• Question: In what way is maths used to aid the landing of rockets?

    Asked by dharrington06 on 9 Nov 2020.
    • Photo: Eduard Campillo-Funollet

      Eduard Campillo-Funollet answered on 9 Nov 2020:

      Maths is used in many ways in rocket science. When landing a rocket like the SpaceX Falcon9, they use mathematical models to predict the trajectory of the rocket, and they use a branch of mathematics known as optimal control to correct the trajectory down to the landing platform.

      When I was a student, we did a short project about the mathematics involved on saving the astronauts on the Apollo 13. There was an explosion on board of the Apollo 13 when it was on its way to the moon, and we computed for how long they needed fire the boosters in order to fly around the moon and get back to Earth! We did it with a modern computer (about 15 years ago), but NASA had to do it with much more pressure, about 50 years ago!

    • Photo: Chris Budd

      Chris Budd answered on 9 Nov 2020:

      The best answer to this question is for you to watch the wonderful film Hidden Figures where you can see mathematicians in action solving the problems needed to land rockets on the moon. But the basic tools of all of these methods are the branches of maths that include mechanics, calculus and differential equations.

    • Photo: Tom Ranner

      Tom Ranner answered on 9 Nov 2020:

      There are a few really cool ways that maths helps to land rockets.

      First, calculations need to be down to work out how long to fire boosters to control particular maneuvers. These are very complicated calculations that are best done by computer to give accurate results quickly. Mathematical calculations are also used to work out things like the weight of the rocket to make sure you get the right answer!

      Second, things often change during a space mission so we need to be able to send and receive messages to the rocket. This is done using special mathematical techniques too!

      Finally the initial design of the rocket had lots of maths put in to it to make sure that it is possible to land the rocket safely. When a rocket returns to earth it gets very hot due to the friction of the air moving past the rocket really quickly. Special materials and sensors have been designed to make sure the rocket doesn’t explode when its coming in to land.

    • Photo: Sophie Carr

      Sophie Carr answered on 9 Nov 2020:

      Lots of maths is needed to land a rocket! There’s mechanics, algebra, calculus – one of the great things about engineering and maths is that it really does take a multi-disciplined team to get a rocket to where it needs to be and land safely.

    • Photo: Nathan Turner

      Nathan Turner answered on 11 Nov 2020:

      Loads of maths is needed and used to help with landing rockets! One really interesting thing to look up on the subject of space travel is escape velocity. This is the speed that an object must travel to escape the gravitational pull of a planet or moon after launch. The speed of an object as it moves away from a planet or moon determines whether it will:
      a) Fall back to the surface (slower)
      b) Go into orbit
      c) Escape and continue to move away (faster)

      According to NASA, a spacecraft leaving the surface of Earth, for example, needs to be going about 11 kilometers (7 miles) per second, or over 40,000 kilometers per hour (25,000 miles per hour), to enter orbit. The escape velocity is dependent on the mass of the planet/moon but not on the mass of the object leaving. Therefore the escape velocity of the moon is much lower than that of the Earth.

Comments

  • Photo: Matthew D

    Matthew D commented on :

    I love this topic – how do they factor in the (drone?) pendulum fallacy, to make sure the rocket won’t tip over?

  • Photo: Chris

    Chris commented on :

    The simple answer is CONTROL. Rockets are not fired into space and left to their own devices. Instead their position and orientation is constantly monitored by on board sensors, and then the rocket is controlled (eg. by moving fins) so that it stays on track. Various sensors are used to do this. The early rockets such as the V2 had gyroscopes on board which could sense the orientation of the rocket and make course corrections. Gyros are still used, but they are combined with electronic sensors such as GPS or links to the ground station which can track the rocket as it moves. There is a whole branch of mathematics called control theory which works out the best way to control the rocket (or any other machine such as an aeroplane of a car engine). Similarly, the methods used to track a rocket are also used in you mobile phone to make sure that it stays connected to the phone masts.