Astronomy Chapter 4 (Motion, Energy, Gravity)

Speed

Example: The speed of a car tells us how far it will go in a certain amount of time.

Orbital Angular Momentum

(earth's orbit around the sun-formula tells us earth's angular momentum at any point in its orbit) Angular momentum = m x v x r M is Earth's mass, V is its orbital velocity (the component of velocity perpendicular to R), and R is the "radius" of the orbit.

Earth's Orbit

1) Earth needs no fuel or push of any kind to keep orbiting the Sun- it will keep orbiting as long as nothing comes along to take angular momentum away. 2) Because of Earth's angular momentum at any point in tis orbit depends on the product of its speed and orbital radius (distance from the Sun), Earth's orbital speed must be faster when it is nearer to the Sun (and the radius is smaller) and slower when it is father from the sun (and the radius is larger). (Kepler's Second Law)

Thermal Energy

A subcategory of kinetic energy, which represents the collective kinetic energy of the many individual particles (atoms and molecules) moving randomly within a substance like a rock or the air or the gas within a distant star. (all objects contain thermal energy when sitting still because the particles within them are jiggling randomly)

Newton's First Law of Motion

An object moves at a constant velocity if there is no net force acting upon it. In other words, objects at rest (velocity=0) tend to remain at rest, and objects in motion tend to remain in motion with no change in either their speed or direction.

Escape Velocity

An object that gains orbital energy moves into an orbit with a higher average altitude moves into an orbit with a higher average altitude. For example, if we want to boost the orbital altitude of a spacecraft, we can give it more orbital energy by firing a rocket. The chemical potential energy released by the rocket fuel is converted to orbital energy for the spacecraft. If we give a spacecraft enough orbital energy, it may end up in an unbound orbit that allows it to escape earth completely.

Momentum

An object's momentum is the product of it's mass and velocity; momentum=mass x velocity (the only way to change an object's momentum is to apply a force to it)

Angular Momentum

Also known as "turning momentum" or "circling momentum". Ex: An ice skater spinning in place. She isn't going anywhere, so she has no overall velocity and hence no momentum. Nevertheless, every part of her body is moving in a circle as she spins, so these parts have momentum even though her overall momentum is zero. (angle of 360 degrees).

Gravitational Encounter

Although orbits cannot change spontaneously, they can change through exchanges of energy. One way that two objects can exchange orbital energy is through a gravitational encounter, in which they pass near enough so that they can feel the effects of the other's Gravity. For example, when a comet happens to pass a near planet, the comet's orbit can change dramatically. (A comet passing by Jupiter loses so much orbital energy that its orbit changes from unbound to bound to elliptical. Jupiter gains exactly as much energy as the comet loses, but the effect is unnoticeable because of Jupiter's greater mass)

Earth's Angular Momentum

Angular momentum due to its rotation: Rotational Angular Momentum. Angular momentum due to its orbit around the sun: Orbital Angular Momentum

Rotational Angular Momentum

As long as Earth isn't transferring any of the angular momentum of its rotation to another object, it keeps going at the same rate. (In fact, Earth is very gradually transferring some of its rotational energy to the Moon, and as a result, Earth's rotation is gradually slowing).

Law of Conservation of Momentum

As long as there are no external forces, the total momentum of interacting objects cannot change; that is, their total momentum is conserved. Ex: The amount of forward momentum the rocket gains is equal to the amount of backward momentum in the gas that shoots out the back. That is why forces between the rocket and gases are always equal and opposite.

Law of Conservation of Angular Momentum

As long as there is no external torque, the total angular momentum of a set of interacting objects cannot change. An individual object can change its angular momentum only by transferring some angular momentum to or from another object.

Astronaut and Density

Astronauts working in Earth orbit are at much greater risk of getting cold than hot. The reason is the extremely low density: although the particles striking an astronaut's space suit may be moving quite fast, there are not enough of them to transfer much thermal energy. This also means that the astronauts become cold given that they cannot transfer much of their own energy to the particles in space. They lose their body heat by emitting thermal radiation.

