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These schedules were made from a Microsoft Excel spreadsheet. The spreadsheet includes Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune. Also included are trip times, delta V from user specified parking orbits, and altitudes of possible parking orbits such as GEO, EML1 for the earth, altitudes of Mars moons Phobos. While a bi-elliptic transfer has a small parameter window where it's strictly superior to a Hohmann Transfer in terms of delta V for a planar transfer between circular orbits, the savings is fairly small, and a bi-elliptic transfer is a far greater aid when used in combination with certain other maneuvers.

In orbital mechanics, the Hohmann transfer orbit (/ˈhoʊmən/) is an elliptical orbit used to transfer between two circular orbits of different radii around the same body in the same plane. The Hohmann transfer orbit uses the lowest possible amount of energy in traveling between these orbits.^[1][2]

The term is also used to refer to transfer orbits between different bodies (planets, moons etc.). They are also often used for these situations, but low-energy transfers which take advantage of the gravity wells of both planets can be more efficient, and also may able to use lighter, less powerful engines.^[3][4][5]

A Hohmann transfer requires that the starting and destination points be at particular locations in their orbits relative to each other. Space missions using a Hohmann transfer must wait for this required alignment to occur, which opens a so-called launch window. For a space mission between Earth and Mars, for example, these launch windows occur every 26 months. A Hohmann transfer orbit also determines a fixed time required to travel between the starting and destination points; for an Earth-Mars journey this travel time is about 9 months.

The orbital maneuver to perform the Hohmann transfer uses two engine impulses, one to move a spacecraft onto the transfer orbit and a second to move off it. This maneuver was named after Walter Hohmann, the German scientist who published a description of it in his 1925 book Die Erreichbarkeit der Himmelskörper (The Attainability of Celestial Bodies).^[6] Hohmann was influenced in part by the German science fiction author Kurd Lasswitz and his 1897 book Two Planets.

• 1Explanation
• 6Hohmann transfer versus low thrust orbits

Explanation

The diagram shows a Hohmann transfer orbit to bring a spacecraft from a lower circular orbit into a higher one. It is one half of an elliptic orbit that touches both the lower circular orbit the spacecraft wishes to leave (green and labeled 1 on diagram) and the higher circular orbit that it wishes to reach (red and labeled 3 on diagram). The transfer (yellow and labeled 2 on diagram) is initiated by firing the spacecraft's engine to accelerate it so that it will follow the elliptical orbit. This adds energy to the spacecraft's orbit. When the spacecraft has reached its destination orbit, its orbital speed (and hence its orbital energy) must be increased again to change the elliptic orbit to the larger circular one.

Due to the reversibility of orbits, Hohmann transfer orbits also work to bring a spacecraft from a higher orbit into a lower one; in this case, the spacecraft's engine is fired in the opposite direction to its current path, slowing the spacecraft and causing it to drop into the lower-energy elliptical transfer orbit. The engine is then fired again at the lower distance to slow the spacecraft into the lower circular orbit.

The Hohmann transfer orbit is based on two instantaneous velocity changes. Extra fuel is required to compensate for the fact that the bursts take time; this is minimized by using high-thrust engines to minimize the duration of the bursts. For transfers in Earth orbit, the two burns are labelled the perigee burn and the apogee burn (or 'apogee kick^[7]); more generally, they are labelled periapsis and apoapsis burns. Alternately, the second burn to circularize the orbit may be referred to as a circularization burn.

Type I and Type II

An ideal Hohmann transfer orbit transfers between two circular orbits in the same plane and traverses exactly 180° around the primary. In the real world, the destination orbit may not be circular, and may not be coplanar with the initial orbit. Real world transfer orbits may traverse slightly more, or slightly less, than 180° around the primary. An orbit which traverses less than 180° around the primary is called a 'Type I' Hohmann transfer, while an orbit which traverses more than 180° is called a 'Type II' Hohmann transfer.^[8][9]

Calculation

For a small body orbiting another much larger body, such as a satellite orbiting Earth, the total energy of the smaller body is the sum of its kinetic energy and potential energy, and this total energy also equals half the potential at the average distance (the semi-major axis):

Solving this equation for velocity results in the vis-viva equation,

where:

• is the speed of an orbiting body,
• is the standard gravitational parameter of the primary body, assuming is not significantly bigger than (which makes Failed to parse (unknown function 'll'): v_M ll v

),

• is the distance of the orbiting body from the primary focus,
• is the semi-major axis of the body's orbit.

