Timing of Mars Space Probe Launches

[RJ Emery]

It has been reported that the window of opportunity to launch a space probe from Earth to Mars occurs every 26 months, owing to the amount of rocket fuel able to propel a spacecraft to Mars.

I do not understand why.

Once a spacecraft is sent on its way to rendezvous with Mars, I presume there will be course corrections en route that would use a minimal amount of fuel. Therefore, why is the 26 month window so critical?

If the launch is one, two or even three months late, no amount of additional rocket fuel is needed for the spacecraft to arrive at its destination. After leaving Earth and have gained a velocity of about 55,000 mph, the spacecraft just coasts to its rendezvous. What difference does it make if the trip takes a few weeks or months longer owing to the positions of the two planets at launch?

[Chris Peterson]

It has been reported that the window of opportunity to launch a space probe from Earth to Mars occurs every 26 months, owing to the amount of rocket fuel able to propel a spacecraft to Mars.

I do not understand why.

Once a spacecraft is sent on its way to rendezvous with Mars, I presume there will be course corrections en route that would use a minimal amount of fuel. Therefore, why is the 26 month window so critical?

If the launch is one, two or even three months late, no amount of additional rocket fuel is needed for the spacecraft to arrive at its destination. After leaving Earth and have gained a velocity of about 55,000 mph, the spacecraft just coasts to its rendezvous. What difference does it make if the trip takes a few weeks or months longer owing to the positions of the two planets at launch?

The minimum energy orbit (cheapest, so usually desirable) is one where the probe's perihelion is at 1 AU (the Earth's orbit) and its aphelion is at Mars's orbit, and with the two planets near their closest to each other (but not quite). That's what defines the optimal launch window. Certainly, you can launch at other times, but it requires more energy to create the necessary orbit (you don't just go in a straight line towards where Mars will be- that's extremely expensive in terms of energy).

[RJ Emery]

Chris,

I appreciate your response, but it still does not make sense to me. It should take the same amount of energy to lift the spacecraft and put it on its trajectory to Mars, whether it coasts for 7 months and 300 million miles or much longer. The time spent coasting to its Mars rendezvous is presumably irrelevant in terms of energy expended.

[geckzilla]

If you throw a baseball ten meters in the air, it takes less energy than if you throw the same baseball twenty meters in the air. That's a good enough analogy. Essentially you want Mars to be at the top of the baseball's arc.

[Chris Peterson]

Chris,

I appreciate your response, but it still does not make sense to me. It should take the same amount of energy to lift the spacecraft and put it on its trajectory to Mars, whether it coasts for 7 months and 300 million miles or much longer. The time spent coasting to its Mars rendezvous is presumably irrelevant in terms of energy expended.

It takes more energy to place the probe in an orbit with a greater aphelion. That is, in a larger orbit. If the aphelion is too short, the probe will never reach Mars. If it's too large, the probe will reach Mars with too much velocity, requiring a large fuel expenditure to slow down. The minimum energy orbit is the one that creates the necessary perihelion and aphelion, and has point of aphelion intersecting Mars's orbit at the exact time that Mars in in that spot in its orbit. That requires just the right geometry between the Earth and Mars at launch.

[geckzilla]

I highly recommend Kerbal Space Program if you want to try to get a feel for what it's like to launch a rocket and get it to go somewhere.

[RJ Emery]

geckzilla,

Thanks, but I would be more interested in the programs NASA or JPL use for interplanetary exploration.

[geckzilla]

Thanks, but I would be more interested in the programs NASA or JPL use for interplanetary exploration.

Oh. Physics is physics, though. Not even sure NASA or JPL have such a thing as general as Kerbal is.

[RJ Emery]

geckzilla,

Yes, physics IS physics, but I have no way of validating and verifying the accuracy of the Kerbal program. With the programs used by NASA and/or JPL, they are of course very well vetted, certainly not cartoonish and probably applicable for all the planets including return voyages. Nevertheless, I thank you for your suggestion.

[geckzilla]

Ok hot shot, but you're currently below Kerbel level of understanding. Denigrate it for its cartoonish appearance all you want. It's a tremendously fun way to learn about rocketry while still offering a significant challenge. There's a demo version so it's not like you have to drop a penny if you hate it. You could really learn a lot.

[Chris Peterson]

geckzilla,

Thanks, but I would be more interested in the programs NASA or JPL use for interplanetary exploration.