The Moon's Synchronous Rotation

Because earth is more massive than the moon, earth's tidal force has a greater effect on the moon than the moon does on the earth. This tidal force gives the moon two bulges along the earth-moon line, much like the tidal bulges the moon creates on earth. The moon does not have visible tidal bulges, but it does indeed have excess mass along the earth-moon line. If the moon rotated through its tidal bulges in the same way as earth, the resulting friction would cause the moon's rotation to slow down. This is exactly what we think happened long ago.

Ball Example

Because energy must be conserved during the ball's flight, the ball's kinetic energy increases when its gravitational potential energy decreases, and vice versa. That is why the ball travels fastest (most kinetic energy) when it is closest to the ground, where it has the least gravitational potential energy. (and vice versa)

Moon Tides part 3

Because of its orbital motion around the earth, the moon reaches its highest point in the sky at any location about every 24 hours and 50 minutes rather than every 24 hours. In other words, the tidal cycle of two high tides and low tides takes about 24 hours and 50 minutes, with each high tide occurring about 12 hours 25 minutes after the previous one.

Moon's Tidal Force

Because the strength of gravity declines with distance, the gravitational attraction of each part of earth to the moon becomes weaker as we go from the side of earth facing the moon to the side facing away from the moon. This difference in attraction creates a "stretching force" or tidal force that stretches the entire earth to create two tidal bulges, one facing the moon and one opposite the moon.

Tidal Friction

Because tidal forces stretch the earth itself, the process creates friction called tidal friction. The moon's gravity tries to keep the tidal bulges on the earth-moon line, while earth's rotation tries to pull the bulges around with it. The resulting compromise keeps the bulges just ahead of the earth-moon line at all times. This causes two things: first, the moon's gravity always pulls back on the bulges, slowing the earth's rotation. Second, the gravity of the bulges pulls the moon slightly ahead in its orbit, causing the moon to move farther from the earth.

Newton vs Aristotle

By recognizing that gravity operates in the heaves as well as on Earth, Newton eliminated Aristotle's distinction between the tow realms and brought the heavens and Earth together as one universe. (heralded the birth of astrophysics)

More Momentum Stuff

Changing an object's momentum means changing its velocity, as long as its mass remains constant. A net force that is not zero therefore causes an object to accelerate. Conversely, whenever an object accelerates, a net force must be causing the acceleration. That is why you feel forces (pushing you forward, backward, sideways) when you accelerate in your car.

Orbital Energy

Consider the orbit of a planet around the sun. The planet has both kinetic energy (because it is moving around the sun) and gravitational potential energy (because it would fall to the ground if the sun stopped orbiting). It's kinetic energy depends on its orbital speed, and it's gravitational potential energy depends on its distance from the sun (the energy varies considering the changing speed distance between the sun and planet during its orbit). However, the planet's total orbital energy- the sum of its kinetic and goe energies- stay the same. This fact is a consequence of the law of conservation of energy. As long as no other object causes the planet to gain or lose orbital energy, it's orbital energy cannot change and its orbit must remain the same.

Gravitational Potential Energy

Depends on its mass and how far it can fall as a result of gravity. An object has more gravitational potential energy when it is higher and less when it is lower. (a ball in the air has higher energy than when close to the ground)

Mass Energy

Einstein discovered that mass itself is a form of potential energy, often called mass energy. The amount of potential energy contained in mass is described by this famous equation: E= mc2(squared). Where E is the amount of potential energy, M is the mass of the object, and C is the speed of light. This equation tells us that a small amount of mass contains a huge amount of energy.

Bound Orbits

Ellipses are the only possible shapes for bound orbits-orbits which an object goes around another object over and over again. (the term bound orbit comes from the idea that gravity creates a bond that holds objects together)

Radiative Energy

Energy carried by light . All light carries energy, which is why light can cause changes in all matter. For example, light can alter molecules in our eyes- thereby allowing us to see- or warm the surface of a planet.