Therefore, the delta-v required for the Hohmann transfer can be computed as follows, under the assumption of instantaneous impulses:

to enter the elliptical orbit at from the circular orbit

to leave the elliptical orbit at to the circular orbit, where and are respectively the radii of the departure and arrival circular orbits; the smaller (greater) of and corresponds to the periapsis distance (apoapsis distance) of the Hohmann elliptical transfer orbit. Typically, is given in units of m³/s², as such be sure to use meters, not kilometers, for and . The total is then:

Failed to parse (unknown function 'text'): Delta v_text{total} = Delta v_1 + Delta v_2.

Whether moving into a higher or lower orbit, by Kepler's third law, the time taken to transfer between the orbits is

Failed to parse (unknown function 'text'): t_text{H} = sqrt{frac{pi^2 a_text{H}^3}{mu}} = pi sqrt{frac {(r_1 + r_2)^3}{8mu}}

(one half of the orbital period for the whole ellipse), where Failed to parse (unknown function 'text'): a_text{H}

In application to traveling from one celestial body to another it is crucial to start maneuver at the time when the two bodies are properly aligned. Considering the target angular velocity being

angular alignment α (in radians) at the time of start between the source object and the target object shall be

Failed to parse (unknown function 'text'): alpha = pi - omega_2 t_text{H} = pileft(1 - frac{1}{2sqrt{2}}sqrt{left(frac{r_1}{r_2} + 1right)^3}right).

Example

Consider a geostationary transfer orbit, beginning at r₁ = 6,678 km (altitude 300 km) and ending in a geostationary orbit with r₂ = 42,164 km (altitude 35,786 km).

In the smaller circular orbit the speed is 7.73 km/s; in the larger one, 3.07 km/s. In the elliptical orbit in between the speed varies from 10.15 km/s at the perigee to 1.61 km/s at the apogee.

The Δv for the two burns are thus 10.15 − 7.73 = 2.42 and 3.07 − 1.61 = 1.46 km/s, together 3.88 km/s.

This is greater than the Δv required for an escape orbit: 10.93 − 7.73 = 3.20 km/s. Applying a Δv at the Low Earth orbit (LEO) of only 0.78 km/s more (3.20−2.42) would give the rocket the escape speed, which is less than the Δv of 1.46 km/s required to circularize the geosynchronous orbit. This illustrates the Oberth effect that at large speeds the same Δv provides more specific orbital energy, and energy increase is maximized if one spends the Δv as quickly as possible, rather than spending some, being decelerated by gravity, and then spending some more to overcome the deceleration (of course, the objective of a Hohmann transfer orbit is different).

Worst case, maximum delta-v

As the example above demonstrates, the Δv required to perform a Hohmann transfer between two circular orbits is not the greatest when the destination radius is infinite. (Escape speed is √2 times orbital speed, so the Δv required to escape is √2 − 1 (41.4%) of the orbital speed.) The Δv required is greatest (53.0% of smaller orbital speed) when the radius of the larger orbit is 15.5817... times that of the smaller orbit.^[10] This number is the positive root of x³ − 15 x² − 9 x − 1 = 0, which is . For higher orbit ratios the Δv required for the second burn decreases faster than the first increases.

Application to interplanetary travel

When used to move a spacecraft from orbiting one planet to orbiting another, the situation becomes somewhat more complex, but much less delta-v is required, due to the Oberth effect, than the sum of the delta-v required to escape the first planet plus the delta-v required for a Hohmann transfer to the second planet.

For example, consider a spacecraft travelling from the Earth to Mars. At the beginning of its journey, the spacecraft will already have a certain velocity and kinetic energy associated with its orbit around Earth. During the burn the rocket engine applies its delta-v, but the kinetic energy increases as a square law, until it is sufficient to escape the planet's gravitational potential, and then burns more so as to gain enough energy to get into the Hohmann transfer orbit (around the Sun). Because the rocket engine is able to make use of the initial kinetic energy of the propellant, far less delta-v is required over and above that needed to reach escape velocity, and the optimum situation is when the transfer burn is made at minimum altitude (low periapsis) above the planet. The delta-v needed is only 3.6 km/s, only about 0.4 km/s more than needed to escape Earth, even though this results in the spacecraft going 2.9 km/s faster than the Earth as it heads off for Mars (see table below).

