# At 556 million mph, how long would it take to get to Neptune to the sun?

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• 7 months ago

d(max) = Neptune's aphelion (farthest distance from the sun) = 2,819,080,000 miles

v = velocity of spaceship = 556,000,000 miles per hour

v = d(max) / T

vT = d(max)

T = d(max) / v

T = time duration of the trip as measured on Earth = 5.07028777 hours

However, since the velocity of the proposed spaceship is a signicant fraction of the speed of light,

the special relativity equation of time dilation becomes relevant.

c = speed of light = 186,262 miles per second x 3,600 seconds per hour = 670,543,200 miles per hour

β = v/c = spaceship velocity as a fraction of the speed of light (c) = 0.829178493 c

T0 = time duration of the trip as measured on the spaceship = to be determined

γ = [gamma] = Lorentz factor = 1 / √(1 - β²) = 1 / √(1 - 0.829c / c) = 1.788960215

T = T0 / √(1 - β²) = T0·γ

T = T0·γ

T0 = T / γ = 5.0703 hrs / 1.78896 = 2.834209352 hours

So, the time that the trip takes would be shorter for the astronaut.

• 7 months ago

56 Minutes minus 12 seconds

Have people forgot about Time Dilation ??

• Anonymous
7 months ago

It would be much quicker to travel faster than the speed of light , yes IT CAN BE DONE, if those dum dum scientists would just work harder at their calculations.

• Anonymous
7 months ago

• Anonymous
7 months ago

301 minutes.

But just getting to 80% of the speed of light would typically take quite a bit longer.

• .
Lv 7
7 months ago

It's 2.7819 billion miles.  So a bit over five hours.

• Fuhr
Lv 6
7 months ago

Me fail English?  That unpossible!

Source(s): Ralph