MIRA Issue No.29

GRAVITY ASSIST
or how to get something for nothing
by Ivor Clarke

We all know that there is no such thing as a free lunch, someone, sometime, somehow must pay the price. Nothing is for free. So how can you launch an interplanetary probe into deep space when you haven?t got enough thrust to reach a speed to get there in a reasonable time frame? After all, if it takes say, 15 to 20 years to get somewhere, what are the chances of a complex piece of equipment arriving in full working order? Back in the early sixties when the idea of constructing deep-space probes to the outer planets was first being debated, any suggestion of making a reliable spacecraft to last ten or more years was not considered possible with the then current technology.

The very thought of a mission to Saturn or beyond was enough to get the spacecraft engineers trembling. The early moon shots had just crashed into the surface or went by into a lunar orbit, likewise the first missions to the planets, Mars and Venus where just fly pasts. All depended on a few hours as the probe neared its target. None of these early craft could be controlled to the fine degree necess

This method is the most economical of energy but takes longer. The direct shortest path across to another planet would use a massive amount of fuel and is not possible even with today?s rockets. Engineers call the measure of the amount of energy needed the Dv (the Greek letter D delta + v for velocity). Thus Sputnik 1 had a Dv of 4.8 miles per second (7.8 km per second) for a low Earth orbit. The Shuttle needs a Dv of 5.7 m/s (9.2 km/s) to reach the height for the space station Freedom. An elliptical orbit with its trajectory just touching the orbits of both planets at perihelion and aphelion uses the smallest amount of fuel, but will take much longer to arrive as it has to travel about half way round the sun to meet the target. As the spacecraft swings round the orbit it loses speed as it travels further out from the sun until it reaches aphelion and its destination. If the target planet was not at the arrival point, the spacecraft would then swing back in an ellipse to its starting point on the other side of the sun.

When it arrived back at its starting point the Earth would not be there as the elliptical orbit of the space craft would be longer or shorter then the Earth?s year depending on whether the spacecraft was inside or outside of the Earth?s orbit.

When to go

This brings us to the concept of the Launch Window; this is the time when the two planets will be at the correct position in their orbits to use the Hohmann Transfer Orbit. As all the planets have a different length of year and speed of orbital velocity, it is obvious that only at certain times can a spacecraft be launched into space to guarantee it will intersect the destination orbit at the exact point in time when the target is there as well. With Mars this is about every 25 months depending on whether Mars is near perihelion or aphelion. With Venus this is about every 520 days and Jupiter about every 13 months. The Earth?s velocity around the sun is 29.8 km/s, varying by only +/- 0.5 km/s due to eccentricity of the orbit. What this means is that all spacecraft can either add too or reduce this velocity to get to different orbits.

The Ulysses mission launched in October 1990, achieved a departure velocity of 11.4 km/s, the highest ever achieved by a space probe. This gave it a combined speed of 41.2 km/s relative to the sun, because it was fired along the direction of the Earth?s orbit. This is a high enough speed to send it past the orbit of Uranus, and out to 22 AU if it wasn?t heading for Jupiter. On the other hand, if it had been fired in the opposite direction, back along the path of the earth?s orbit, it would have been travelling at 18.4 km/s. relative to the sun. This is lower then the speed needed to stay in orbit around the sun at Earth?s distance and so it would have dropped in towards the sun, going to 0.23 AU, about half the distance of Mercury from the sun. Both of these orbits would then return the craft to its starting position, the outer one many years later.
Only once every 175 years

But how can you get to Neptune if the fastest thing ever flown can only just make it out to just past the orbit of Uranus? The answer is by Gravity Assist. Voyager 2 had a Dv of 36 km/s when it left Earth, far short of the Dv of 50 km/s it would have needed to get to Neptune from Earth without gravity assistance. But if you launch a satellite into space round a planet or moon with enough velocity, then it will stay in the orbit it was placed in if it is not subject to any other forces such as atmospheric drag or the gravitational pull of another large body. This means that at any position in an elliptical orbit, the speed of the satellite will be the same on the in journey as on the out at identical distances from the moon or planet. If the satellite is orbiting in an even ellipse it can?t be otherwise. This is the position that the spacecraft Hipparcos is now in after its motor failed to fire to put it in a geostationary orbit.ary to attempt the interplanetary billiards of today. The first was Mariner 10 launched in November 1973, which flew on to Mercury by way of Venus. The first multi-planet mission to use the gravity of one planet to get to another. All single journey planetary probes use what?s called a Hohmann Transfer Orbit to arrive at the target. This was named after the German engineer Walter Hohmann, who in 1925 hit on the idea of using an elliptical orbit to travel from one planet to another.