Kinetic Energy

Energy of motion (kinetic comes from the Greek word meaning "motion"). Falling rocks, orbiting planets, and the molecules moving in the air are all examples of objects with kinetic energy. The kinetic energy of a moving object is 1/2 mv2(squared), where M is the object's mass and V is its speed.

Universal Law of Gravitation part 1

Every mass attracts every other mass through the force called gravity.

Acceleration

Ex: The car has an acceleration if its velocity is changing in any way, whether in speed or direction or both. (in science, it is acceleration if you slow down or turn) Slowing=negative acceleration (turning is a form of acceleration even if your speed remains constant)

Newton's Third Law of Motion

For any force, there is always an equal and opposite reaction force. This law is very important in astronomy because it tells us that objects always attract each other through gravity. Ex: Your body always exerts a gravitational force on Earth identical to the force that Earth exerts on you, except that it acts in the opposite direction. (pg 117 look up)

Newton's Second Law of Motion

Force = mass x acceleration (F= ma) or Force = rate of change in momentum. This law explains why you can throw a baseball farther than you can throw a shot in the shot put. Astronomically, the law explains why a large planet such as Jupiter has a greater effect on asteroids and comments than a planet (much smaller) like Earth. (Jupiter exerts a stronger gravitation force on asteroids and comets, and sends them scattering with a greater acceleration)

Atmospheric Drag

Friction can cause objects to lose orbital energy. Consider a satellite orbiting earth. If the orbit is fairly low, such as a few hundred kilometres above earth's surface, the satellite experiences a bit of a drag from earth's thin upper atmosphere. This drag gradually causes the satellite to lose orbital energy and plummet to earth. The satellit's orbital energy is converted to thermal energy which is why a falling satellite usually burns up.

Centre of Mass examples

In a binary star system in which both stars have the same mass, we would see both stars tracing ellipses around a point halfway between them. When one object is more massive than the other, the center of mass lies closer to the more massive object. Same for the sun and planets. However the sun is so much more massive than the planets that the center of mass between the sun and any planet lies either inside or nearly inside the sun.

Leaning Tower of Pisa

In an experiment Galileo dropped weights from the tower and demonstrated that gravity accelerates all objects by the same amount, *regardless of their mass.

Tidal Effects on Other Worlds

In some worlds synchronous rotation is common. Jupiter's four large moon's, (Io, Europa, Ganymede, and Callisto), keep nearly the same face toward Jupiter at all times, as do many other moon's. Pluto and its moon Charon both rotate synchronously. Many binary star systems rotate the same way. There are exceptions, like Mercury. It rotates exactly three times for every two orbits of the sun. This pattern ensures that Mercury's tidal bulge always aligns with the sun at perihelion, where the son exerts its strongest tidal force.

Law of Conservation of Energy

Like momentum and angular momentum, energy cannot appear out of nowhere or disappear into nothingness. Objects can gain or lose energy only by exchanging energy with other objects.

Particle Accelerators

Machines that create subatomic particles from energy.

Temperature

Measures the average kinetic energy of the particles. For a particular object, a higher temperature simply means that the particles on average have more kinetic energy and hence are moving faster.

Gravity in Space

Most people guess that there's no gravity in space but that's not true. After all, it is gravity that makes the Space Station orbit Earth. Astronauts feel weightless for the same reason you are weightless when you jump off a chair: they are in free-fall.

Unbound Orbits

Newton discovered that objects can also follow unbound orbits- paths that bring an object close to another object just once. For example, some comets that enter the inner solar system follow unbound orbits. They come in from afar just once, loop around the sun, and never return.

Conic Sections

Newton showed that orbital paths can be ellipses, parabolas, or hyperbolas. Bound orbits are ellipses and unbound orbits are parabolas or hyperbolas. Together, these shapes are known as conic sections, because they can be made by slicing a cone at different angles. They move faster when they are closer to the object they are orbiting, and slower when they are farther away.

