Prepared By:Suraj Jha – Class-XI-B

Anoop Kr. Singh – Class-XI-B

Early AstronomyAs far as we know, humans have

always been interested in the motions of objects in the sky.

Not only did early humans navigate by means of the sky, but the motions of objects in the sky predicted the changing of the seasons, etc.

Early AstronomyThere were many early attempts both to describe and explain the motions of stars and planets in the sky.

All were unsatisfactory, for one reason or another.

The Earth-Centered UniverseA geocentric (Earth-centered) solar system

is often credited to Ptolemy, an Alexandrian Greek, although the idea is very old.

Ptolemy’s Solar SystemPtolemy’s solar system could be made to fit

the observational data pretty well, but only by becoming very complicated.

Copernicus’ Solar SystemThe Polish cleric Copernicus proposed a

heliocentric (Sun centered) solar system in the 1500’s.

Objections to CopernicusHow could Earth be moving at enormous

speeds when we don’t feel it?(Copernicus didn’t know about inertia.)

Why can’t we detect Earth’s motion against the background stars (stellar parallax)?

Copernicus’ model did not fit the observational data very well.

Galileo & CopernicusGalileo became convinced that Copernicus

was correct by observations of the Sun, Venus, and the moons of Jupiter using the newly-invented telescope.

Perhaps Galileo was motivated to understand inertia by his desire to understand and defend Copernicus’ ideas.

Kepler’s Laws:Kepler’s First Law

Kepler determined that the orbits of the planets were not perfect circles, but ellipses, with the Sun at one focus.

Sun

Planet

Kepler’s Second LawKepler determined that a planet moves faster

when near the Sun, and slower when far from the Sun.

Sun

Planet

Faster Slower

Kepler's Third LawT 2 α R 3

The above equation was formulated in 1619 by the German mathematician and astronomer Johannes Kepler (1571-1630). It expresses the mathematical relationship of all celestial orbits. Basically, it states that the square of the time of one orbital period (T2) is directly proportional to the cube of its average orbital radius (R3).

Why?Kepler’s Laws provided a complete

kinematical description of planetary motion (including the motion of planetary satellites,

like the Moon) - but why did the planets move like that?

The Apple & the MoonIsaac Newton realized that the motion of a

falling apple and the motion of the Moon were both actually the same motion, caused by the same force - the gravitational force.

Universal GravitationNewton’s idea was that gravity was a

universal force acting between any two objects.

At the Earth’s SurfaceNewton knew that the gravitational force

on the apple equals the apple’s weight, mg, where g = 9.8 m/s2.

W = mg

Universal GravitationFrom this, Newton reasoned that the

strength of the gravitational force is not constant, in fact, the magnitude of the force is inversely proportional to the square of the distance between the objects.

Universal GravitationNewton concluded that the gravitational force is:Directly proportional to the masses of both objects.

Inversely proportional to the distance between the objects.

Law of Universal GravitationIn symbols, Newton’s Law of Universal

Gravitation is:

Fgrav = G

Where G is a constant of proportionality.G = 6.67 x 10-11 N m2/kg2

Mmr 2

An Inverse-Square Force

The Gravitational FieldDuring the 19th century, the notion

of the “field” entered physics (via Michael Faraday).

Objects with mass create an invisible disturbance in the space around them that is felt by other massive objects - this is a gravitational field.

The Gravitational FieldSo, since the Sun is very massive, it creates an intense gravitational field around it, and the Earth responds to the field. No more “action at a distance.”

Gravitational Field StrengthNear the surface of the Earth, g =

F/m = 9.8 N/kg = 9.8 m/s2.In general, g = GM/r2, where M is

the mass of the object creating the field, r is the distance from the object’s center, and G = 6.67 x10-11 Nm2/kg2.

Gravitational Field Inside a PlanetIf you are located a distance r from

the center of a planet: all of the planet’s mass inside a sphere of radius r pulls you toward the center of the planet.

All of the planet’s mass outside a sphere of radius r exerts no net gravitational force on you.

Gravitational Field Inside a PlanetThe blue-shaded partof the planet pulls youtoward point C.

The grey-shaded partof the planet does not pull you at all.

Gravitational Field Inside a Planet

Half way to the center of the planet, g has one-half of its surface value.

At the center of the planet, g = 0 N/kg.

Variation of ‘g’ Due To Altitude, Latitude And Depth

(i)Variation of g with altitude : Let M be the mass of the earth and R be the

radius of the earth. Consider body of mass m is situated on the earth's surface. Let g be the acceleration due to gravity on the earth's surface.

