Suppose that there is a spaceship that leaves the solar system at a velocity of v = (3/5)c, headed for a planet that is 20 c • yrs away. Assume that the Sun and the planet are both at rest and that their clocks have been synchronized such that both read zero when the spaceship leaves.  How far apart are the sun and the planet in the spaceships's frame of reference?

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Suppose that there is a spaceship that leaves the solar system at a velocity of v = (3/5)c, headed for a planet that is 20 c • yrs away. Assume that the Sun and the planet are both at rest and that their clocks have been synchronized such that both read zero when the spaceship leaves. 

How far apart are the sun and the planet in the spaceships's frame of reference?

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From spectial theory of relativity x' = x-vt1-v2c2but according to question t  = 0x' = x1-v2c2but x = 50c yrs and v = (3/5)cso x' = 50c yrs1-((3/5)c)2c2x' = 50c yrs×525-16x' = 50c yrs×59x' = 50c yrs×53x'  = 83.33c yrs

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