The starships of the Solar Federation are marked with the symbol of the Federati

Question

The starships of the Solar Federation are marked with the symbol of the Federation, a circle, whereas starships of the Denebian Empire are marked with the Empire's symbol, an ellipse whose major axis is 1.30 times its minor axis

The starships of the Solar Federation are marked with the symbol of the Federation, a circle, whereas starships of the Denebian Empire are marked with the Empire's symbol, an ellipse whose major axis is 1.30 times its minor axis How fast, relative to an observer, does an Empire ship have to travel for its markings to be confused with those of a Federation ship? Use c = 3.00 times 108m/s for the speed of light in a vacuum.Express your answer in terms of n and c. did some calculation and got v=c sqrt(1-1/n^2) but it told me to "use the numeric value of n in your answer."

Explanation / Answer

According to Lorentz contraction

L' = L (undefined)

For the ellipse of empire to be seen like a circle

a should be equal to b

that is

if L = a

then L' shouls be equal to b

b = a (undefined)

b = nb (undefined)

squaring on both sides

1/n^2 = 1 - v^2/c^2

v^2/c^2 = 1 - 1/n^2

v = c (undefined)

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