Centre of Mass

Newton showed that two objects attracted by gravity actually both orbit around their common centre of mass- the point at which the two objects would balance if they were somehow connected.

New Horizons Spacecraft

On its way to Pluto, the New Horizons spacecraft was deliberately sent past Jupiter on a path that allowed it to gain orbital energy at Jupiter's expense. This extra orbital energy boosted the spacecraft's speed; without this boost, it would have needed four extra years to reach Pluto.

More stuff on orbits

Orbits cannot change spontaneously. Left undisturbed, planets would forever keep the same orbits around the sun, moons would keep the same orbits around their planets, and stars would keep the same orbits in their galaxies.

Potential Energy

Otherwise known as stored energy, which might later be converted into kinetic or radiative energy. For example, a rock perched a ledge has gravitational potential energy because it will fall if it slips off the edge, and gasoline contains chemical potential energy that can be converted into the kinetic energy of a moving car.

Stars and Galaxies blurb (pg 119)

Stars and galaxies are both born from clouds of gas that start out much larger in size. These clouds almost inevitably have some small net rotation, though it may be imperceptible. Like the spinning skater as she pulls in her arms, they must therefore spin faster as gravity makes them shrink in size.

Acceleration of Gravity

The acceleration of a falling object (g). On earth, the acceleration of gravity causes falling objects to fall faster by 9.8 meters per second (m/s), or about 10m/s, with each passing second.

Mass

The amount of matter in your body. (your mass stays the same no matter how the elevator moves)

Mass Energy part 2

The energy released by a 1-megaton H-bomb comes from converting only about 0.1 kilogram of mass (a quarter can of pop) into energy. Just as Einstein's formula tells us that mass can be converted into other forms of energy, it also tells us that energy can be transformed into mass. (energy from the big bang turned into mass from which we are made).

Escape Velocity part 2

The escape velocity from earth's surface is about 40,000 km/hr or 11km/s, meaning that this is the minimum velocity required to escape the earth's gravity for a spacecraft that starts near the surface. Velocity does not depend on the mass of the escaping object- any object must travel at a velocity of 11km/s to escape earth.

Synchronous Rotation part 2

The moon probably once rotated much faster than it does today. As a result, it did rotate though it's tidal bulges, and it's rotation gradually slowed. Once the moon's rotation slowed to the point at which the moon and it's bulges rotated at the same rate, that is, synchronously with the orbital period, there was no further source for tidal friction. The moon's synchronous rotation was therefore a natural outcome of earth's tidal effects on the moon. If the earth and moon stay together long enough, a few hundred billion years, the gradual slowing of earth's rotation will eventually make earth keep the same face to the moon as well.

Net Force

The net force (or overall force) acting on an object represents the combined effect of all individual forces put together. *(a change in momentum occurs only when the net force is not zero)

Sun Tides part 2

The overall tidal force caused by the sun is a little less than half that caused by the moon. When the tidal forces of the sun and moon work together, as is the case at both new moon and full moon, we get the especially pronounced spring tides (the water seems to spring up from earth). When the tidal forces of the sun and moon counteract each other, as is the case with first and third quarter moon, we get relatively small tides known as neap tides.

Gravitational Potential Energy part 2

The same general idea explains how stars become hot. Before a star forms, its matter is spread out in a large, cold cloud of gas. Most of the individual gas particles are far from the centre of this large cloud and therefore have a lot of gravitational potential energy. The particles lose gravitational potential energy as the cloud contracts under its own gravity, and this "lost" potential energy ultimately gets converted into thermal energy, making the centre of the cloud hot.

Weight

The source that a scale measures when you stand on it ; that is, weight depends both on your mass and the forces (including gravity) acting on your mass.

Universal Law of Gravitation part 3

The strength of gravity between two objects decreases with the square of the distance between their centers. We therefore say that the gravitational force follows an inverse square law. For example, doubling the distance between two objects weakens the force of gravity by a factor of 2squared or 4. (pg 123 for the equation and picture)

Universal Law of Gravitation part 2

The strength of the gravitational force attracting any two objects is directly proportional to the product of their masses. For example, doubling the mass of one object doubles the force of gravity between the two objects.

