This document summarizes key concepts from Physics Lecture 13 on universal gravitation and Newton's law of gravitation. The summary includes:
1) Newton's law of universal gravitation states that every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
2) Gravity is explained by an inverse square law determined by the gravitational constant G.
3) Kepler's laws describe planetary motion, including elliptical orbits with the sun at one focus, equal areas swept in equal times, and the cube-square relationship between orbital periods and distances.
It is always amazing to see the interaction of planets, Sun, Stars, and other celestial objects in space which leads to astronomical events. In this chapter we will learn certain laws of physics which explains gravitation between celestial objects, free fall of body, mass and weight of the objects.
It is always amazing to see the interaction of planets, Sun, Stars, and other celestial objects in space which leads to astronomical events. In this chapter we will learn certain laws of physics which explains gravitation between celestial objects, free fall of body, mass and weight of the objects.
Law Of Gravitation PPT For All The Students | With Modern Animations and Info...Jay Butani
Law Of Gravitation PPT For All The Students | With Modern Animations and Infographics
All the Students od Class 1,2,3,4,5,6,7,8,9,10,11,12 and all the students of engineering, medical, CBSE, GSEB, U.P from beginner to Top and high level can get used. All The informtion are gathered to help you all the people.
All colleges and School students can use it.
All the people can reuse it by downloading by giving credits.
Copyright @ Jay Butani 2019
DISCLAIMER :- ALL THE INFORMARION ARE NOT EXACT OR 100% CORRECT THERE MAY BE MISTAKE. WE ARE NOT RESPONSIBLE OVER THAT.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Law Of Gravitation PPT For All The Students | With Modern Animations and Info...Jay Butani
Law Of Gravitation PPT For All The Students | With Modern Animations and Infographics
All the Students od Class 1,2,3,4,5,6,7,8,9,10,11,12 and all the students of engineering, medical, CBSE, GSEB, U.P from beginner to Top and high level can get used. All The informtion are gathered to help you all the people.
All colleges and School students can use it.
All the people can reuse it by downloading by giving credits.
Copyright @ Jay Butani 2019
DISCLAIMER :- ALL THE INFORMARION ARE NOT EXACT OR 100% CORRECT THERE MAY BE MISTAKE. WE ARE NOT RESPONSIBLE OVER THAT.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
2. 11/23/2022
Universal Gravitation
Newtonian Gravitation
Free-fall Acceleration &
the Gravitational Force
Gravitational Potential
Energy
Escape Speed
Kepler 1st Law
Kepler 2nd Law
Kepler 3rd Law
3. 11/23/2022
Newton’s Law of
Universal Gravitation
The apple was attracted
to the Earth
All objects in the Universe
were attracted to each
other in the same way the
apple was attracted to the
Earth
4. 11/23/2022
Newton’s Law of
Universal Gravitation
Every particle in the Universe attracts every
other particle with a force that is directly
proportional to the product of the masses and
inversely proportional to the square of the
distance between them.
2
2
1
r
m
m
G
F
5. 11/23/2022
Universal Gravitation
G is the constant of universal gravitation
G = 6.673 x 10-11 N m² /kg²
This is an example of an inverse square law
Determined experimentally
Henry Cavendish in 1798
2
2
1
r
m
m
G
F
6. 11/23/2022
Universal Gravitation
The force that mass 1 exerts
on mass 2 is equal and
opposite to the force mass 2
exerts on mass 1
The forces form a Newton’s
third law action-reaction
The gravitational force exerted by a uniform
sphere on a particle outside the sphere is the
same as the force exerted if the entire mass of the
sphere were concentrated on its center
7. 11/23/2022
Billiards, Anyone?
Three 0.3-kg billiard balls
are placed on a table at
the corners of a right
triangle.
(a) Find the net gravitational
force on the cue ball;
(b) Find the components of
the gravitational force of
m2 on m3.
8. Free-Fall Acceleration
Have you heard this claim:
Astronauts are weightless in space, therefore there is no gravity in
space?
It is true that if an astronaut on the International Space Station
(ISS) tries to step on a scale, he/she will weigh nothing.
It may seem reasonable to think that if weight = mg, since weight = 0,
g = 0, but this is NOT true.
If you stand on a scale in an elevator and then the cables are cut,
you will also weigh nothing (ma = N – mg, but in free-fall a = g, so
the normal force N = 0). This does not mean g = 0!
Astronauts in orbit are in free-fall around the Earth, just as you
would be in the elevator. They do not fall to Earth, only because of
their very high tangential speed.
