Designing a ship for travel to Mars (simple version)

Suppose that we have built a spaceship and placed it into orbit far above the Earth -- far enough that the gravitational influence of the Earth is small. The plan is to drive the ship out to the orbit of Mars.

Now, in real life, rocket scientists have to take into account a HOST of effects, such as angular momentum, orbital velocity, the rocket effect, and many others. We are going to ignore all that for now (though we will start to learn about some of those other factors soon enough), and pay attention to just one little bit of the problem: the difference in Gravitational Potential Energy (GPE) between the orbits of the Earth and Mars.

Let's use the following values:



 mass of Sun                  M     =   1.99 x 10³⁰ kg

 mass of ship                 m     =   1 kg

 radius of Earth's orbit      Re    =   1.50 x 10¹¹ m

 radius of Mars's orbit       Rm    =   2.28 x 10¹¹ m

Can you calculate the following quantities? (Hint: they are exactly the same size)

the work done on the ship by the Sun's gravitational force over the course of the journey
the change in the gravitational energy of the ship from start to finish

Now, suppose that we give the ship engines which burn a refined version of kerosene (RP1) and oxygen. The energy released when these two chemicals combine is



    energy released   E  =  12 x 10⁶ Joules per kg

(This represents the energy released when the optimal ratio of kerosene to oxygen is mixed together: about 2.5 kg of oxygen for every 1 kg of kerosene).

How much fuel (kerosene + oxygen together) will it take to send our ship from Earth to Mars?

How does that compare to the mass of the ship?

Do you see a problem here?

Remember, this is a very simplified view of the situation. As we will see soon, analyzing real rockets requires a careful treatment of the momentum of the rocket and its exhaust.

For more information

Using momentum to analyze rockets