AFAIK there are no such programs that exist in what you might call a "finished" state with some kind of simple user interface. There is a good deal of public code available, solving these kinds of orbits using both Newtonian analysis as well as numerical integration. But they're routines that people wrap up in their own code.

[neufer]

It should take the same amount of energy to lift the spacecraft and put it on its trajectory to Mars, whether it coasts for 7 months and 300 million miles or much longer. The time spent coasting to its Mars rendezvous is presumably irrelevant in terms of energy expended.

Rocket fuel energy primarily ends up in the kinetic & potential energy of the ejected rocket fuel molecules themselves; only a fraction ends up in the kinetic & potential energy of the spacecraft. If you are going to do an energy analysis (not recommended) you have to take all the energies into account.

[BMAONE23]

When the Mars Global Surveyor reached it's destination it was traveling approximately 5KPS faster than Mars' relative velocity. To achieve orbit insertion and be successfully captured by Mars' Gravity Well the orbiter needed to shed about 1KPS of speed which required sufficient fuel for a 20 to 25 minute engine burn. Traveling faster to reach Mars sooner would require more fuel for the Orbital Insertion Burn. If you are traveling twice the speed to get to Mars (10KPS relative to Mars) you would need to slow down by 6 kilometers per Second and would need significantly more fuel upon arrival. If you were a manned mission with all the necessary supplies, you would carry even more kinetic energy due to the total mass than a lighter probe/lander and slowing would require even more fuel

[neufer]

When the Mars Global Surveyor reached it's destination it was traveling approximately 5KPS faster than Mars' relative velocity. To achieve orbit insertion and be successfully captured by Mars' Gravity Well the orbiter needed to shed about 1KPS of speed which required sufficient fuel for a 20 to 25 minute engine burn. Traveling faster to reach Mars sooner would require more fuel for the Orbital Insertion Burn.

An elliptical orbit that intercepts Mars's orbit at aphelion should be traveling slower than Mars (resulting in any non-intercept returning back down to Earth's orbit at perihelion).

[BMAONE23]

Got it. Mars is traveling through space at a little over 24KPS. So when the MGS arrived at a speed of 5KPS, while it was traveling significantly slower than Mars' solar orbit, it was traveling faster than Mars escape velocity and as such needed to reduce speed to 4KPS to ensure orbital insertion. So the trick is in arriving with sufficient fuel to be able to slow to below Mars escape velocity to achieve orbit. So no matter how fast you travel to get there you still have to slow to below 4KPS for orbital insertion

[RJ Emery]

When the Mars Global Surveyor reached it's destination it was traveling approximately 5KPS faster than Mars' relative velocity. To achieve orbit insertion and be successfully captured by Mars' Gravity Well the orbiter needed to shed about 1KPS of speed which required sufficient fuel for a 20 to 25 minute engine burn. Traveling faster to reach Mars sooner would require more fuel for the Orbital Insertion Burn. If you are traveling twice the speed to get to Mars (10KPS relative to Mars) you would need to slow down by 6 kilometers per Second and would need significantly more fuel upon arrival. If you were a manned mission with all the necessary supplies, you would carry even more kinetic energy due to the total mass than a lighter probe/lander and slowing would require even more fuel

Most interesting. Can you cite a source for this information?

[neufer]

Got it. Mars is traveling through space at a little over 24KPS. So when the MGS arrived at a speed of 5KPS, while it was traveling significantly slower than Mars' solar orbit, it was traveling faster than Mars escape velocity and as such needed to reduce speed to 4KPS to ensure orbital insertion. So the trick is in arriving with sufficient fuel to be able to slow to below Mars escape velocity to achieve orbit. So no matter how fast you travel to get there you still have to slow to below 4KPS for orbital insertion

If MGS had intercepted Mars at aphelion then Mars would have overtaken it at ~2KPS.

If MGS had intercepted Mars at perihelion then Mars would have overtaken it at ~3.3KPS.

---

It looks as if MGS was overtaken by Mars nearer
to perihelion at a closing speed of ~3KPS.

After falling most of the way to the surface MGS would have reached an orbital speed of ~5.8KPS [=sqrt(3² + 5²)] due to energy conservation (with an escape velocity of ~5KPS). The MGS then retrofires (Mars Orbit Insertion -1KPS) to slow down to ~4.8KPS (below the ~5KPS escape velocity) at which point the MGS is in a long elliptical orbit.

Finally a careful re-positioning places MGS's perimars just inside the out atmosphere such that the MGS slowly descends to a circular orbit.

