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$\bullet$ The starships of the Solar Federation are marked with thesymbol of the Federation, a circle, while starships of theDenebian Empire are marked with the Empire's symbol, anellipse whose major axis is 1.40 times its minor axis $(a=1.40 b$ in Figure 27.25$)$How fast, relative to an observer, does an Empire ship have to travel for its markingsto be confused with those of a Federation ship?

$=\left[2.1 \times 10^{8} \mathrm{m} / \mathrm{s}\right]$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Cornell University

Simon Fraser University

University of Winnipeg

McMaster University

Lectures

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

03:18

Sir Isaac Newton described the law of universal gravitation in his work "Philosophiæ Naturalis Principia Mathematica" (1687). The law states that every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

03:12

The starships of the Solar…

0:00

01:18

03:52

he starships of the Solar …

03:20

Two spaceships are observe…

04:52

(II) An observer on Earth …

01:01

The insignia painted on th…

02:11

A Klingon spacecraft moves…

01:43

A Klingon space ship moves…

How fast does a 250 -m spa…

so and this probably have two spaceships. The first spaceship is the Fed Federation's spaceship. So it's putting here the federation and the 2nd 1 is the M Fire spaceship. And we know that in part of spaceship as an ellipse with lens, a major left a in minor lens. Be so we want to know what should be this Pete, Let's go off a spaceship of the Empire. So what observer outside of the ship confused the Empire ship by one of the federation. So let's think about the relativity in this problem. A person looking outside the Empire Ship sis, the length a contract because of the effects of relativity. So we actually seen Let's go a prime the length that your observer sees. So the lens of the rib service is the is the actual length a contract by gamma. Okay, so we know the problem. Say, ace, that a equals 1.4 be so we can see that the length that observer outside this scene is a prime and B because he doesn't change. So this is just going to be eight. Brian equals 1.4. Be divided by Gammon. We know that a prime is equal be in this case. So this is just be equal game and be actually equals 1.4 b in cross being here. So we have that gamma coast 1.4 and we know that gamma is defined by one divided by one minus V square C square. Describe bridge because 1.4, If we rearrange this, we're going to get see going to get V equals. See Scrabble. It's off one miners, one divided by 1.4 square in the square. Brit. So after we calculate off this we get at the velocity. The speed is actually zero point seven see or for simplify. We can say this is two point 18 0.10. Actually, there is no 18 2.2 point one times 10 to the power off eight meters per second. And that's should be the speed off the spaceship. So on observer outside, a sheep spaceship confused the empire with one of the federation. That's all

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