physics-class-11-unit-08-chapter-04-galilean-laws-kepler-laws-centripetal-forces-gravitation-l-4-7-uxctwbaa5hk

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> Astronomical Distances </primary>
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* Let the radius of the Earth be $r_E$.

* Radius of the Moon's orbit R.

* Distance covered =$2\pi R$.

* Use the time taken by moon to cross the Earth's shadow during <span style="color:green">lunar eclipse</span>.

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<footer style = "font-size: 18px">Galilean Law, Kepler's Laws and Centripetal Forces $\rightarrow$ Astronomical Observations Ancient $\rightarrow$ <span style = "color:blue"> Astronomical Distances </span> $\rightarrow$ Gravitation $\rightarrow$ Eclipse </footer>

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> Gravitation </primary>
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- Estimating the distance between the earth and the moon.

- Earth Moon Distance : R

- Radius of the Earth : $r_E$

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<footer style = "font-size: 18px">Astronomical Observations Ancient $\rightarrow$ Astronomical Distances $\rightarrow$ <span style = "color:blue"> Gravitation </span> $\rightarrow$ Eclipse $\rightarrow$ Lunar Eclipse </footer>

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> Eclipse </primary>
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- There are two eclipses:

- <span style="color:green">Lunar eclipse</span>: when the earth comes between the sun and moon.

- <span style="color:green">Solar eclipse</span>: when the moon comes between the earth and the sun.

- $t_{\text{transit time}}= 2 r_e$ is the time taken duration of the eclipse.

- Assume that the moon is moving with a constant angular velocity.

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<footer style = "font-size: 18px">Astronomical Distances $\rightarrow$ Gravitation $\rightarrow$ <span style = "color:blue"> Eclipse </span> $\rightarrow$ Lunar Eclipse $\rightarrow$ Earth Sun Distance </footer>

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> Lunar Eclipse </primary>
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- Lunar eclipse takes place on a full moon day and the solar eclipse takes place on a new moon day.

- $2 \pi R$

- T $\approx 30$ days.

- $2\pi R = 30$ days

- $2r_e$ = transit time

- $\frac {R}{r_E} =\frac {T}{t_{transit}}\simeq 60$

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<footer style = "font-size: 18px">Gravitation $\rightarrow$ Eclipse $\rightarrow$ <span style = "color:blue"> Lunar Eclipse </span> $\rightarrow$ Earth Sun Distance $\rightarrow$ Earth Sun Distance </footer>

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> Earth Sun Distance </primary>
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- $R$ = distance between earth and the moon.

- $R_s$ = distance between the earth and the sun. 
	
- $\tan \theta = \frac{R_s}{R}$
	
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<footer style = "font-size: 18px">Eclipse $\rightarrow$ Lunar Eclipse $\rightarrow$ <span style = "color:blue"> Earth Sun Distance </span> $\rightarrow$ Earth Sun Distance $\rightarrow$ The Galilean Revolution </footer>

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> The Equivalence Principle </primary>
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- The word equivalence principle was coined by Einstein almost 500 years after Galileo made the observation.

- It is a fundamental principle.

- Equivalence principle is embedded in Galilean law of a freely falling body.
	
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<footer style = "font-size: 18px">Earth Sun Distance $\rightarrow$ The Galilean Revolution $\rightarrow$ <span style = "color:blue"> The Equivalence Principle </span> $\rightarrow$ Equivalence Principle $\rightarrow$ Equivalence principle </footer>

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> Equivalence Principle </primary>
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- Rate of change of momentum of a body is equal to the applied force.

- $\frac{d \vec{p}}{d t}=\overrightarrow{F_{a p p}}$

- Different applied forces characterized by different properties.

- $\overrightarrow{F_{a p p}}= -{k} \vec {r} \rightarrow$ Hooke Law.

- $\overrightarrow{F_{a p p}}= q(\vec{V} \times \vec{B}) \rightarrow$ Lorentz Force

- $\overrightarrow{F_{a p p}}= \overrightarrow{q E} \rightarrow$ Coulomb Force

- $\overrightarrow{F_{a p p}}= -\vec{k}|\vec{v}| \rightarrow$ Frictional Force

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<footer style = "font-size: 18px">The Galilean Revolution $\rightarrow$ The Equivalence Principle $\rightarrow$ <span style = "color:blue"> Equivalence Principle </span> $\rightarrow$ Equivalence principle $\rightarrow$ Freely Falling Body </footer>

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> Freely Falling Body </primary>
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- Let us assume that we take balls of lead, iron, and, stone (different masses).

- All of them are released from rest.

- If they are released simultaneously, all move together at any given time.

- They will reach the earth at the same time.

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<footer style = "font-size: 18px">Equivalence Principle $\rightarrow$ Equivalence principle $\rightarrow$ <span style = "color:blue"> Freely Falling Body </span> $\rightarrow$ Freely falling $\rightarrow$ Freely falling </footer>

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> Equivalence Principle </primary>
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- The force exerted by the earth on the bodies is independent of their mass.

- $m\vec a = m\vec g$

- There is a universality of earth's pull on the bodies.

- Galilean law of freely falling bodies has given the equivalence principle that earth attracts all bodies towards it with the same acceleration.

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<footer style = "font-size: 18px">Freely falling $\rightarrow$ Freely falling $\rightarrow$ <span style = "color:blue"> Equivalence Principle </span> $\rightarrow$ Frame of Reference $\rightarrow$ Frame of Reference </footer>

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> Frame of Reference </primary>
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- A person has a long thread and is moving in a circular motion of radius $R$.

- <span style="color:blue">Center is origin</span>

- x= R $cos \omega t$

- y= R $sin \omega t$

- $x^2+y^2= R^2$, circular motion.

- <span style="color:blue">Center is shifted</span>

- $\left (x-x_0\right) = R \cos\omega t$

- $\left (y-y_0\right) = R \sin\omega t$

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<footer style = "font-size: 18px">Freely falling $\rightarrow$ Equivalence Principle $\rightarrow$ <span style = "color:blue"> Frame of Reference </span> $\rightarrow$ Frame of Reference $\rightarrow$ Heliocentric Model of the Planetary System </footer>

### <Success style="font-size:25px"> Galilean Laws Kepler Laws Centripetal Forces Gravitation L-4 </Success>
### <primary style="font-size:24px"> Frame of Reference </primary>
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- $\sqrt{x^2}=\sqrt{2 x x_0+R^2 \cos ^2 \omega t+x_0^2}$

- $\sqrt{y^2}=\sqrt{2 y y_0+R^2 \sin ^2 \omega t-y_0^2}$

- <span style="color:blue">New origin with velocity</span>

- $x = x - x_0 - vt$

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<footer style = "font-size: 18px">Equivalence Principle $\rightarrow$ Frame of Reference $\rightarrow$ <span style = "color:blue"> Frame of Reference </span> $\rightarrow$ Heliocentric Model of the Planetary System $\rightarrow$ Thank You </footer>