How do spacecraft get a speed boost from gravity assists?


Most space probes launched today don’t have enough fuel to reach their destination directly, so how do they manage to get where they need to be? Jake Port explains.


No rocket ever made could have provided the acceleration, or deltaV budget, to propel Rosetta to the speed it needed to rendezvous with comet 67P.
ESA

Back in 2014, the Rosetta spacecraft arrived at its destination, comet 67P/Churyumov-Gerasimenko, after a 10-year journey. The moment was significant as it again demonstrated that how much fuel a spacecraft carries did not necessarily determine how far it could go.

But how was this possible and what forces are at play when it comes to making spacecraft travel further than they should?

Scientists designing rocket missions have a few tricks up their sleeve that allow them to accelerate an object to a speed that is higher than its fuel store would allow. To understand this better let’s start with how astronomers and space scientists view energy.

DeltaV

When you describe how far a form of transport on Earth can go – its range – you might express it in kilometres or miles.

This makes sense because we know burning fuel at a certain rate dictates how far you will travel. Forces acting against forward motion, such as drag and resistance, mean that an object without thrust will soon come to a stop when its propellant is spent.

In space, though, this rationale begins to fall apart. Space, as the name suggests, is devoid of any real resistance.

Because of this, space missions are not designed around “range” but what is known as a deltaV budget.

DeltaV refers to the change in velocity of an object. It is expressed in metres, kilometres or feet per second.

Let’s say you are designing a mission to get a payload into low earth orbit. The typical deltaV requirement to achieve that is around 10,000 metres per second or 10 kilometres per second.

A spacecraft does not have a top speed. Instead has a maximum deltaV, the maximum amount of velocity change it will experience if it expels all of its fuel.

The convenient aspect of a deltaV budget is that it takes into account multiple aspects of the craft, including weight and efficiency, with the force of gravity to give a single measurement.

Gravity assists

Let’s now look at how a craft can beat this seemingly finite velocity change.

Gravity is a force at work wherever we look, whether that’s at an apple falling from a tree or a galaxy spinning around its supermassive black hole.

Gravity can hold us onto the Earth's surface but it can also be used to make an object go faster.

If I were to say that, as a probe approaches Earth, it experiences the force of gravity and so it accelerates, your response would probably be, “yes, but as it moves away from Earth again the force of gravity is now pulling it backwards and so canceling the energy it gained on its way in”.

This is, in fact, completely correct.

But let’s not forget that all of the planets are moving around the sun, travelling at massive speeds as they circle their star.

Earth, for instance, travels at nearly 30 kilometres per second while a planet such as Jupiter travels at around 13 kilometres per second.

When an object approaches a planet as large as Jupiter it does not gain any energy overall from its gravity, but because Jupiter is moving at high speed in a particular direction it still “pulls” the probe, imparting a little bit of its planetary motion and so altering the probe's course. This, in turn, imparts more speed, creating a change in velocity and so deltaV. This is known as a “gravity assist”.

The video by TechLaboratories below gives an excellent visual representation of this phenomenon.


In the case of the Rosetta mission, it was launched with a deltaV budget that was thousands of metres per second short of what it would have needed to travel directly to Comet 67P.

In fact, there simply is not a rocket powerful enough to do this. Instead, the mission plan was designed to take the probe past Earth for its first gravity assist, followed by another gravity assist around Mars and then another two assists around the Earth. All up, this meant four trips around the sun.

It is a complex manoeuvre and the European Space Agency has prepared an excellent interactive video of Rosetta’s mission profile. You can watch it here.

Gravity assists allow spacecraft to travel at speeds far beyond what their fuel capacities would allow, making them a highly efficient way of generating extra deltaV. But, as demonstrated by the Rosetta mission, it can take multiple orbits and a decade to reach certain targets – a less-than-ideal scenario when these spacecraft start carrying human passengers.

It is for this reason that a variety of highly efficient engines are being developed to allow for a direct route.

You can find out about some of these in our article on 10 of the most feasible future propulsion systems by our resident physicist Cathal O'Connell.

  1. http://sci.esa.int/where_is_rosetta/
  2. https://cosmosmagazine.com/technology/antimatter-ion-drives-nasas-plans-deep-space-propulsion
  3. https://cosmosmagazine.com/contributors/cathal-o-connell
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