Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

How to get to Mars

You are in charge of designing a mission to take astronauts from Earth to Mars. At their closest approach, the distance between the two planets is roughly D = 80 million km. Let's make the number of significant figures explicit by writing the distance as D = 8.0 x 1010 m. 



  Q:  How many significant figures are in the distance?

Your rocket engineer says that he can build engines which will accelerate the ship at a = 1 gee = 9.8 m/s2. (Notice that the acceleration is also given to two significant figures).

Fast Flyby
Suppose that the engines fire at full throttle for the entire trip, continuously accelerating the ship towards the Red Planet.
  1. How long will it take to get from Earth to Mars? Express your answer in seconds. Then, convert the answer to days. Please provide the proper number of significant figures in each case.
  2. How fast will the ship be moving when it reaches Mars?

Fast Rendezvous
The astronauts who read your plan complain that they won't be able to disembark from the ship and land safely on Mars, because the ship will be moving too fast.

"Fine," you mutter. "I'll re-design the mission so that the ship accelerates for half the distance, then turns around and DE-celerates for the other half. It will reach Mars with zero velocity."

  1. How long will it take to get from Earth to Mars under this plan? Express your answer in seconds, and also in days.

Finite Fuel
Your rocket engineer comes back after a few weeks and delivers some bad news. "We don't have an infinite supply of fuel, so the engines can only fire for a total of exactly one hour = 3600.0 seconds. "

"Ugh," you groan. "We'll have to use half the fuel to accelerate to a top speed of vmax, then coast at that speed until we are almost to Mars, then turn the ship around and de-celerate so that we hit zero speed at Mars itself."

  1. What is the top speed vmax under this plan?
  2. How far will the ship travel as it is accelerating?
  3. What distance will the ship have to coast before decelerating?
  4. How long will the entire mission take under this plan?

None of these possibilities is very close to the actual journey that astronauts might take to Mars. In our examples, we've completely ignored the forces of gravity from the Earth, Mars, and the Sun, and we've also ignored the fact that the Earth and Mars are both moving through space in their orbits. A realistic trip to Mars will follow a "Hohmann orbit"; you can learn more about them

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.