You are designing a spaceship that will carry roughly 2000 humans to a nearby st

Question

You are designing a spaceship that will carry roughly 2000 humans to a nearby star system, Tau Cell, 11.8 light years away. To sustain your crew for the mission, you require a ship with a dry mass (without fuel) of approximately 2.5 billion kilograms to contain the biomes and habitats for the citizens of your ship. Using current technology, we can accelerate this ship up to 0.1 c, but the designers are asking you to speculate on the feasibility of a cruising speed of 0.9 c. So you will need to use relativity for your calculations. To make things easier, the relativistic rocket equation relates the speed you can achieve with respect to your payload mass, m_p, your total mass (payload plus fuel), m, and the specific impulse of your engines, I_sp. v/c = tan h (I_sp/c ln (m_t/m_p)) Where c is the speed of light. Specific impulse has units of velocity, and represents how quickly you can shoot propellant out of the back of the spacecraft. An |sp/c of 1.0 is the ideal matter/antimatter engine. Right now, your engineers can give you about 0.3. Given this information, complete the table below. You have been working on a new quantum containment drive that uses magnetic fields to compress the region around an ionized proton to about 1 femtometer. If we assume the maximum possible speed of such a particle (as determined by the uncertainty principle) is the new specific impulse, how does the total mass of the ship change? Finally, draw a space time diagram of this mission from the perspective of Earth and from the ship itself. Start each diagram from the bottom and label all information. To hand in: This sheet with calculated values Your work (model, visualize, solve, etc) If you choose to use excel, a printout of your worksheet

Explanation / Answer

1. what is the total mass relative to the payload mass?

for accelerate the velocity of the ship we need a light masses spaceship, if spaceship having a low mass then it can be go with higher speed.so if we want to accelearte spaceship to the 0.9 c velocity we have to decrease spaceship mass.

there is another option that we can increase the fuel mass which is help us to accelerate the spaceship velocity.

2. what is the flight time measured from the earth ?

flight tme will be for 0.9 c speed will be around 360 years and for 0.1c speed will be around 3240 years

3. what is the flight time measured on the spaceship ?

there is only minor difference in a time period which is from the earth.

4.& 5. with the mass of substance speed and distance will be increase so we can say that for only 1 g substance earth and spaceship both can cover far distance compare to previous.

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