[BMAONE23]

When the Mars Global Surveyor reached it's destination it was traveling approximately 5KPS faster than Mars' relative velocity. To achieve orbit insertion and be successfully captured by Mars' Gravity Well the orbiter needed to shed about 1KPS of speed which required sufficient fuel for a 20 to 25 minute engine burn. Traveling faster to reach Mars sooner would require more fuel for the Orbital Insertion Burn. If you are traveling twice the speed to get to Mars (10KPS relative to Mars) you would need to slow down by 6 kilometers per Second and would need significantly more fuel upon arrival. If you were a manned mission with all the necessary supplies, you would carry even more kinetic energy due to the total mass than a lighter probe/lander and slowing would require even more fuel

Most interesting. Can you cite a source for this information?

Absolutely R J
http://www.msss.com/mars/global_surveyo ... tion5.html
See section 5.1.1 Mars Orbit Insertion Maneuver

[BMAONE23]

Got it. Mars is traveling through space at a little over 24KPS. So when the MGS arrived at a speed of 5KPS, while it was traveling significantly slower than Mars' solar orbit, it was traveling faster than Mars escape velocity and as such needed to reduce speed to 4KPS to ensure orbital insertion. So the trick is in arriving with sufficient fuel to be able to slow to below Mars escape velocity to achieve orbit. So no matter how fast you travel to get there you still have to slow to below 4KPS for orbital insertion

If MGS had intercepted Mars at aphelion then Mars would have overtaken it at ~2KPS.

If MGS had intercepted Mars at perihelion then Mars would have overtaken it at ~3.3KPS.

---

It looks as if MGS was overtaken by Mars nearer
to perihelion at a closing speed of ~3KPS.

After falling most of the way to the surface MGS would have reached an orbital speed of ~5.8KPS [=sqrt(3² + 5²)] due to energy conservation (with an escape velocity of ~5KPS). The MGS then retrofires (Mars Orbit Insertion -1KPS) to slow down to ~4.8KPS (below the ~5KPS escape velocity) at which point the MGS is in a long elliptical orbit.

Finally a careful re-positioning places MGS's perimars just inside the out atmosphere such that the MGS slowly descends to a circular orbit.

I've seen quoted speeds of between 3KPS and 5KPS as the MGS arrival speed, the faster speed being from the MGS mission plan here
http://www.msss.com/mars/global_surveyo ... tion5.html

[neufer]

If MGS had intercepted Mars at aphelion then Mars would have overtaken it at ~2KPS.

If MGS had intercepted Mars at perihelion then Mars would have overtaken it at ~3.3KPS.

---

It looks as if MGS was overtaken by Mars nearer
to perihelion at a closing speed of ~3KPS.

After falling most of the way to the surface MGS would have reached an orbital speed of ~5.8KPS [=sqrt(3² + 5²)] due to energy conservation (with an escape velocity of ~5KPS). The MGS then retrofires (Mars Orbit Insertion -1KPS) to slow down to ~4.8KPS (below the ~5KPS escape velocity) at which point the MGS is in a long elliptical orbit.

Finally a careful re-positioning places MGS's perimars just inside the out atmosphere such that the MGS slowly descends to a circular orbit.

I've seen quoted speeds of between 3KPS and 5KPS as the MGS arrival speed,
the faster speed being from the MGS mission plan here:
http://www.msss.com/mars/global_surveyo ... tion5.html

---

The 3KPS MGS arrival speed corresponds my stated closing speed of ~3KPS...before falling into Mars's gravitational field.

The 5KPS MGS arrival speed corresponds roughly to my stated hyperbolic orbital speed of ~5.8KPS [=sqrt(3² + 5²)]...just prior to the Mars Orbit Insertion retro-fire of -1KPS.

My error, perhaps, was assuming that the escape velocity at peri-mars was the same as the escape velocity at the surface of ~5KPS (rather than ~4KPS).

[BMAONE23]

And my mistake was in not considering the effect of Mars' gravity causing an increase in speed prior to the Orbital Insertion Burn

[neufer]

And my mistake was in not considering the effect of Mars' gravity causing an increase in speed prior to the Orbital Insertion Burn

• At least no one confused KPS with MPS and truly deserved to be slugged.

<<The slug (~32.174 lb_m) is a unit of mass that accelerates by 1 ft/s² when a force of one pound is exerted on it. The blob is the inch version of the slug (1 blob = 12 slugs). This unit is also called a slugette, and a snail. (Similar metric units include the "glug" in the cgs system, and the "mug" in the mks system.)>>