Plan a one-way trip to the Solar System destination of your choice

Your job is to figure out the amount of food and water needed for a one-way journey to some object in our Solar System.

Pick any body you wish that is beyond the Moon's orbit. Assume that your spaceship travels along a Hohmann transfer orbit, which minimizes the amount of rocket fuel required. You can compute the duration of the journey in two steps.

First, figure out the semi-major axis of the orbit, which starts at the Earth and ends at the destination.

where r₁ is the radius of the Earth's orbit in meters, and r₂ is the radius of your target's orbit in meters.

Next, use the following formula to compute the time to make each leg of the trip; in other words, t_H is the one-way travel time, in units of seconds.

Here, use the values G = 6.67 x 10^-11 N*m^2/kg^2 for the gravitational constant, and M_☉ = 1.99 x 10³⁰ kg for the mass of the Sun.

If you're not sure about your calculations, you can check with the properties of a trip to Mars: when you plug in the values for Earth's orbital radius and Mars' orbital radius, you should find that a one-way trip takes about 258 days.

So -- for YOUR destination, how long will it take?

Now comes the section that requires some imagination and planning on your part. Assume that you are the only passenger aboard this vessel.

Estimate the amount of food and water that you will require for this one-way voyage. Assume that no waste is recycled during the trip.
Compute the volume required to store the food and water that you will need. Make any reasonable estimates or assumptions you wish, but state them explicitly.
Design a "capsule" for yourself, which provides all the space needed for your living quarters during the trip. It will take a while, so be sure to give yourself enough room to get some sort of exercise, even if it's just a spring-loaded Nautilus machine. The capsule must also contain all the space needed for your food and water supplies.
Compare the size of this capsule to the size of the largest payloads currently being launched into space today; say, on the SpaceX Falcon 9, or any other commercial booster you wish.

Finally, comment on the practicality of your journey: if you had several billion dollars, do you think you could purchase a launch which could take your capsule into space?

Scan or photograph all your drawings and notes, creating a single PDF file with all the material. Submit the PDF file via the myCourses "Assignments" facility.