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# Gravity

## How does gravity affect the velocity of a falling object?

### g =  10.0 m/s2  (good approximation)

(*) air resistance will change this. That’s a separate topic.

### Here’s an example of how a falling body picks up speed, with a more precise number. ### The value of g is different on other planets and celestial bodies. ## The Falling Moon

### Newton’s canon.

Dr. William Romanishin, emeritus professor of astronomy at the U. of Oklahoma, writes:

Imagine shooting a cannonball from a cannon parallel to the surface of the Earth from a high mountain. The faster the cannonball moves, the further it would travel before hitting the Earth. At a certain speed, the cannonball would fall around the curving Earth, and would come back and hit the cannon. Such a path is called an orbit.

If the cannonball were above the Earths atmosphere, so that there was no friction with the air, it would just go around and around forever. The cannonball is in “free fall”- it is falling around the Earth- but it never gets any closer to the surface! The cannonball (or Space Shuttle or whatever) does not need any further “push” once it gets into an orbit.

A simple way to think about what is going on is to think about tying a string around a rock and swinging it around in a circle. The string exerts a force on the rock which causes it to keep moving in the circle, rather than in a straight line. (If the string breaks, the rock flies off in a straight line.)

In an orbit, *gravity* provides the “string” that holds the orbiting body in place. So, a body in an orbit is constantly being pulled by gravity into a curved path. By Newton’s first law, a curved path requires a force- if there were no force then the object would move in a straight line.

http://hildaandtrojanasteroids.net/A1504-11feb11.html

### http://interactives.ck12.org/simulations/physics/newtons-cannon/app/index.html ## Who is orbiting whom?

### What would this same system look like, as seen from the side? Enter a captionhttp://spaceplace.nasa.gov/barycenter/en/

### What would this look like, if 2 objects of similar size orbited around each other? The Pluto–Charon system ### The Sun wobbles even more than this due to the pull from other worlds: Jupiter has a large mass, it causes a big wobble.

We can even use this wobble to detect the presence of planets around other stars. See One way to find a planet: Watch for a star’s wobble (NASA)

# Let’s try this – plug in numbers

### Cavendish showed that the strength of gravity is very small: # Gravitational Field

### Or place a bunch of small compasses around a bar magnet – this shows us the existence of a field.

https://kaiserscience.wordpress.com/physics/electromagnetism/magnetism/

### The Earth is a giant magnet, with a magnetic field reaching out into space. # Gravity inside a planet?

### The gravitational field of Earth at its center is zero. _________________________

## Force gravity = (G•M•m) / r2                     For r >= REarth # Orbits

### Thus gravitational force and centripetal acceleration of m2 are always same sign.

https://www.wyzant.com/resources/lessons/science/physics/gravitation

## Free Fall

“Ask someone why astronauts in the Space Shuttle or the MIR space station float in their cabins, and quite often you’ll hear that it’s because there’s zero gravity in space…. but that answer is completely wrong. It is true that the pull of gravity is less on the astronauts and their craft, but the pull is only slightly less. With the center of the Earth 3,960 miles away from someone standing on the surface and 4,060 miles away from someone orbiting 100 miles above, the difference in the pull of gravity is only about 5 percent. That means if you weigh 100 pounds on Earth, you would weigh 95 when 100 miles high. No, the real reason that astronauts float around is that they’re in a continuous free fall. ”

PBS NOVA Explanation of free fall

## Galileo

### Einstein’s success in explaining gravity as warps and curves in the fabric of space and time set him on a quest to unify gravity with electricity and magnetism. View the “A New Picture of Gravity” segment (7 minutes) from “The Elegant Universe” (NOVA)  Gravity, from PBS The Elegant Universe

Introductory topics

Blueberry earth: A thought experiment in planet formation

Gravitational repulsion and the Dipole Repeller

## Apps

Gizmos Gravity physics apps HTML5

http://astro.unl.edu/classaction/animations/renaissance/kepler.html

http://www.windows2universe.org/physical_science/physics/mechanics/orbit/orbit_shape_interactive.html

Newton’s canon

http://waowen.screaming.net/revision/force&motion/ncananim.htm

http://interactives.ck12.org/simulations/physics/newtons-cannon/app/index.html

## Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

8.MS-ESS1-2. Explain the role of gravity in ocean tides, the orbital motions of planets, their moons, and asteroids in the solar system.

HS-PS2-4. Use mathematical representations of Newton’s law of gravitation and Coulomb’s law to both qualitatively and quantitatively describe and predict the effects of gravitational and electrostatic forces between objects.

Next Generation Science Standards

HS-PS2.B.1 ( High School Physical Sciences ): Newton’s law of universal gravitation and Coulomb’s law provide the mathematical models to describe and predict the effects of gravitational and electrostatic forces between distant objects.

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

PS2.B: TYPES OF INTERACTIONS
Gravitational, electric, and magnetic forces between a pair of objects do not require that they be in contact. These forces are explained by force fields that contain energy and can transfer energy through space. These fields can be mapped by their effect on a test object (mass, charge, or magnet, respectively). Objects with mass are sources of gravitational fields and are affected by the gravitational fields of all other objects with mass. Gravitational forces are always attractive. For two human-scale objects, these forces are too small to observe without sensitive instrumentation. Gravitational interactions are non-negligible, however, when very massive objects are involved. Thus the gravitational force due to Earth, acting on an object near Earth’s surface, pulls that object toward the planet’s center. Newton’s law of universal gravitation provides the mathematical model to describe and predict the effects of gravitational forces between distant objects.

Learning Standards: Common Core Math
All the math standards necessary for success in this chapter come from Common Core 7th grade math content.
CCSS.MATH.CONTENT.7.EE.B.4  Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
CCSS.MATH.CONTENT.8.EE.C.7  Solve linear equations in one variable
CCSS.MATH.CONTENT.HSA.SSE.B.3  Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (including isolating a variable)
CCSS.MATH.CONTENT.HSA.CED.A.4  Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

Standards related to understanding the inverse-square law
CCSS.Math.Content.7.RP.A.2a ( Grade 7 ): Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

CCSS.Math.Content.7.RP.A.2c ( Grade 7 ): Represent proportional relationships by equations.
CCSS.Math.Content.7.RP.A.3 ( Grade 7 ): Use proportional relationships to solve multistep ratio and percent problems.