Authors: Daniel Sykes, Max Jones and Francis Milne
With NASA’s recent pledge to put the first woman on the moon in 2024, and SpaceX’s ambitious goal of colonising Mars, interest in space exploration has never been greater. For the first time in 50 years, humans will be travelling beyond low Earth orbit. But, space is vast and entering orbit around another planet requires costly burns and colossal launch vehicles. An aerocapture is an orbital manoeuvre that aims to fix this, by instead using a planet’s atmosphere to bleed off speed. Despite its benefits, the manoeuvre remains untested, so to explore its feasibility the team planned a mission to Venus and modelled it in the programming language “MATLAB”. This was part of a Modelling Techniques assignment led by Dr Alan Hunter, aiming to apply various numerical methods used to solve ordinary differential equations.
Venus was an ideal candidate; it is Earth’s closest neighbour and has an atmosphere that is 100 times thicker than Earth’s. In stage 1 of the mission, a 1500kg satellite launches from Earth aboard a two-stage rocket. The rocket places the satellite into a 170km high parking orbit, before performing a second burn to escape Earth’s gravity and enter interplanetary space. A pair of differential equations were derived to model the 2-dimensional motion of the spacecraft, factoring in variable thrust, mass, gravity, and atmospheric drag, and these were solved using the Runge-Kutta-4 method in MATLAB.
Stage 2 was the interplanetary cruise, which required modelling gravity from the Earth, the Sun, and Venus simultaneously, and forming a model of the solar system to track the positions of the planets. Finally, after 167 days of space travel, the probe reaches Venus, where it shaves the atmosphere killing off most of its speed such that only a small burn would be required to put it into a circular orbit. Due to time constraints, this final burn was not modelled, so the spacecraft crashes into the surface hopefully taking some interesting footage along the way!
Overall, the model showed the benefits of an aerocapture to be immense, but safety concerns were raised, with the spacecraft’s maximum acceleration reaching 12G – unsafe for crewed travel. By sacrificing some performance, the acceleration can be reduced, but the main hurdle is insulating the spacecraft from the high temperatures endured. The team had great fun modelling the mission, with it drawing from many of the topics covered in the Modelling Techniques 1 module, and an animation of the full mission was produced (see top of page).
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