Physics.... UGHH

Gravity is

the force of nature that attracts one mass to another mass. (holds you on the Earth, causes apples to fall)

On a larger scale, gravity is responsible for…

the motion of the Moon, Earth, and other planets.

Newton’s Law of Universal Gravitation says

the force of gravity between any two objects with masses m1 and m2 separated by a distance r is attractive and has a magnitude F.

Newton’s Law of Universal Gravitation formula

F= G*(m1m2)/r²

The constant G in the equation F= G*(m1/m2)/r² is referred to as

the universal gravitation constant

The numerical value of G is

6.67 x 10−11 N*m^2/kg^2

According to Newton's law of gravity, all objects in the universe …

attract all other objects in the universe. In short, everything in the universe

"feels" everything else.

As is shown in the figure below, Newton's law of gravity states that ….

the force between two masses is directed along a line connecting the masses.

Both masses in the figure experience an ….

attractive force of the same magnitude, F = Gm1m2/r²

The force of gravity between the two object form…

an action-reaction pair.

Due to the tiny numerical value of G, 0.0000000000667 N*m2/kg2, gravity is…

the weakest force of nature.

The force of gravity between objects of everyday size is ….

imperceptible. It only becomes important for large objects such as planets and stars.

Gravity decreases with ….

the inverse square of the distance, 1/r2. Because of this, we say that gravity obeys an inverse square force law.

As the graph below shows, even though the force of gravity diminishes rapidly with distance, it …

never completely vanishes. Thus gravity is a force of infinite range.

If a mass experiences gravitational forces from a number of other masses, then the total force acting on it is …

the vector sum of all those individual forces.

The fact that the forces of gravity add together like vectors is referred to as

^…

superposition.

Any object sets up a gravitational force field that extends from…

one end of the universe to the other.

According to Newton's second law, an object …

moves with constant speed in a straight line unless acted on by a force.

To make an object move in a circle with constant speed, a force that is …

directed toward the center of the circle must act on the object.

The force acting on the ball is always…

perpendicular to the motion of the ball. Therefore, it changes the ball's direction, but not its speed.

Since the ball is acted on by a force that is directed toward the center of the circle, it …

follows that the ball must be accelerating toward the center of the circle.

The acceleration resulting from the center-directed force is referred to as …

the centripetal acceleration (a cp)

From experience, you know that the faster a car goes around a curve, the more you feel pushed or pulled to one side or the other. Similarly, the tighter the curve…

, the greater the acceleration.

Experiments and mathematical calculations show that the magnitude of the centripetal acceleration is …

equal to the speed squared divided by the radius.

Centripedal acceleration formula

(speed)²/radius

Magnitude of centripedal force equation

f=(m*acp)=mv²/r

When a car goes into a skid, road wisdom states that you should turn the car in the direction of the skid. While this may seem counterintuitive, it works because…

it increases the turning radius and decreases the centripetal acceleration. This, in turn, decreases the tendency to skid.

Perhaps you have noticed that you feel heavier when the car you are riding in encounters a dip in the road. This change in apparent weight is due to …

the approximately circular motion of the car. As you go through the dip, the normal force acting on the car, and on you, must increase to supply the centripetal force.

Using the methods of calculus, Newton was able to prove that a spherical mass exerts…

the same gravitational force on masses outside it as it would if all the mass of the sphere were concentrated at its center.

the force between a point mass and a sphere is the same as it would be if …

all the mass of the sphere were concentrated at its center. The magnitude of this force is F = GmM/r2.

The gravitational force experienced by a mass m on the Earth's surface is also given by mg. Therefore, mg =

GmME/RE^2.

Gravity on other astronomical bodies may be

found by applying a modified version of the

equation for g on Earth. The equation can be

rewritten to apply to any mass and radius as

follows:

g= GM/R²

Newton reasoned that if an object is launched from a mountaintop with sufficient speed and in the absence of air resistance, then ..

the object would go into orbit

A description of planetary motion remained a

problem throughout history. It was … who finally deduced three laws that

planets obey in their orbits.

Johannes Kepler

Kepler's first law states that planets …..

follow elliptical orbits, with the Sun at one focus of the ellipse.

Newton was able to show mathematically that, because the force of gravity decreases with the inverse square of the distance, or 1/r2, …

closed orbits must have the form of ellipses or circles.

Kepler's second law relates …

speed and distance. It states that as a planet moves in its orbit, it sweeps out an equal amount of area in an equal amount of time

Kepler's third law relates …

the distance of a planet from the Sun and its orbital period, the time it takes for the planet to complete one orbit.

Kepler’s Third Law

The period, T, of a planet, increases as its distance from the Sun, r, raised to the 3/2 power. That is, T = (constant) r^(3/2)

In general, the period of an orbiting planet or moon depends on…

the mass

being orbited. The period does not depend on the mass of the planet or moon itself.

Kepler's law can be applied to a moon or

satellite orbiting a planet. To find the period of a

satellite orbiting the Earth, we replace the mass

of the Sun with the mass of the Earth,

T= (2pi/root(GMe)r^(3/2)