What is a black hole? Do they really exist? How do they form? How are they related to stars? What would happen if you fell into one? How do you see a black hole if they emit no light? What’s the difference between a black hole and a really dark star? Could a particle accelerator create a black hole? Can a black hole also be a worm hole or a time machine? In Astro 101: Black Holes, you will explore the concepts behind black holes. Using the theme of black holes, you will learn the basic ideas of astronomy, relativity, and quantum physics. After completing this course, you will be able to: • Describe the essential properties of black holes. • Explain recent black hole research using plain language and appropriate analogies. • Compare black holes in popular culture to modern physics to distinguish science fact from science fiction. • Describe the application of fundamental physical concepts including gravity, special and general relativity, and quantum mechanics to reported scientific observations. • Recognize different types of stars and distinguish which stars can potentially become black holes. • Differentiate types of black holes and classify each type as observed or theoretical. • Characterize formation theories associated with each type of black hole. • Identify different ways of detecting black holes, and appropriate technologies associated with each detection method. • Summarize the puzzles facing black hole researchers in modern science.
01.08 – Escape Velocity
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From the course by University of Alberta
Astro 101: Black Holes
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From the lesson
Introduction to Black Holes
Hello and welcome to the first module of Astro 101! In this module, you will become familiar with the basic structure of a black hole, learn the terminology used to describe them, and explore the history of black hole physics.
Meet the Instructors
Sharon MorsinkAssociate Professor
Department of Physics, University of Alberta
Before we go into orbit,
let's discuss an important difference in physics;
the difference between weight and mass.
On Earth, we say that the two are equivalent.
I weigh 75 kilograms and I have a mass of 75 kilograms.
But that only works here on Earth, in Earth gravity.
On planets with different gravity from Earth,
weight and mass have different values.
Mass is a property of an object that can
describe as the ability for that object to resist acceleration.
Weight, on the other hand,
depends on the local gravitational field.
Mass always stays the same.
If my mass is 75 kilograms,
I'll be 75 kilograms whether I'm here on Earth,
on the moon, or somewhere in deep space.
But weight is actually a measurement of
the force felt by an object within a gravitational field,
which means that weight can change in different gravities.
It's a product of the mass and the local gravitational field.
So, weight is equal to M times G in multiples of one Earth's gravity.
On the moon where gravity is roughly one-sixth of Earth's gravity,
my mass is still 75 kilograms but my weight is reduced by a factor of six.
That means that on the moon,
my weight would be 12.5 kilograms even though my mass is still 75 kilograms.
What does it mean to be weightless if weight depends on the local gravity?
Well, imagine a region of space so far from stars and
planets that the local gravitational field is very close to zero.
What would someone with a mass of 75 kilograms
feel when there is zero gravitational force on them?
They would feel a weight of zero kilograms.
So, when an astronaut is floating freely in space, are they weightless?
No. It's a common misconception that astronauts experience
weightlessness when they are above earth's atmosphere where gravity is weak.
In fact, there's still enough gravity in the environment
around earth that they have a measurable weight.
However, this is different from experiencing free fall,
acceleration in a gravitational field that is not restricted by any other forces.
Astronauts feel weightless because both the spacecraft that they're in and
the astronauts themselves are in a state of free fall above the earth.
A body is in free fall whenever gravity is the only force acting upon it.
If I release a ball either here or from up high in space,
the only force acting on the ball while it's moving is gravity.
When it's moving, it's in a state of free fall and experiences weightlessness.
Since the force of gravity acts on it,
the ball accelerates and moves towards the earth until it hits the Earth's surface.
What do you think would happen when the ball is thrown horizontally?
Newton was the first to imagine what would happen if you climbed
a tall mountain in order to fire a cannonball horizontally.
Newton reasoned that the cannonball would curve towards the Earth due to gravity.
If the cannonball was fired at a faster speed it would go a longer distance.
Eventually, if the cannonball could be fired fast enough,
it would fall towards the ground on
a curved trajectory that matches the curvature of Earth's surface.
This was the first time someone had reckoned about orbital motion.
This is very similar to how flying is described in
Douglas Adams' A Hitchhiker's Guide To The Galaxy whereas as stated,
there is an art to flying,
or rather, a knack.
The knack lies in learning how to throw yourself at the ground and miss.
When an astronaut orbits the Earth in the International Space Station,
the only force acting on the astronaut is gravity.
The astronaut is traveling in a stable orbit around the Earth.
So, although gravity is pulling on the astronaut towards the earth,
the circular motion makes it possible for the astronaut to miss the Earth.
One way to experience weightlessness without being in orbit or at
a vast distance from the earth is to fly in an airplane on a parabolic trajectory.
Special aircraft that can withstand many times the force of gravity navigate to
a high altitude before climbing into an inverted parabolic flight path.
