Astronomer class

Question

NASA is currently developing the Space Launch System, or SLS, which will be arguably the most powerful rocket ever built. It is designed primarily to transport astronauts to Mars with a travel time of only a few months each way. Suppose that we wanted astronauts to travel to the edge of the Solar System instead on an expedition to Neptune. Given that the SLS rocket will have a top speed of around 3.19 x 10⁸ km yr^-1 (kilometers per year), at least how long would it take astronauts to get to Neptune? Give your answer in units of years (yr).

Answer 1

I'll try to answer this here, but depending on the level of difficulty this astronomy class is intended to be, this could get very complicated. I'll answer assuming the simplest situation: that neither neptune or earth are moving, and that the SLS rocket is traveling in a straight line at a constant speed

We will need two pieces of information:

1) the definition of velocity:

Velocity = Distance / Time

2) the shortest distance between Neptune and Earth:

According to Space.com: 4.3 Billion (10^9) km

We know the velocity of the spacecraft, so now we solve the definition of velocity for time. We do this by multiplying both sides of the equation by time, and dividing both sides by velocity:

time = distance / velocity

Now we plug the numbers into a calculator:

4.3 * 10^9 km

time = ------------------ = 13.4796238245 yr

3.19 * 10^8 km/yr

If you are worried about significant figures, 13.5 years would be the appropriate answer