Sun Tides

The sun also exerts a tidal force on earth, causing earth to stretch along the sun-earth line. The gravitational force between earth and the sun is much greater than the force between the earth and moon, which is why earth orbits the sun. However, the much greater distance to the sun means that the difference in the sun's pull on the near and far sides of earth is relatively small.

Kelvin

The temperature scale used in science. The Kelvin scale does not have negative temperatures, because it starts from the coldest possible temperature, known as absolute zero (0K).

Thermal Energy part 2

The thermal energy of a parked car due to the random motion of its atoms is much greater than the kinetic energy of the car moving at highway speed. Thermal energy measures the total kinetic energy of all the randomly moving particles in a substance.

Torque

The type of force that can change an object's angular momentum (a "twisting force"). The amount of torque depends not only on how much force is applied, but also on where it is applied.

Velocity

The velocity of a car tells us both its speed and its direction. Ex: 100 km per hour going due north

Thermal Energy part 3

Thermal energy depends on temperature, because a higher average kinetic energy for the particles in a substance means a higher total energy. But thermal energy also depends on the number and density of the particles. (boiling water vs oven: if you put your hand in the water it would burn you quicker because the density is much higher than the density of the air in the oven. Many more molecules strike your skin each second in the water)

Tidal Friction part 2

These effects are barely noticeable on human time scales, for example, tidal friction increases the length of a day by only about 1 second every 50,000 years, but they add up over billions of years. Early in earth's history, a day may have been only 5 or 6 hours long and the moon may have been one tenth or less its current distance from earth. These changes also provide a great example of conservation of angular momentum and energy. The moon's growing orbit gains the angular momentum and energy that earth loses as its rotation slows.

Moons of Jupiter and Mars

These moons may once have orbited the sun independantly, and their orbits could not have changed spontaneously. However, the outer planets were probably once surrounded by a cloud of gas, and the friction would have slowed objects passing through this gas. Some of these small objects may have lost just enough energy to friction to allow them to be captured as moons.

Conservation of Angular Momentum continued

This also explains why we see so many spinning disks in the universe, such as the disks of galaxies like the Milky Way and disks of material orbiting young stars. Ex: Imagine an ice skater spinning in place.Because there is so little friction on ice, the angular momentum of the ice skater remains essentially constant. When she pulls in her extended arms, she decreases her radius- which means her velocity of rotation must increase.

Newton's Version of Kepler's Third Law

This equation allows us to measure orbital period and distance in any units we wish, and also shows that the relationship between orbital period and average distance depends on the masses of the orbiting objects. When an object is much less massive than the object it orbits, we can calculate the mass of the central object from the orbital period and average distance of the orbiting object. This law also shows that the orbital period of a small object orbiting a much larger object depends only on its orbital distance, not its mass.

Moon Tides part 2

Tides affect both land and ocean, but we generally notice only the ocean tides because water flows much more readily than land. Earth's rotation carries any location through each of the two bulges each day, creating two high tides. Low tides occur when the locations at the points halfway between the two tidal bulges. The two daily tides actually come slightly more than 12 hours apart.

Law of Conservation of Momentum continued

When no net force acts on an object, there is no way for the object to transfer any momentum to or from any other object. In the absence of a net force, and object's momentum must therefore remain unchanged- which means the object must continue to move exactly as it has been moving.

Elevator Example

When the elevator moves at a constant velocity (or is stationary) your weight is normal. When the elevator accelerates upward, you weigh more. When the elevator accelerates downward, you weigh less. If the cable breaks so that you are in free-fall, you are weightless.

Free-Fall

When you fall without any resistance to slow you down. The floor drops away at the same rate that you fall, allowing you to "float" freely above it, and the scale reads zero because you are no longer held to it. (you are weightless)