During the arc of the parabola,
the airplane and the occupants within it only experience the force of gravity and,
therefore, they feel weightless.
These moments feel like zero gravity but they only last about 20 seconds.
The airplane can't stay in free fall for very long for obvious reasons.
Guidance is internal, 12, 11, 10, nine,
ignition sequence start, six, five, four,
three, two, one, zero, all engines running.
We have a lift off, lift off on Apollo 11.
[inaudible] forward, drifting to the right a little. Thirty seconds [inaudible] .
Rockets like the Saturn 5 that carried the crew of the Apollo 11 mission to
the Moon must expend energy to climb through Earth's gravitational field.
The speed of a spacecraft dictates how high it will go in a given scenario.
So, just how much energy is required for a rocket to escape from a planet entirely?
Let's consider an example of a rocket escaping from Earth.
Kinetic energy is the energy associated with the speed of an object
which is applied to a rocket by burning fuel and expelling it from the rocket's nozzles.
The energy required to break the gravitational grasp of a planet like Earth
depends on the mass of the planet as well as its size.
When a speed is associated with kinetic energy of a departing rocket,
we call it the escape velocity.
Earth has an escape velocity which is roughly 11.2 kilometers per second,
which is more than 40,000 kilometers per hour.
But let's not get too carried away.
Getting to space is much more complicated than
merely getting a vehicle to the right speeds.
This calculation considers the pure physics
involved in climbing out of the gravitational potential well.
So, we ignore otherwise important factors like air resistance.
Eleven point two kilometers per second is
the instantaneous velocity you'd need travelling
directly upwards from Earth's surface in order to escape Earth's gravitational well.
At sea level, 11.2 kilometers per second is equivalent to Mach
33 which is fast enough to make the air around the spaceship into a boiling plasma.
So, instead, rockets accelerate out of our atmosphere starting from a standstill.
Although we used Apollo 11 to introduce you to the concept of escape velocity,
it's worth pointing out that in order to reach the moon,
the astronauts never exceeded Earth's escape velocity at all.
The moon is gravitationally bound to Earth and voids there
hasn't escaped from Earth's gravitational sphere of influence.
The moon itself is also trapped within Earth's gravitational well.
Out of all the spacecraft launched by humanity,
only a few have achieved Earth's escape velocity,
those spacecraft which traveled to other planets in our solar system.
But a small subset of spacecraft have voyaged well beyond
the Earth's grasp and escaped from the gravitational pull of the entire solar system.
One such spacecraft, Voyager II,
launched in 1977 and is now considered to be an interstellar traveler.
The red line in this graph represents the changes in speed experienced by Voyager II from
1977 to 1989 on its journey past the outer planets.
In order for Voyager II to achieve escape velocity from our solar system,
it needed a gravity assist from the planet Jupiter.
A gravity assist as a way for a space probe to boost
its kinetic energy by stealing the orbital energy from a heavy body like Jupiter.
Over the course of Voyager II's transit through the solar system,
it was repeatedly boosted by encounters with planets Saturn, Uranus, and Neptune.
At present, Voyager II is traveling at 15.4 kilometers
per second on its way to the outermost edge of our solar system.
By contrast, the fastest humans have ever
traveled was accomplished by the crew of Apollo 10 in
1969 achieving a top speed of nearly 11.08 kilometers per second.
However, their speed record was on their way
back through Earth's atmosphere and not on the way out.
But even faster than the Voyager spacecraft,
the current speed record held by a human object is
the New Horizons probe which took pictures of Pluto in a flyby in 2015.
New Horizons accelerated away from Earth achieving
a whopping 16.26 kilometers per second,
making it the fastest spacecraft ever launched.
Deriving the formula for escape velocity is relatively straightforward.
It involves setting the gravitational potential energy equation
of an object on the surface of a body,
which is GMM over r,
equal to its kinetic energy,
which is equal to one half mv squared.
Since the little m, mass,
which represents the mass of the object you want to
move appears on both sides of the equation,
we can eliminate those from the equation altogether.
This means that the escape velocity of an object does not depend on its own mass.
We can finally rearrange the terms of this equation,
solving for ve, the escape velocity.
So, escape velocity, ve,
can be calculated by multiplying 2 times the universal gravitational constant, G,
times the mass of the body, capital M,
and dividing by the radius of the body's surface,
r, all taken underneath a square root sign.
So, increasing the mass of a body will increase its escape velocity,
and decreasing the radius of a body will also increase its escape velocity.
In order for spacecraft to escape from Earth,
escape velocity is required to ensure the gravitational potential well can be climbed.
In fact, if you'd like to explore these ideas further,
we've created an escape velocity calculator that
you can use to plan a mission across the solar system.
What could escape velocity possibly have to do with black holes?
We'll chew on this for a minute.
What if we calculated the density of an object for which
the speed of light is equal to the object's escape velocity?
The answer is something sinister, something dark.
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