As Elon Musk Rushes to Mars, Looking at Practical Routes

optimal delta-v and flight length considered

By Jonny Lupsha, Wondrium Staff Writer

Elon Musk continues to ramp up his efforts to get humanity to Mars, Ars Technica reported last week. He hopes to build 1,000 spaceships to settle on the red planet. Optimal trajectory and the length of the flight have been considered.

3D illustration of the planet Mars
During space travel, a spacecraft can gain kinetic energy from the gravitational pull from another planet as it passes by during a planned slingshot maneuver. Photo by Dotted Yeti / Shutterstock

The Ars Technica piece outlined Musk’s endeavors with his space team, SpaceX, to put a human on Mars, highlighting how excited Musk is to undertake the project. “He will not live forever, and the money may eventually run dry,” the article said. “He knows this. One day, the window to spread humanity to Mars may close, but Musk doesn’t know when. So he needs to squeeze through before the window shuts.”

A hiring spree last month helped move things along, though the multibillionaire behind Tesla automobiles continues to ramp things up with SpaceX. Amid the spaceship blueprints and new-hire paperwork, some very practical questions have already been answered. In particular, how will we get there and how long will it take?

The Slingshot Maneuver

The first question that comes to mind when considering a mission that leaves Earth’s atmosphere is just how to get off this big blue ball we call home.

“It’s important to recognize that the single biggest cost to a space mission is the change in velocity required, or delta-V,” said Dr. James W. Gregory, Professor of Mechanical and Aerospace Engineering at The Ohio State University. “Getting somewhere in space is all about the increase in kinetic energy, rather than a change in altitude, and a higher delta-V is going to require more fuel, and more fuel will increase the mass of the system that is launched into space.”

For this reason, Dr. Gregory said, one popular idea is known as the gravity-assist or “slingshot maneuver.” In this situation, the ship is placed on a path in which another planet’s gravitational pull will lend the ship’s flight a helping hand.

“The trajectory of the spaceship can be planned such that it approaches the planet from behind, and the planet’s gravity will pull it along, redirecting its trajectory and adding kinetic energy to the spacecraft,” Dr. Gregory said. “The amount of extra velocity imparted to the spacecraft depends on the velocity of the spacecraft, the velocity of the planet itself, the approach angle, and how much the trajectory is deflected, which depends on the gravitational field of the planet being flown by.”

Remember to Bring a Book

With fuel-efficiency tricks like the slingshot maneuver, a manned flight to Mars would be made as short as possible. Yet the questions remain: How short is that, and how do we determine the length of the flight?

“Time of flight depends strongly on the distance that must be traveled,” Dr. Gregory said. “It’s equal to pi times the square root of the cube of the semi-major axis of the transfer ellipse, divided by the Sun’s gravitational parameter.”

Put simply, from Earth to Mars, it’s eight and a half months.

“There are other trajectory options available to get to Mars, but all of them will require more fuel burn and more propellant,” Dr. Gregory said. “However, no matter what we do, it’s going to be a long journey, and once humans make it to Mars, they’re going to have to wait a long time before the next launch window arrives for any possibility of a return to Earth.”

While Earth-Mars space flight may still be in its infancy, the bare bones of such an endeavor have been laid out. Humanity is closer than ever to setting foot on another planet in our solar system.

Dr. Gregory is Professor of Mechanical and Aerospace Engineering

Dr. James W. Gregory contributed to this article. Dr. Gregory is Professor of Mechanical and Aerospace Engineering at The Ohio State University. He received a bachelor of science degree in Aerospace Engineering from Georgia Tech and a doctorate in Aeronautics and Astronautics from Purdue University.