From this equation it is obvious that acceleration due to gravity goes on decreasing as altitude of body from the earth's surface increases.

(ii) Variation of g due to depth : 

Let M be the mass "of the earth and R be the radius of the earth. The acceleration due to gravity on the surface of the earth is given by,

Consider the earth as sphere of uniform density.

Consider a point P at the depth d below the surface of the earth where the acceleration due to gravity be gA. Distance of point P from centre of the earth is (R-d).The acceleration due to gravity at point P due to sphere of radius (R-d) is

This is the expression for acceleration due to gravity at depth d below the earth surface. From this expression, it is clear that acceleration due to gravity decreases with depth. Note At the centre of the earth, d = R Therefore gd = 0Thus, if the body of mass m is taken to the centre of the earth, its weight will be equal to zero but mass of the body will not be zero. The above consideration shows that the value of g is maximum at the surface of the earth and it goes on decreasing (i) with increase in depth below the earth's surface. (ii) with increase in the height above the earth's surface. 

Escape Velocity:

The velocity needed for an object to completely escape the gravity of a large

body such as moon, planet, or star

If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit).

Escape velocity

For object to escape gravity must have:

E k ≥ E p

½m v 2 ≥ mgh

Or for Earth, h = R

vesc ≥ √2 g R ≥ √ 2 G M/R

independent of mass of object

Escape velocity from Earth ≈ 11 km/s from sea level

(about 40,000 km/hr)

Escape and orbital velocities don’t depend

on the mass of the cannonball.

Orbital Velocity and Altitude

A rocket must accelerate to at least 25,039 mph (40,320 kph) to completely escape Earth's gravity and fly off into space.

Earth's escape velocity is much greater than what's required to place an Earth satellite in orbit. With satellites, the object is not to escape Earth's gravity, but to balance it. Orbital velocity is the velocity needed to achieve balance between gravity's pull on the satellite and the inertia of the satellite's motion -- the satellite's tendency to keep going. This is approximately 17,000 mph (27,359 kph) at an altitude of 150 miles (242 kilometers). Without gravity, the satellite's inertia would carry it off into space. Even with gravity, if the intended satellite goes too fast, it will eventually fly away. On the other hand, if the satellite goes too slowly, gravity will pull it back to Earth. At the correct orbital velocity, gravity exactly balances the satellite's inertia, pulling down toward Earth's center just enough to keep the path of the satellite curving like Earth's curved surface, rather than flying off in a straight line.

SatellitesSatellites can be classified by their functions. Satellites are launched into space to do a specific job. The type of satellite that is launched to monitor cloud patterns for a weather station will be different than a satellite launched to send television signals across Canada. The satellite must be designed specifically to fulfill its function.Below are the names of nine different types of satellites. There are also nine pictures of satellites. Each picture is an example of one type of satellite.

Main Types Of Satellites and their examples:Astronomy satellites - Hubble Space Telescope Atmospheric Studies satellites – Polar Communications satellites - Anik E

Black Holes

When a very massive star gets old and runs out of fusionable material, gravitational forces may cause it to collapse to a mathematical point - a singularity. All normal matter is crushed out of existence. This is a black hole.

Black Hole Gravitational Force

How Black Hole Looks Like

Black Hole Gravitational ForceThe black hole’s gravity is the same

as the original star’s at distances greater than the star’s original radius.

Black hole’s don’t magically “suck things in.”

The black hole’s gravity is intense because you can get really, really close to it!

THE BLACK HOLE

Earth’s TidesThere are 2 high tides and 2 low tides per

day.The tides follow the Moon.

Why Two Tides?Tides are caused by the stretching of a

planet.Stretching is caused by a difference in

forces on the two sides of an object.Since gravitational force depends on

distance, there is more gravitational force on the side of Earth closest to the Moon and less gravitational force on the side of Earth farther from the Moon.

How does gravity cause tides?

• The Moon’s gravity pulls harder on near side of Earth than on far side.

• The difference in the Moon’s gravitational pull stretches Earth.

Why the Moon?

The Sun’s gravitational pull on Earth is much larger than the Moon’s gravitational pull on Earth. So why do the tides follow the Moon and not the Sun?

Why the Moon?Since the Sun is much farther from Earth

than the Moon, the difference in distance across Earth is much less significant for the Sun than the Moon, therefore the difference in gravitational force on the two sides of Earth is less for the Sun than for the Moon (even though the Sun’s force on Earth is more).

The Sun does have a small effect on Earth’s tides, but the major effect is due to the Moon.

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