At the other end, the spacecraft will need a certain velocity to orbit Mars, which will actually be less than the velocity needed to continue orbiting the Sun in the transfer orbit, let alone attempting to orbit the Sun in a Mars-like orbit. Therefore, the spacecraft will have to decelerate in order for the gravity of Mars to capture it. This capture burn should optimally be done at low altitude to also make best use of Oberth effect. Therefore, relatively small amounts of thrust at either end of the trip are needed to arrange the transfer compared to the free space situation.

However, with any Hohmann transfer, the alignment of the two planets in their orbits is crucial – the destination planet and the spacecraft must arrive at the same point in their respective orbits around the Sun at the same time. This requirement for alignment gives rise to the concept of launch windows.

The term lunar transfer orbit (LTO) is used for the Moon.

It is possible to apply the formula given above to calculate the Δv in km/s needed to enter a Hohmann transfer orbit to arrive at various destinations from Earth (assuming circular orbits for the planets). In this table, the column labeled 'Δv to enter Hohmann orbit from Earth's orbit' gives the change from Earth's velocity to the velocity needed to get on a Hohmann ellipse whose other end will be at the desired distance from the Sun. The column labeled 'v exiting LEO' gives the velocity needed (in a non-rotating frame of reference centered on the earth) when 300 km above the Earth's surface. This is obtained by adding to the specific kinetic energy the square of the speed (7.73 km/s) of this low Earth orbit (that is, the depth of Earth's gravity well at this LEO). The column 'Δv from LEO' is simply the previous speed minus 7.73 km/s.

Note that in most cases, Δv from LEO is less than the Δv to enter Hohmann orbit from Earth's orbit.

To get to the Sun, it is actually not necessary to use a Δv of 24 km/s. One can use 8.8 km/s to go very far away from the Sun, then use a negligible Δv to bring the angular momentum to zero, and then fall into the Sun. This can be considered a sequence of two Hohmann transfers, one up and one down. Also, the table does not give the values that would apply when using the Moon for a gravity assist. There are also possibilities of using one planet, like Venus which is the easiest to get to, to assist getting to other planets or the Sun.

Hohmann transfer versus low thrust orbits

Low-thrust transfer

Low-thrust engines can perform an approximation of a Hohmann transfer orbit, by creating a gradual enlargement of the initial circular orbit through carefully timed engine firings. This requires a change in velocity (delta-v) that is greater than the two-impulse transfer orbit^[11] and takes longer to complete.

Engines such as ion thrusters are more difficult to analyze with the delta-v model. These engines offer a very low thrust and at the same time, much higher delta-v budget, much higher specific impulse, lower mass of fuel and engine. A 2-burn Hohmann transfer maneuver would be impractical with such a low thrust; the maneuver mainly optimizes the use of fuel, but in this situation there is relatively plenty of it.

If only low-thrust maneuvers are planned on a mission, then continuously firing a low-thrust, but very high-efficiency engine might generate a higher delta-v and at the same time use less propellant than a rocket engine.

Going from one circular orbit to another by gradually changing the radius simply requires the same delta-v as the difference between the two speeds.^[11] Such maneuver requires more delta-v than a 2-burn Hohmann transfer maneuver, but does so with continuous low thrust rather than the short applications of high thrust.

The amount of propellant mass used measures the efficiency of the maneuver plus the hardware employed for it. The total delta-v used measures the efficiency of the maneuver only. For electric propulsion systems, which tend to be low-thrust, the high efficiency of the propulsive system usually compensates for the higher delta-V compared to the more efficient Hohmann maneuver.

