
30 Tidal Force Examples: Interacting GalaxiesACS S&E Team, HST “Tadpole” galaxy: Tidal tail in a later stage. Looking at many peculiar, tidally disturbed galaxies we can build up a picture of galaxy evolution.
31 Tidal Force Examples: Interaction and MergerJ. Barnes & J. Hibbard Galaxies consist of stars, gas, dust, AND “dark matter”. Material that consists of both objects that don’t emit much light (small stars, planets, black holes, very cold gas) and exotic matter like neutrinos and more. The red sphere is the dark matter “halo”, the yellow is the stellar bulge, and the blue is the stellar disk. Using Newton’s Law of Gravity, every particle in the simulation feels the gravitational force between it and every other particle. Note the bridge and the tails forming. Also that it replicates the observations of The Mice galaxies. Animation of computer simulation of interacting galaxies. Each particle feels the force of gravity between it and every other particle.
32 Tidal Force Examples: Groups of GalaxiesImage credit: J. English Galaxies residing in groups also feel tidal forces.
33 Tidal Force Examples: Groups of Galaxies – velocity fieldsNote the single arm out to the left in the left hand galaxy. This is a signature of a minor merger. J. English 2 tidal arms in the upper galaxy – major merger. One long arm to the left in the left galaxy – minor merger. Cloud is likely to be tidal debris.
34 Tidal Force Examples: Clusters of GalaxiesJ. Dubinski Groups which have hundreds to thousands of galaxies are called clusters. Gravitas -
35 Motion in a Gravitational FieldCan we predict the velocity at which a planet orbits a star? Does a falling heavy object speed up compared to a falling light object? How do we know that there is Dark Matter?
36 Combining Forces of Motion and Gravity: Constant AccelerationWe have 2 equations for F. “F” is the force. The “m” is the mass of the object in orbit. “M” is the mass of the object that m is orbiting. The “a” is acceleration. The “r” is the radius (i.e. distance from the centre of M). G is the gravitational constant. If these forces were not equal, the small object would leave orbit. Think of the ball on a string. Force on an object due to orbital motion is equal to the force on object due to gravity. mass of the smaller object cancels out.
37 Combining Forces of Motion and Gravity: Constant AccelerationConsider 2 objects of different mass feeling the pull of gravity from M. mass of these objects doesn’t matter. Start 2 objects at same distance from centre of gravity acceleration on them is constant. Think about this for the next class.