How Long Does It Take to Get to Pluto?

Image Credit: NASA.

A spaceship accelerates at a constant rate of 10 m / s2 for the first half of the trip and then slowing down at the same rate for the second half of the trip. The distance between Earth and Pluto is 4.773 * 1012 m. Can you calculate how long does it take to get to Pluto?

Solution.

We will use equation of the motion in a straight line

X = Xo + Vo * t + 0.5 * a * t2

where Xo – the initial position of the object, Vo – the initial velocity, a – the acceleration and t – the time it takes the object to move.

We could consider that Xo = 0 and Vo = 0.
Thereby,

X = 0.5 * a * t2 or

t = √(2*X/a)

The spaceship accelerates half of the trip, so X will be equal to
4.773 * 1012 / 2 = 2.3865 * 1012 m.

Substitute the values of X and a into the equation

t = √(2 * 2.3865 * 1012 / 10)

Hence,

t = 6.91 * 105 s

and the total time of the trip will be

6.91 * 105 * 2 = 1.38 * 106 s or 16 days.

Of course, there is more, a lot more, to space travel than just speeding up and slowing down. We have to keep track of gravitational forces, fuel supply and other things that make a 16 days trip to Pluto impossible, at least for now.