why was the usa the only one to go to the moon?

[raven]

Or it was a really small telescope.

Ooo, I think I had a plastic one as a child that was literally just a toy--no magnification at all.

I hard one like that. Several in fact, only mine were completely biodegradable.

[Chew]

I have a question about orbits that may have something to do with TLI and how it is accomplished.

Check out Bob's page about the TLI: http://www.braeunig.us/apollo/apollo11-TLI.htm

FYI, the Moon's orbit is inclined 5.1° to the Ecliptic, not the equator.

[smartcooky]

I have a question about orbits that may have something to do with TLI and how it is accomplished.

Check out Bob's page about the TLI: http://www.braeunig.us/apollo/apollo11-TLI.htm

FYI, the Moon's orbit is inclined 5.1° to the Ecliptic, not the equator.

Aha, that will probably answer my question. The angle of the ecliptic is 23.4°, so the moon could potentially be ± 5.1 degrees either side of that... 18.3° to 28.5° depending on time of month, so the insertion point for a lunar equatorial orbit could be another 1.5° on top of that... 16.8° to 30°. 

[ka9q]

It seems to me that a TLI burn at an earth orbital inclination of 32° is not going to send the spacecraft anywhere near the moon .

The inclination isn't as important as the argument of perigee. When the argument of perigee is exactly 180 degrees, apogee occurs on a descending (N->S) equator crossing regardless of the orbital inclination. You vary the argument of perigee by varying the time (and hence the latitude) of TLI, and that moves apogee north or south of the earth's equatorial plane. (Apogee was actually somewhat past the moon, so you adjust to just cross the moon's orbital plane when you get out there.)

The inclination of the Apollo parking orbit was chosen for two reasons: first, to broaden the daily launch window; and second, to permit transit of the Van Allen belts at a relatively high geomagnetic latitude, well outside the dense part of the inner belt.

[Andromeda]

Even though Alex was trolling, this thread has been excellent for me to learn some new things.

[smartcooky]

It seems to me that a TLI burn at an earth orbital inclination of 32° is not going to send the spacecraft anywhere near the moon .

The inclination isn't as important as the argument of perigee. When the argument of perigee is exactly 180 degrees, apogee occurs on a descending (N->S) equator crossing regardless of the orbital inclination. You vary the argument of perigee by varying the time (and hence the latitude) of TLI, and that moves apogee north or south of the earth's equatorial plane. (Apogee was actually somewhat past the moon, so you adjust to just cross the moon's orbital plane when you get out there.)

The inclination of the Apollo parking orbit was chosen for two reasons: first, to broaden the daily launch window; and second, to permit transit of the Van Allen belts at a relatively high geomagnetic latitude, well outside the dense part of the inner belt.

OK, so this is why you have "launch windows"; this argument of perigee is not going to be right every day for the whole month is it?

[ka9q]

Many factors go into setting launch windows. Unless all your conditions are met, the window is closed.

For Apollo, the main consideration was lighting at the landing site; it had to be early morning at the time of landing. This constrained launch to a few days every month.

Within each monthly period was a daily launch window set by the required right ascension of the ascending node. That's the only Keplerian orbital parameter that changes with launch time if you fly the same trajectory over the earth; it increases 360 degrees as the earth rotates once every sidereal day. You have to launch when the launch site rotates through the desired transfer orbit plane, which must also include the moon at arrival time.

To keep the daily launch windows from being too narrow, the launch azimuth (and the inclination of the transfer orbit) varied throughout the daily window. Since the minimum inclination without an expensive plane change maneuver is equal to the launch site latitude (28.5 deg), a larger inclination than this had to be used. A due east launch gives you a 28.5 deg inclination; larger inclinations can be reached by deflecting the launch azimuth either north or south, depending on where you want the ascending node to be.

If you really want the details there are some good NASA descriptions of Apollo lunar flight trajectory planning.

[armillary]

Well, a couple of factors interact. Basically, the 180° is relative to the point of LOI, so that's less critical. You launch into an Earth orbit that's already in a plane where you want the transfer orbit by adjusting the time of launch and direction. After that, wait until the right time, then fire the third stage, and the resulting orbit will take you to the moon.

The real issue is that the orbit must also intersect the moon's orbital plane near apogee. Since the Earth orbit is inclined, you can adjust it north or south by timing the TLI burn, but there's definitely times that are more optimal. There's also room for course correction during the lunar transit.

Finally, the issue was combining it so that the landing will take place during lunar morning.

Most of you probably know this, but lunar morning was chosen for two reasons; one, the long shadows would enable the commander to avoid any large boulders or other hazards during landing, and two, the LM was designed to maintain a reasonable working temperature during lunar morning. This also meant that the rear of the spacecraft always faces the sun in the pictures.


(I'm probably repeating other posters, but sometimes it helps to formulate things in different words)

[Echnaton]

Welcome to the board, armillary.  Thanks for the clear explanation. 

[Noldi400]

I have a question about orbits that may have something to do with TLI and how it is accomplished.

I have difficulty in understanding how Apollo 11 could have made an near equatorial orbital insertion at the moon

Firstly, the moon's orbit is inclined to the earth's equator by about 5.1°, and the moon's equator is inclined to its own orbit by 1.5°. This means that, depending upon where the moon is in its orbit, the actual inclination of the moon's equator could be anywhere between 6.6° (5.1° + 1.5°) and 3.6° (5.1° - 1.5°). It is  beautifully illustrated in this gif.



Secondly, AIUI, Apollo 11 launched from Cape Canaveral into an earth orbit of about 32° inclination. This seems high (was it due to the Cape's latitude of 28½° N?).

It remained in that orbit for only 1½ revolutions before TLI.

