This is Earth.
It has a mass of 5.972 × 10^24 kg and a diameter of 12,742 km. It is 149.6 million km from the Sun and is, on average, 225 million km, being farthest away at 401 million km and closest at 54.6 million km.
Mars, in turn, is 227.9 million km from the sun and is similar to Earth in mass and diameter- with a 6.39 × 10^23 kg mass and 6,779 km diameter respectively. In terms of planets other than Earth, it is a suitable place to live, with reasonable temperatures and atmosphere. Many space agencies, NASA and SpaceX among them, plan to set up colonies on Mars, in order to increase the human species chances of survival, and Mars is the optimum, and closest planet for this. SpaceX especially, aims to colonise Mars with a million people via a rocket that will hold a hundred people at a time. SpaceX in particular aims to send a rocket to Mars by 2020.
To first send a rocket to Mars, first you must be able to put a satellite into orbit. SpaceX has already achieved sending payloads into Low-Earth Orbit. In order to do this, the spacecraft is directed outwards from the Earth slow enough to be constantly falling towards it, due to gravitational pull, but fast enough to constantly miss landing on it. To calculate the velocity needed to keep a satellite in Low-Earth Orbit (referred to as the orbital velocity), the formula derived from Newton’s Law of Universal Gravitation () and Newton’s Second Law of Motion () is used; , G being the gravitational force and M being the mass of the object being orbited, in this case, 5.972 × 10^24 kg. For Low-Earth Orbit, the orbital velocity is 27,600 km/h. However, large amounts of energy are needed for this, as, rather than flying, the rocket pushes itself away from the earth, using conservation of momentum as its driving force. The engine that powers SpaceX’s especially engineered rocket engine, the Merlin, has anywhere from 845 kilo-Newtons (as it lifts off) to 914 kilo-Newtons (as it leaves Earth’s atmosphere) of thrust, and not only that, but SpaceX builds rockets with nine of them. However, the energy required to leave Low-Earth Orbit, is much greater, requiring enough energy to eventually leave the gravitational pull of the Earth all together and use the added momentum to guide the spacecraft further, in this case, Mars.
The Interplanetary Transport System, as is named the rocket to carry people to Mars a hundred at a time, uses an entirely different engine, the Raptor, which produces up to 277 tonnes of force. The ITS has 42 engines to provide vast amounts of force.
The rocket is also required to be streamlined and precisely controlled. An error in the coding involved (as what happened with NASA), or a corroded nut (as what happened with SpaceX) could ruin the coordination of take-off and cause the rocket to malfunction, or fall apart.
Mars is the prime contender for a settlement, in its similarity to Earth and our own environment and there are a varying amount of factors that contribute to how difficult it is to send a rocket to colonise Mars, not only things such as money, but also the engineering difficulties in overcoming the physical constraints, and the need to understand motion and gravitation.