Download Escape Velocity and Newton`s Laws

Escape Velocity
Enter Newton
(Newton’s Laws of Gravity)
Newton’s Brain
• Neil deGrasse Tyson on Isaac Newton.
• http://www.cleanvideosearch.com/media/acti
on/yt/watch?videoId=7S3uAgyNyrs
Leaving Earth
• https://www.youtube.com/watch?v=OnoNITE
-CLc.
• We have gotten to the point where we do not
take much notice of space ships blasting off.
Newton and His Laws
• Starting with the works of Galileo and Kepler
(then adding his own), Newton deduced three
laws of motion which:
– describe any moving object (from automobiles to
galaxies colliding).
– were the underpinnings for Newton’s
understanding of gravity.
• Published in “Mathematical Principles of Natural
Philosophy” – 1687.
For a constant mass, force equals mass times acceleration: F=ma
Newton’s First Law
Newton’s Second Law
F=ma (or F=mg – where g is the strength of a constant gravitational field)
• The acceleration of a body is inversely proportional to its
mass, directly proportional to the force, and in the same
direction as the force.
This law establishes cause and
effect. Objects do not just move,
they accelerate due to the action
of a force.
Question
• How does Newton’s 2nd law account for your
weight?
Newton’s Third Law
Universal Mutual Gravitation
• From his laws, Newton derived the law of
universal gravitation.
• Law of Universal Gravitation States:
1. Gravity is an Attractive force between all pairs of massive
objects - drawing them closer together
2. Gravity is a Universal force: It operates everywhere in
the Universe.
3. Gravity is a Mutual force: It works between pairs of
massive objects.
4. Gravitational force is proportional to the masses, and
inversely proportional to the square of the distance
between them.
Question
• Think about the gravitational force of Jupiter.
• How would Jupiter’s gravitational effect on
Mars differ from its effect on Earth?
G – The Gravitational Constant
• From his calculations, Newton derived the
constant G, which is the gravitational
constant.
• G is the constant that connects mass to gravity
– and a term in our formula to figure escape
velocity (from Earth or any other planet/star
in the universe).
Escape Velocity
The lowest velocity that a
body must attain in order to
escape the gravitational
attraction of a particular
planet or other object.
Earth’s escape velocity is
11.2 km/s or 24,600 mph.
Escape Velocity
• We can calculate the speed needed to escape
from the Earth’s gravity and from that of any
other astronomical body.
• Escape velocity is that speed and it has a
simple formula.
– The escape velocity is directly proportional to the
objects mass (the Earth in our case) times the
gravitational constant/the radius of the object.
– The square root of the resulting number is then
taken.
Escape Velocity Formula
Escape Velocity
• Once the calculations are done, we find that the
escape velocity for Earth is 11.2 km/s or
approximately 24,600 mph.
• Notice that the escape velocity formula depends
on both its mass and radius.
– Therefore, a large body could have a low escape
velocity if it has a large radius and a low density
(example - Mars).
– Conversely, a small body could have a very large
escape velocity if it has a small radius and very high
density (example – a black hole).
Escape Velocity for Other Planets
on Mercury
Mercury's gravity:
4.3 km/s
on Venus
Venus's gravity:
10.3 km/s
on Earth
the Earth's gravity:
11.2 km/s
on the Moon
the Moon's gravity:
2.4 km/s
on Mars
Mars' gravity:
5.0 km/s
on Jupiter
Jupiter's gravity:
on Ganymede
Ganymede's gravity:
on Saturn
Saturn's gravity:
35.6 km/s
on Uranus
Uranus' gravity:
21.2 km/s
on Neptune
Neptune's gravity:
23.6 km/s
on Pluto
Pluto's gravity:
on the event horizon
a black hole's gravity:
59.5 km/s
2.7 km/s
1.2 km/s
= 299,792 km/s (Speed of
light)
Escape Velocity
• Last Words