It seems to me that a TLI burn at an earth orbital inclination of 32° is not going to send the spacecraft anywhere near the moon . I know there are mid course corrections, but correcting a deviation of at least 26° seems a bit extreme. To insert the spacecraft into a near-Lunar equatorial orbit would mean that it would have to approach the moon near the plane of its equator, and I imagine that would need to be set up a considerable distance and time advance.

I feel I am missing something really simply, but what?

I can't give you a precise answer, but I believe I can get you started.

First, the moon's orbit is inclined about 5.1^o to the ecliptic, not to the equator, which puts it around a 23^o inclination to the equator. That gets you a lot closer right off the bat.

As to the 32^o, there may have been other reasons, but a primary one was to avoid the thickest part of the VAB, which lies mostly between 30^o north and south of the equator.

================================================
ETA: Woops. Neglected to turn the page and didn't see those more detailed answers. Ah, well.

[Bob B.]

I have difficulty in understanding how Apollo 11 could have made an near equatorial orbital insertion at the moon.

To be honest, I’ve never been able to find the orbital elements of the lunar orbits.  I’ve only found the altitudes of the orbits, from which I can get semimajor axis and eccentricity.  However, none of the documents I’ve looked at has given me inclination, longitude of the ascending node, etc.  If anybody has this information or knows where I can find it, please let me know.

It seems to me that a TLI burn at an earth orbital inclination of 32° …

There was typically a small plane change performed during TLI (up to nearly 2° in a couple cases), so the inclinations of the translunar trajectories varied slightly from those of the Earth parking orbits.  You can see the differences in the following documents:

Earth Orbit Data:  http://history.nasa.gov/SP-4029/Apollo_18-21_Earth_Orbit_Data.htm
Translunar Injection:  http://history.nasa.gov/SP-4029/Apollo_18-24_Translunar_Injection.htm

A small one or two degree plane change can be performed for very little Δv when combined with an altitude change. 

Aha, that will probably answer my question. The angle of the ecliptic is 23.4°, so the moon could potentially be ± 5.1 degrees either side of that... 18.3° to 28.5° depending on time of month, so the insertion point for a lunar equatorial orbit could be another 1.5° on top of that... 16.8° to 30°.

It’s not a function of the time of month; it’s a function of where the Moon is in its 18.6-year nodal precession cycle.  In July 1969 it was at the maximum of 28.5°.  By December 1972 the angle had reduced to about 25.4°.


I’m going to refrain from repeating what others have already said, but I will add one thing.  As we see, the inclination of the Moon’s orbit varied between 25.4°-28.5°, and the inclinations of the translunar orbits varied between 28.5°-32.5°.  Clearly the two orbital planes are inclined to one another by a few degrees.  The line connecting the Earth with the Moon at the time of intercept is the line of intersection of the two planes.  I’m not sure this was perfectly clear in the previous explanations, so I thought it worth mentioning.

[onebigmonkey]

I have difficulty in understanding how Apollo 11 could have made an near equatorial orbital insertion at the moon.

To be honest, I’ve never been able to find the orbital elements of the lunar orbits.  I’ve only found the altitudes of the orbits, from which I can get semimajor axis and eccentricity.  However, none of the documents I’ve looked at has given me inclination, longitude of the ascending node, etc.  If anybody has this information or knows where I can find it, please let me know

Not sure if this helps, but the apollo image atlas has info here

www.lpi.usra.edu/resources/mapcatalog/apolloindex/

Mostly it's locations of photos, from which you can infer orbits, but some have the orbits drawn precisely.

My own site (see my sig) has google moon kmz files plotting image locations that show the orbital paths.

[Bob B.]

As to the 32^o, there may have been other reasons, but a primary one was to avoid the thickest part of the VAB, which lies mostly between 30^o north and south of the equator.

Avoiding the Van Allen Radiations Belts was certainly a major consideration.  But, as ka9q mentioned, a spacecraft can't be launched into an orbit with an inclination less than the latitude of the launch site.  You can insert into a high inclination but not a lower one.  (Well, technically you can insert into a slightly lower inclination by doglegging the launch path.)  Since the launch pads were located at about 28.6° N latitude, that's the lowest inclination orbit possible.

There were actually many things that came together very conveniently for Apollo.  In 1969, the latitude of the launch site (28.6°) almost exactly matched the inclination of the Moon's orbit (28.5°).  The high inclination was also just what was needed to mitigate the VARB hazard.  Also, the combination of the timing that was needed to arrive with the correct lighting conditions, and the location of Earth magnetic pole, meant that the spacecraft departed in a direction that maximized the angular separation between the spacecraft and the geomagnetic equator.  This further reduced any potential radiation hazard.

Chew kindly linked to it earlier, but the following page graphically shows Apollo 11's orbit and how it bypassed the VARB.

http://www.braeunig.us/apollo/apollo11-TLI.htm

[Bob B.]

Not sure if this helps, but the apollo image atlas has info here

www.lpi.usra.edu/resources/mapcatalog/apolloindex/

Mostly it's locations of photos, from which you can infer orbits, but some have the orbits drawn precisely.

My own site (see my sig) has google moon kmz files plotting image locations that show the orbital paths.

Thanks, that helps some.

[gwiz]

To be honest, I’ve never been able to find the orbital elements of the lunar orbits.  I’ve only found the altitudes of the orbits, from which I can get semimajor axis and eccentricity.  However, none of the documents I’ve looked at has given me inclination, longitude of the ascending node, etc.  If anybody has this information or knows where I can find it, please let me know.

The DRA Table of Space Vehicles gives inclinations, period and eccentricity.  The inclinations for Apollo are:
8 - 168   10 - 174.4   11 - 178.75   12 - 164.7   14 - 165.6   15 - 151.28   16 - 169.3   17 - 159.9