Transfer orbit using electrical propulsion or low-thrust engines optimize the transfer time to reach the final orbit and not the delta-v as in the Hohmann transfer orbit. For geostationary orbit, the initial orbit is set to be supersynchronous and by thrusting continuously in the direction of the velocity at apogee, the transfer orbit transforms to a circular geosynchronous one. This method however takes much longer to achieve due to the low thrust injected into the orbit ^[12]

Interplanetary Transport Network

In 1997, a set of orbits known as the Interplanetary Transport Network (ITN) was published, providing even lower propulsive delta-v (though much slower and longer) paths between different orbits than Hohmann transfer orbits.^[13] The Interplanetary Transport Network is different in nature than Hohmann transfers because Hohmann transfers assume only one large body whereas the Interplanetary Transport Network does not. The Interplanetary Transport Network is able to achieve the use of less propulsive delta-v by employing gravity assist from the planets.^{[citation needed]}

See also

References

1. ↑'Hohmann transfer orbit diagram'. www.planetary.org. Retrieved 2018-03-27.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
2. ↑'Homann Transfers'. jwilson.coe.uga.edu. Retrieved 2018-03-27.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
3. ↑Williams, Matt (2014-12-26). 'Making the Trip to Mars Cheaper and Easier: The Case for Ballistic Capture'. Universe Today. Retrieved 2019-07-29.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
4. ↑Hadhazy, Adam. 'A New Way to Reach Mars Safely, Anytime and on the Cheap'. Scientific American. Retrieved 2019-07-29.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
5. ↑'An Introduction to Beresheet and Its Trajectory to the Moon'. Gereshes. 2019-04-08. Retrieved 2019-07-29.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
6. ↑Walter Hohmann, The Attainability of Heavenly Bodies (Washington: NASA Technical Translation F-44, 1960) Internet Archive.
7. ↑Jonathan McDowell, 'Kick In the Apogee: 40 years of upper stage applications for solid rocket motors, 1957-1997', 33rd AIAA Joint Propulsion Conference, July 4, 1997. abstract. Retrieved 18 July 2017.
8. ↑NASA, Basics of Space Flight, Section 1, Chapter 4, 'Trajectories'. Retrieved 26 July 2017. Also available spaceodyssey.dmns.org.
9. ↑Tyson Sparks, Trajectories to Mars, Colorado Center for Astrodynamics Research, 12/14/2012. Retrieved 25 July 2017.
10. ↑Vallado, David Anthony (2001). Fundamentals of Astrodynamics and Applications. Springer. p. 317. ISBN0-7923-6903-3.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
11. ↑ ^11.011.1MIT, 16.522: Space Propulsion, Session 6, 'Analytical Approximations for Low Thrust Maneuvers', Spring 2015 (retrieved 26 July 2017)
12. ↑Spitzer, Arnon (1997). Optimal Transfer Orbit Trajectory using Electric Propulsion. USPTO.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
13. ↑Lo, M. W.; Ross, S. D. (1997). 'Surfing the Solar System: Invariant Manifolds and the Dynamics of the Solar System'. Technical Report. IOM. JPL. pp. 2–4. 312/97.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>

Sources

• Walter Hohmann (1925). Die Erreichbarkeit der Himmelskörper. Verlag Oldenbourg in München. ISBN3-486-23106-5.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
• Thornton, Stephen T.; Marion, Jerry B. (2003). Classical Dynamics of Particles and Systems (5th ed.). Brooks Cole. ISBN0-534-40896-6.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
• Bate, R.R., Mueller, D.D., White, J.E., (1971). Fundamentals of Astrodynamics. Dover Publications, New York. ISBN978-0-486-60061-1.CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link)<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
• Vallado, D. A. (2001). Fundamentals of Astrodynamics and Applications, 2nd Edition. Springer. ISBN978-0-7923-6903-5.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
• Battin, R.H. (1999). An Introduction to the Mathematics and Methods of Astrodynamics. American Institute of Aeronautics & Ast, Washington, DC. ISBN978-1-56347-342-5.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>

External links

• 'Orbital Mechanics'. Rocket and Space Technology. Robert A. Braeunig.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>
• '4. Interplanetary Trajectories'. Basics of Spaceflight. JPL: NASA.<templatestyles src='Module:Citation/CS1/styles.css'></templatestyles>

Hohmann transfers are not just for Earth orbiting spacecraft - they can also be used for interplanetary transfers. Calculating an interplanetary Hohmann transfer is very similar to calculating a Hohmann transfer for an Earth orbiting spacecraft. The only difference we have is that we have one more thing to calculate: The necessary phase angle for the two planets.

