Space Flight Basics: Planetary Orbits (2023)

By the end of this chapter, you will be able to describe in general terms the use of Hohmann transfer orbits and how spacecraft use them for interplanetary travel. You will be able to describe the general concept of angular momentum exchange between planets and spacecraft to achieve gravity-assisted trajectories.

WWhen traveling between planets, it is best to minimize the mass of propellant required by spacecraft and launch vehicles. That way, such flights are possible with current launch capabilities and not too expensive. The amount of propellant required depends largely on the route you choose. Therefore, orbits that by their nature require the least amount of propellant are of great interest.

Hohmann transfer orbit

Launching a spacecraft from Earth to an exoplanet like Mars using as little propellant as possible starts with considering that the spacecraft is already in orbit around the sun while it's on the launch pad. The existing solar orbit must be adjusted to take the spacecraft to Mars: the perihelion (closest distance from the sun) of the desired orbit will be at the distance of Earth's orbit, and the aphelion (furthest distance from the sun) will be at the distance of Earth's orbit distance from the orbit of Mars. this is calledempathy homantrack. The portion of a spacecraft's orbit around the sun from Earth to Mars is called an orbit.trajectory.

We know from the previous chapter that the mission is to increase the apogee (aphelion) of the spacecraft's current orbit around the sun. Remember Chapter 3...

The apoapsis altitude of the spacecraft can be increased by increasing the energy of the spacecraft at the periapsis.

Well, the ship is already at periapsis. So the spacecraft lifts off from the launch pad, rises above the Earth's atmosphere, and is accelerated using rockets.Along the direction of the earth's orbit around the sunAt some point, the added energy at periapsis (perihelion) will cause its new orbit to have an aphelion equal to that of Mars. acceleration isTangentialto the existing track. How much power should be added? look atSpace and Rocket Technologywebsite.

After briefly accelerating away from Earth, the spacecraft has reached its new orbit and will cruise along the coast for the remainder of its journey. Chapter 14 covers the startup phase in detail.

From Earth to Mars via Minimum Energy Orbit

Space Flight Basics: Planetary Orbits (1)

Getting to Mars, not just its orbit, requires a spacecraft to insert itself into its interplanetary orbit at the right time to reach Mars orbit while Mars is there. This task can be likened to throwing a dart at a moving target. You have to guide the target point to the correct position to hit the target. Approximately every 25 months there is an opportunity to launch a spacecraft into a minimal energy transfer orbit around Mars.

To be captured in orbit around Mars, a spacecraft would have to be fired using retrograde rockets or otherwise decelerated relative to Mars. To land on Mars from orbit like Viking did, the spacecraft must use retrograde ignition to decelerate further to the point where the nadir of its Martian orbit intersects the Martian surface. Since Mars has an atmosphere, final deceleration could also be achieved by direct aerobraking and/or parachutes in interplanetary orbit and/or further retrograde activation.

Internal restrictions

To launch a spacecraft from Earth to an inner planet like Venus using less propellant, its existing sun orbit (as shown on the launch pad) would have to be adjusted to bring it to Venus. That is to say, the aphelion of the spacecraft is already at the distance of the earth's orbit, and the perihelion will be at the orbit of Venus.

The task this time isreduce periapsisThe spacecraft's current sun orbit (perihelion). Remember Chapter 3...

The periapsis altitude of a spacecraft can be reduced by reducing the energy of the spacecraft at apoapsis..

To achieve this, the spacecraft lifts off the launch pad, rises above the Earth's atmosphere, and is accelerated using rockets.the oppositeThe direction in which the Earth orbits the Sun, soreduce its orbital energyAnd in apogee (aphelion), the perihelion of its new orbit will be equal to the distance of the orbit of Venus. The acceleration is again tangential to the existing orbit. How much power should be added? look atSpace and Rocket Technologywebsite.

Of course, the spacecraft will continue to travel in the same direction that the Earth orbits the sun, but now at a slower speed. Getting to Venus, not just its orbit, again requires the spacecraft to be inserted into its interplanetary orbit at the right time so that it can reach Venus' orbit while Venus is there. Venus launch opportunities occur approximately every 19 months.

Earth reaches Venus via minimum energy orbit

Space Flight Basics: Planetary Orbits (2)

Type I and Type II trajectories

If the interplanetary trajectory takes the spacecraft within 180 degrees of orbiting the sun, it is called a Type-I trajectory. If the path takes you 180 degrees or more around the sun, it's called Type II.

gravity assisted trajectory

Chapter 1 states that the planets retain most of the angular momentum of the solar system. This momentum can be used to accelerate a spacecraft on a so-called "gravity-assisted" trajectory. It is often said in the media that spacecraft such as Voyager, Galileo, and Cassini use the gravity of the planet to launch it further into space when they fly by the planet. How does this work? Use gravity to take advantage of Earth's enormous angular momentum.

In a gravity-assisted trajectory, angular momentum is transferred from a planet orbiting the sun to a spacecraft that approaches behind the planet as it orbits the sun.

use: Experimenters and educators may be interested inGravity Assisted Machinery Simulator, a device that you can build and manipulate to gain an intuitive understanding of how gravity-assisted trajectories work. Linked pages include "Primer"With gravity assist.Space Flight Basics: Planetary Orbits (3)Consider Voyager 2, which toured the planet Jupiter. The spacecraft was launched into a Homan II transfer orbit at Jupiter. If Jupiter is not there when the spacecraft arrives, the spacecraft will recede toward the sun and remain in an elliptical orbit as long as there are no other forces acting on it. The perihelion is about 5 AU from Jupiter, and the aphelion is about 1 AU from Jupiter.

