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.

Your rocket engineer says that he can build engines which will accelerate the ship at a = 1 gee = 9.8 m/s2.

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 and days.
  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 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 one hour."

"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?

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