Playing the space billiard game in sending spacecraft millions of kilometres on interplanetary space missions

In humankind's quest for knowledge, understanding our universe and our neighbours, we often take to the space to explore some of the planets near and far from us.

On 5th May 2018, NASA launched a rover, Insight to Mars to explore the underneath of the Mars. Most other robotic rovers travel around collecting data, but Insight will be probing the internal structure of the second smallest planet in our Solar System- Mars.

The anticipated landed date is 26 November 2018, a whopping 205 days! It is not like the Insight is moving along sluggishly, its velocity is 6.3 kilometres per second or 14,100 miles per hour, i.e. at more than six times the muzzle velocity(the speed a fired bullet leaves a gun's muzzle) of a modern rifle. The only problem we have here is Mars is far. Depending on the Sun's orbit position of both Earth and Mars, at its closest the distance is 54.6 million kilometres, at its farthest, the length could get as big as 401 million kilometres (250 million miles). The average range is taken to be approximately 225 million kilometres or 140 million miles.

Well if you think that Mars is far and the Insight is up for a long journey, then you should doff your hat to Cassini, the Saturn explorer. The robotic spacecraft spent 13 years plus orbiting the Saturn aka Ring Planet and sending us those beautiful high-resolution images of the Saturn and its rings.

To get us those crispy images is a journey fit for a Sci-Fi movie. Cassini had to travel some much longer distance to get to Saturn. Saturn's distance from the Earth is around 1.2 billion kilometres (746 million miles). This distance is when it is closest to Earth, it can get up to 1.7 billion kilometres apart at their farthest distance.

It took Cassini took seven years, between 1997 to 2004, to get to Saturn. It was not a straightforward journey as that will require a massive amount of fuel. Instead, space engineers devised a trick to use the gravitational moves of other planets to move the spacecraft while conserving fuel.

The Gravitational Maneuver

We may already know that gravity is available to act on any object that has mass. The more mass a planet has, the more its gravitational pull. Your weight on earth is because of the gravitational effect on you, that is why someone that weighs 45kg (100 lbs) on earth will weigh 7.7kg (17 lbs) on Moon and 48.5kg (107lbs) on Saturn. The mass of Moon is 7.357 x 10²² kg while that of Saturn is 5.683 x 10²⁶ kg. The Earth's mass is a bit smaller than Saturn at 5.972 x 10²⁴kg.

You can see the gravitational pull differs by mass of the planet. In the gravitational slingshot manoeuvre, the spacecraft utilises the momentum it gets from another planet on its travel to propel forward with zero rocket power.

You can easily picture this manoeuvre by running a little experiment. If you hurl a tennis ball at a car's bumper moving at a velocity of 100 km/h. The speed the ball will return to you will be very much faster than the speed you threw it at the truck.

This added velocity is because of the momentum gained by the ball which is the result of the transfer of energy from the speeding vehicle.

In the case of the probes, the momentum it gets is not as a result of physical contact but rather as a result of the effects of gravity.

Launching off a spacecraft to take advantage of gravity assist is the equivalence of playing a space billard (snooker).
You launch the spacecraft with the hopes it will somewhat borrow some speed from other balls (planets) on the table (space) and land on the corner pocket (intended planet). By setting off the spaceship in the same direction as earth's travel, you can check my post here for more details; the spacecraft does its first "steal" of Earth's momentum.

From Newton's second law of motion, we know that the force describes the rate of change of momentum. Since momentum cannot be created nor destroyed, the conservation of energy entails for an object to gain momentum, another object must lose some momentum.
The spacecraft gains momentum by flying close to the other planets; the planets lose momentum. Due to how massive the planets were when compared to the spacecraft, the change in momentum due to the lost momentum is infinitesimally small and goes unnoticed.

The game of using the gravity assist is one for the patient. The scientists/engineers must wait for the perfect alignment of planets before shooting off the "ball".

To get it right, they must launch only when the aligmnet of orbit path around the Sun is optimum.

An interplanetary alignment is sometimes a rare event. That is why Voyager spacecraft in the 70s launch date was sped up to meet up with the rare alignment that occurs once every 175 years. We should blame Neptune's 164.5-year orbital period around the Sun for a bunch of the delay. That means if they miss the 1976 to 1980 window the only other time that window of opportunity will present itself will be around the year 2151 to 2154.

If you input the date, 5th September 1977, which is the launch date of Voyager 1 into this simulator, you will see how nicely the four planets (Jupiter, Saturn, Uranus, and Neptune) align.

While the gravity can assist spacecraft to go faster, it can also slow the aircraft too. The process involves flying in the opposite direction of a planet's orbit.

This process was how NASA's MESSENGER used for deceleration in other to enter planet Mercury. This process is known as aerobraking.

^REFERENCES

• ^{Gravity assist}
• ^{FAQ: Cassini, Saturn and Titan}
• ^Cassini
• ^{How far away is Saturn}
• ^{Grand tour program}

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