11/23/2022
9. 11/23/2022
Free-Fall Acceleration and the
Gravitational Force
Consider an object of mass m near the Earth’s
surface
Acceleration ag due to gravity
Since
we find at the Earth’s surface
km
1
.
6378
E
R
kg
10
9742
.
5 23
E
M
2
2
m/s
8
.
9
E
E
g
R
M
G
a
g
E
E
ma
R
mM
G
F
2
2
2
2
1
E
E
R
mM
G
r
m
m
G
F
10. 11/23/2022
Consider an object of mass m at a height h above
the Earth’s surface
Acceleration ag due to gravity
ag will vary with altitude
Free-Fall Acceleration and the
Gravitational Force
2
)
( h
R
M
G
a
E
E
g
g
E
E
ma
R
mM
G
F
2
2
2
2
1
)
( h
R
mM
G
r
m
m
G
F
E
E
11. 11/23/2022
Gravitational Potential
Energy
U = mgy is valid only near the earth’s
surface
For objects high above the earth’s surface,
an alternate expression is needed
Zero reference level is infinitely far from the
earth, so potential energy is everywhere
negative!
Energy conservation
E
M m
U G
r
2
1
2
E
M m
E K U mv G
r
12. Energy of an Orbit
Consider a circular orbit of a planet around the Sun. What keeps
the planet moving in its circle?
It is the centripetal force produced by the gravitational force, i.e.
That implies that
Making this substitution in the expression for total energy:
Note the total energy is negative, and is half the (negative)
potential energy.
For an elliptical orbit, r is replaced by a:
11/23/2022
2
2
mv Mm
F G
r r
2
1
2
2
GMm
mv
r
2
1
2 2
GMm GMm GMm
E mv
r r r
(circular orbits)
2
GMm
E
r
(elliptical orbits)
2
GMm
E
a
13. 11/23/2022
Escape Speed
The escape speed is the speed needed for an
object to soar off into space and not return
For the earth, vesc is about 11.2 km/s
Note, v is independent of the mass of the
object
E
E
esc
R
GM
v
2
2
1
0
2
E
M m
E K U mv G
r
14. 11/23/2022
Kepler’s Laws All planets move in
elliptical orbits with the
Sun at one of the focal
points.
A line drawn from the
Sun to any planet
sweeps out equal areas
in equal time intervals.
The square of the orbital
period of any planet is
proportional to cube of
the average distance
from the Sun to the
planet.
15. 11/23/2022
Kepler’s First Law
All planets move in
elliptical orbits with
the Sun at one
focus.
Any object bound to
another by an
inverse square law
will move in an
elliptical path
Second focus is
empty
16. Ellipse Parameters
Distance a = AB/2 is the semi-major
axis
Distance b = CD/2 is the semi-minor
axis
Distance from one focus to center of
the ellipse is ea, where e is the
eccentricity.
Eccentricity is zero for a circular
orbit, and gets larger as the ellipse
gets more pronounced.
11/23/2022
17. 11/23/2022
Kepler’s Second Law
A line drawn from
the Sun to any
planet will sweep
out equal areas in
equal times
Area from A to B
and C to D are the
same
18. 11/23/2022
The square of the orbital period of any planet is
proportional to cube of the average distance
from the Sun to the planet.
T is the period of the planet
a is the average distance from the Sun. Or a is the
length of the semi-major axis
For orbit around the Sun, K = KS = 2.97x10-19 s2/m3
K is independent of the mass of the planet
Kepler’s Third Law
s
s
GM
K
2
4
3
2
Ka
T
19. 11/23/2022
Calculate the mass of the Sun noting that the
period of the Earth’s orbit around the Sun is
3.156107 s and its distance from the Sun is
1.4961011 m.
The Mass of the Sun
2
2 3
4
T a
GM
2
3 30
2
4
1.99 10 kg
M a
GT
20. 11/23/2022
From a telecommunications point of view, it’s
advantageous for satellites to remain at the same
location relative to a location on the Earth. This can
occur only if the satellite’s orbital period is the same as
the Earth’s period of rotation, 24 h. (a) At what
distance from the center of the Earth can this
geosynchronous orbit be found? (b) What’s the orbital
speed of the satellite?
Geosynchronous Orbit
2
3
4
24h = 86400 s
E
T a
GM
1/3 1/3
2 2 2 2
/ 4 (6.67e 11)(5.97e24)(86400 s) / 4 41500km
E
a GM T