However, Voyager's arrival at Jupiter was carefully timed so that it passed in Jupiter's orbit around the sun. As the spacecraft enters Jupiter's gravitational influence, it falls toward Jupiter, increasing its velocity to a maximum during its closest approach to Jupiter. Since all mass in the universe is attracted to each other, Jupiter greatly accelerates the spacecraft,and spaceships pulled from jupiter, causing the giant planet to lose some of its orbital energy.

The spacecraft passes Jupiter because Voyager's speed is greater than Jupiter's escape velocity, and of course it slows down again relative to Jupiter as it leaves the massive gravitational field. The velocity component of its exit velocity relative to Jupiter is reduced to be the same as its entry leg.

But relative to the sun, it never slowed down to the speed it initially approached Jupiter. It increases the angular momentum around Jupiter and steals it from Jupiter. Jupiter's gravity ties the spacecraft to the planet's ample reserves of angular momentum. This technique was repeated on Saturn and Uranus.

Voyager 2 Gravity Assisted Transmission

Voyager 2 is moving away from Earth at about 36 km/s relative to the sun. As it moves away, it loses most of the initial velocity provided by the launch vehicle. As it approaches Jupiter, its velocity is increased by the planet's gravity, and the spacecraft's velocity exceeds the escape velocity of the solar system. Voyager left Jupiter at a faster speed relative to the Sun than it did when it arrived. The same goes for Saturn and Uranus. The Neptune flyby was designed to have Voyager fly closer to Neptune's moon Triton, rather than go faster. Diagram courtesy of Steve Matousek, JPL.Space Flight Basics: Planetary Orbits (4)

The same goes for the acceleration of a baseball when it's hit by a bat: angular momentum is transferred from the bat to the slower-moving ball. The bat decelerates in a "track" above the hitter, greatly accelerating the ball. The bat is connected to the ball not through gravity in the back like a spaceship, but through direct mechanical force (electricity, if you will, on the molecular scale, if you will) at the front of the bat as it moves words) the batter, converting the angular momentum of the bat into the high velocity of the ball.

(Of course, to make an analogy, planets have attraction and bats have repulsion, so the voyager must approach Jupiter from the opposite direction of Jupiter's path, and the ball approaches the bat from the direction of the bat's trajectory).

Space Flight Basics: Planetary Orbits (5)The vector diagram on the left shows the velocity of the spacecraft relative to Jupiter during a gravity-assisted flyby. Relative to Jupiter, the spacecraft decelerates to the same speed it exited as it entered, even though its orientation has changed. Also note that the speed temporarily increases as you approach the maximum zoom.

When the same situation is viewed relative to the Sun in the lower and right panels, we see that Jupiter's orbital velocity relative to the Sun adds to the velocity of the spacecraft, the spacecraft does not lose this component as it departs. Instead, the Earth itself would lose energy. The loss of a massive planet is too small to measure, but the gain of a tiny spacecraft could be very large. Imagine a mosquito flying into the tracks of a speeding freight train.

Space Flight Basics: Planetary Orbits (6)

Gravity assist can also be used to decelerate a spacecraft to fly in front of an object in its orbit, giving some of the spacecraft's angular momentum to the object. When the Galileo spacecraft arrived at Jupiter, it was close to Jupiter’s satellite Io in orbit, and Galileo lost energy relative to Jupiter, which helped it achieve Jupiter’s orbit and reduced the propellant required for orbit by 90 kilograms.

Michael Minovitch pioneered gravity-assisted technology in the early 1960s while a graduate student at UCLA, working summers at the Jet Propulsion Laboratory. Before the adoption of gravity assist technology, it was thought that traveling to the outer solar system could only be achieved by developing extremely powerful launch vehicles that used nuclear reactors to generate enormous thrust, basically blowing up the Hohmann transfer device even more every time.

An interesting fact to consider is that although a spaceship can double its speed with the help of gravity, it feels no acceleration at all. If you were on Voyager 2, you would just feel the constant sensation of falling as you more than double your speed with the help of the gravity of the outer solar system. There is no acceleration. This is due to the balance compensation of the angular momentum mediated by the gravity of the planet and the spacecraft.

Enter the ion engine

All of the above discussion of interplanetary orbits is based on the current use of chemical rocket systems, where a single launch vehicle provides the propellant power for nearly all spacecraft. A few times a year, the spacecraft can fire short bursts from its chemical rocket boosters to make small adjustments to trajectory. Otherwise, the spaceship is in free fall and is heading towards its destination. Gravity assist can also provide short periods of time when a spacecraft's trajectory changes.

But ion propulsion, as demonstrated on the Deep Space 1 interplanetary mission and employed on the Dawn asteroid science mission, works differently. Electric propulsion is not a burst of relatively strong thrust for a short period of time, but a smoother thrust that is used for months or even years. It is an order of magnitude more efficient than chemical propulsion for those missions sufficient to use the technology. The ion engine will be discussed laterpropulsionin Chapter 11.

Click the image above to learn more about Deep Space One. Japan Aerospace Exploration Agency's asteroid probe.HayabusaIt also used ion engines.

Even ion-powered spacecraft must be launched with chemical rockets, but because of their efficiency, they can be smaller and require less powerful (and cheaper) launch vehicles. Initially, then, the ion-powered vehicle's trajectory might resemble a Hohmann transfer orbit. But for long periods of continuous operation of the motor, the trajectory will no longer be a purely ballistic arc.

further research

Select the "Links" section below for additional references, including math tutorials and sample problems.
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