In this section, we will cover:

1.Calculating an Interplanetary Hohmann Transfer

2.Modeling an Interplanetary Hohmann Transfer

Calculating an Interplanetary Hohmann Transfer

Calculating the Δv required for an interplanetary Hohmann transfer is exactly like how we did it in the Hohmann Transfer tutorial. Our 'parking' orbit SMA is actually our departure planet's SMA about the Sun. Our 'target' orbit SMA is the arrival planet's SMA about the Sun.

However, like the Hohmann Transfer tutorial, we must assume that the two planets are both circular and co-planar. Since this definitely isn't the case with any of our solar system's planets in the real world, these calculations only present a conceptual idea of the amount of Δv required for an interplanetary transfer.

One more thing we need to do in addition to the Δv calculations is calculating the necessary phase angle between the planets. The planets need to be at a certain position relative to each other so that when the interplanetary spacecraft reaches the other side of the Hohmann transfer, the arrival planet is there as well. The phase angle 'Φ' is shown here:

Phase Angle Diagram

You can calculate the phase angle using the following formula:

For this formula, you need the period of the Hohmann transfer, and the angular velocity of the target planet. What we are essentially doing is finding how many degrees the target planet will travel during the time of the Hohmann transfer, which is half of the Hohmann transfer period. To calculate the period of the Hohmann transfer and the angular velocity of the target orbit, we need the following formulas:

It is important to note that the formula for the angular velocity is only true when dealing with a circular orbit. Because our interplanetary Hohmann transfer assumes a perfectly circular orbit for both planets, we can use this formula.

Modeling an Interplanetary Hohmann Transfer

When calculating Hohmann transfers, we must first assume that both orbits are circular. In the real world, the orbits of Earth and Mars are not circular. So to model an interplanetary Hohmann transfer, we will be using Spacecraft in heliocentric circular orbits with the same SMA as the planets they are representing. Because basic interplanetary Hohmann transfers only rely on the gravity of the central body, we do not need to model the departure and arrival planets' gravities in our problem.

•Create a new Mission Plan and save it as 'InterplanetaryHohmann.MissionPlan'

Adding in Spacecraft

•Create a Spacecraft with the following elements:

oCentral Body: 'Sun'

oReference Frame: 'Mean of J2000 Earth Ecliptic'

oA: 149,597,871 km (This is 1 AU)

oE: 0

oI: 0 deg

oRAAN: 0 deg

oW: 0 deg

oTA: 0 deg

NOTE: Remember that you need to change the Element Type to 'Keplerian' to access these elements

•Rename the Spacecraft to 'InterplanetarySC'

•Click on the 'Force Model' on the left-hand side

•Uncheck the 'Earth' and 'Moon' boxes

•Click on 'Propagator' on the left-hand side

•Change the step size to 1 day

•Click 'Ok' to close the editor

•Clone 'InterplanetarySC'

•Rename the clone to 'MarsSC' (this Spacecraft will represent Mars)

•Change A to 227,987,155 km (This is 1.524 AU)

•Click on 'Visualization' on the left-hand side

•Change the tail color to green

•Click 'Ok' to close the editor

Adding in the ViewWindow

•Create a ViewWindow through the Object Browser

•Double click on 'ViewWindow1' to open the editor

•Check each Spacecraft in the 'Available Objects'

•Click on 'Spacecraft' in the 'Available Objects' to select both Spacecraft, then check 'Show Name'

•Change the history mode to 'Unlimited' (for both Spacecraft)

Since we won't be needing to show the real Earth and the real Mars, let's hide them from the ViewWindow.

•Click on the 'Solar System' section on the left-hand side

•Click on 'Earth'

•Uncheck 'Show Object' in 'Object Options'

•Click on 'Mars'

•Uncheck 'Show Object' in 'Object Options'

Solar System Properties in the ViewWindow Editor

Hohmann Transfer Moon

Now we can continue with the rest of the settings for the ViewWindow.

•Click on 'Viewpoints' on the left-hand side

•Change the reference frame to 'Inertial'

•Change the Source to 'Sun'

•Click 'Copy to Target/Tail Ref.'

•In 'Source Offsets', change the radius to 500,000,000 km

•Click 'Ok' to close the editor

Adding an ImpulsiveBurn

•Create an ImpulsiveBurn object through the Object Browser

•Double-click on 'ImpulsiveBurn1' to open the editor

•Change the attitude system to 'VNB'

Hohmann Transfer Ksp

•Click 'Ok' to close the editor

Building the Mission Sequence

Hohmann Transfer Orbits

To start, we'll propagate the entire solar system for a while so we can see each planet's orbit better.