Its orbit is 36,000 km at apogee but only 500 km at perigee, with a period of about 10 hours. So how can you increase speed? Back in 1965 a graduate of Caltech working at the Jet Propulsion Laboratory in Pasadena, named Gary Flandro, came up with the answer while working under Elliot Cutting. Cutting suggested that he examine the possibility of using the gravity of one planet to sling a spacecraft on to another. So the concept of sling-shot? or gravity assist was born. Astronomers had known for a long time that if a comet strayed to close to Jupiter or Saturn it would be deflected into another orbit or even thrown out of the solar system at a high speed by the transfer of kinetic energy from the planet to the comet. But back in the mid sixties most of the engineers at JPL had doubt about the possibility of using gravity to boost the speed of a spacecraft. It was thought that the gain on the approach would balance the loss on the outward flight so that the net gain would be zero, as in a normal elliptical orbit.

Flandro recalled in 1989, "My gravity-boost idea wasn?t new, astronomers had known for a long time that a comet speeds up when it passes close to a planet. I was the first to apply the same idea to a spaceship.* Luckily the idea was just in time to catch all the large outer planets in just the right position and the Grand Tour was on. The next time they will be in the correct position will be in 2150! Voyager II has given us the only close-up views we will have of Uranus and Neptune this century.

Speed for nothing?

So how does gravity help us to fly to the outer planets? To use gravity assist to speed up a spacecraft, it must approach the intended planet from inside and behind the planets direction of travel in its orbit and aim to go behind the planet as seen from the sun. As the spacecraft approaches it will start to fall into the gravity well of the planet. Because the planet is moving along its orbit in roughly the same direction, the craft will be dragged along as it nears the planet picking up speed. The spacecraft will be travelling faster than the planets escape velocity at this distance and so will add to its speed without any danger of being captured. As both the planet and the spacecraft are travelling at different speeds and angles in respect to the sun, the gravity of the planet can be used to either slow down or speed up the craft.

For instance if the craft goes behind the planet in respect to the sun it will speed up by an amount depending on how close it goes to the planet. If the craft goes in front of the planet it will be slowed and could even go into orbit. The angle at which it approaches the path of the planet?s orbit in respect of the sun and its miss-vector? or distance it will miss the planet by will govern the swing-by, with a small miss? driving the probe deeper into the planets gravity well; resulting in a larger deflection angle adding greater speed. This will bend the spacecraft?s path into a hyperbolic curve, so its path is now changed to a shallower angle to the sun (if it has gone behind the planet). It is because the speed of the craft is greater then any orbital speed of any satellite and it is approaching at a steeper angle to the planet?s orbital path then it leaves in respect to the sun that add?s to its speed. This is why it increases in speed, because it is not pulling away from the sun as fast as before the encounter.

At the Saturn encounter Voyager 2 reached its highest speed on its long journey to the stars. Of cause a space craft must not fly too close to planets like Jupiter because of its strong magnetic fields and radiation belts unless its been especially hardened and protected. But as the spacecraft gains kinetic energy, so the planet loses some of its orbital momentum by the same amount of energy. The tiny space craft can gain much from the giant planets in speed and energy. But the books must be balanced and the planet will be slowed down in its rate of spin and also loses some orbital momentum. In the case of Jupiter, this was about a billionth of a second longer to its year, nothing to loose much sleep over! This change in the angle of travel of the spacecraft, in relation to the sun, can results in enormous amounts of energy being transferred to the craft, resulting in greatly increased speed.

The trick of cause, is to know the mass of the planet, its diameter, height of its atmosphere, also are there any of its own satellites or rings in the way, then hit the spot aimed for at the right speed and distance to bend the spacecraft?s direction to exactly the correct requirement needed. On the Voyager small adjustments can be achieved by the spacecrafts Attitude and Articulation Control Subsystem (AACS) control jets. There are 12 tiny thrusters to control the attitude and another 4 are used to correct the trajectory of the craft to that computed on Earth both before and after an encounter with a planet. This is now done to an amazing accuracy with probes arriving on target only seconds out after years in space, light hours from earth. Gravity Assist has given us the means to explore the whole of the solar system at much lower cost and much sooner than anyone would have dreamed of a few decades ago. Both of the two latest probes, the Ulysses Out-of-Ecliptic mission over the sun?s poles and the Gallileo mission to Jupiter and its moons make use of the technique of gravity assist. Indeed neither of the missions would have flown by using just the power of today?s rockets. I am sure we have not seen the last of interplanetary billiards?.