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How long does it take to get to Titan from Earth in a rocket that's going 2,500 miles per hour?
Question Date: 2016-05-02
Answer 1:

It's not my job to solve this very complicated question for you. After all, people pay scientists lots of money to come up with lots of complicated questions and answers like this. But just for fun, let's talk about what you need to do to solve this problem.

The first thing I noticed is that the answer depends on when you leave from Titan. Or, if you don't care when you leave from Titan, the answer depends on when you want to arrive on Earth. This is because Saturn and the Earth are orbiting the Sun at different speeds.

It takes the Earth one year to complete one orbit, but it takes Saturn about 29 years to complete one orbit. At one time, the Earth might be in between the Sun and Saturn. Then the distance from the Earth to Saturn is as short as it can be. But at another time, the Earth might be on the other side of the Sun. Then the distance from the Earth to Saturn is much longer. So when you're driving your rocket away from Saturn's neighborhood, you have to keep in mind that the Earth is also moving in its orbit around the Sun. You want to drive towards the place that the Earth will be, not towards where it is now.

On top of that, we have to think about the fact that Titan is in orbit around Saturn. So all in all, to solve this problem, we need to know:

- a start time, or an end time (not both);
- the path of the Earth, orbiting the Sun;
- the path of Saturn, orbiting the Sun; and
- the path of Titan, orbiting Saturn.

For each of these orbits, we need to think about:

- the current position of the orbiting body;
- the radius, which is the distance to the center body;
- the period, which is the time to complete one cycle; and
- the plane of the orbit, which is the angle that it makes in space.

And we can get a better answer if we also think about the shape of the orbit, which is not perfectly circular. This means that the radius will change with time, too.

I hope this gives you an idea of how complicated this problem is, and why scientists have important jobs. It's a lot of work to solve this kind of problem, and not everyone can do it. If you study hard, maybe someday someone will pay you lots of money to solve math and science problems.

Answer 2:

That depends on where Earth and Saturn (Saturn, because Titan is a moon of Saturn) are in their respective orbits.

Doing a very quick calculation, the answer I get is about 36 years for when Earth and Saturn are closest together. 2,500 miles per hour is not a fast speed for a rocket.

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