•Drag and drop a while loop into the Mission Sequence

•Change the while loop argument to '(InterplanetarySC.ElapsedTime < TIMESPAN(500 days))'

•Drag and drop a FreeForm script editor inside that while loop

•Open the script editor and rename it to 'Step and Update'

In this script, we will step both Spacecraft with an epoch sync, and update the ViewWindow. To do this, we write:

Let's go back to the Mission Sequence.

•Drag and drop a FreeForm script editor after the while loop

•Open the script editor and rename it to 'Calculate Hohmann Delta V'

In this FreeForm script editor, we will calculate the necessary Δv needed and assign it to the ImpulsiveBurn object we created. To do this, we write:

Next, we need to calculate the phase angle. Let's add another FreeForm script editor to the Mission Sequence.

•Drag and drop a FreeForm script editor after the 'Calculate Hohmann Delta V' FreeForm

•Open the script editor and rename it to 'Calculate Phase Angle'

In this script, we need to calculate the necessary phase angle for the Hohmann transfer. To do this, we can use the formulas given in the Calculating an Interplanetary Hohmann Transfer section. We will need to write:

Now that we've calculated the phase angle, we should try and calculate another very helpful thing: the next epoch at which this phase angle occurs. To do this, we will need to calculate two things: the current phase angle, and the phase angular velocity (the rate at which the phase angle changes).
The current phase angle is pretty easy to calculate. If we take the position vectors of each Spacecraft and use the 'VertexAngle' method, we can calculate the angle between the two.

However, this method will not return a value greater than 180 degrees. If Earth is ahead of Mars, we need to add 180 degrees to the phase Angle. To do this, we can take the z component of the cross product of InterplanetarySC.Position and MarsSC.Position, and check to see if it's negative. If it is, that means we need to add 180 degrees. To do this, we write:

Hohmann Transfer To Mars

Now, we need to calculate the phase angular velocity. In this scenario, this will simply be the difference between Earth's angular velocity and Mars's angular velocity. To calculate this, we write:

Now that we have the phase angular velocity, we can calculate how long it will take until we've reached our departure position. To calculate this, we take the difference of our current phase angle, and our departure phase angle. If we divide this difference by the phase angular velocity, we will have the amount of time (in seconds) until we've reached our departure position. Then, we can add that to our current epoch to calculate the departure epoch. To do this, we write:

We have done all the necessary calculations for our first maneuver. Now, we need to step to the departure date, maneuver, then step to the arrival date. Let's go back to the Mission Sequence.

•Drag and drop a FreeForm script editor after the 'Calculate Phase Angle' FreeForm

•Open the script editor and rename it to 'Step to Departure, Maneuver, Step to Arrival'

In this script, we will step to the departure epoch, maneuver the Spacecraft, change the Spacecraft tail color for a better visualization, calculate the arrival epoch, and step to the arrival epoch. To do this, we write:

The last thing we need to do for this transfer is to match our speed with our target. Let's go back to the Mission Sequence.

•Drag and drop a FreeForm script editor after the 'Step to Departure, Maneuver, Step to Arrival' FreeForm

•Open the script editor and rename it to 'Orbit Matching Maneuver'

In this script, we will need to calculate speed of Mars's orbit, calculate the Δv required to match the orbit, maneuver the spacecraft, then propagate for 300 days to visualize this change. To do this, we write:

One more thing we need to add to the script - the thing we've been looking for all along! We need to report the Δv, and the time of flight in days. For the time of flight, we can simply take the difference of the arrival epoch and the departure epoch as these are measured in days. To report these values, we write:

Your Mission Sequence should look something like this:

Mission Sequence Example

Save and run your Mission Plan, then try and answer these questions:

How much total Δv was required for the transfer?

How many days did the transfer take?

Try reporting the distance between the two spacecraft at the time where InterplanetarySC 'meets' MarsSC (right before the orbit matching maneuver). To do this, you can add the command 'Report InterplanetarySC.RadialSeparation(MarsSC)' right before the command to perform the second maneuver. About how far apart were the Spacecraft?

See Also

Hohmann Transfer Stk

•Interplanetary Topics

Hohmann Transfer Math

•Next Topic: Patched Conics Transfer