לזכות ידיד נפשי הרב ר' שמחה דן גיסינג'ר שליט"א לברכה והצלחה בכל מעשי ידיו יחד עם כל בני ביתו!!

Says the Mishna [Pesachim 93b]: 

איזו היא דרך רחוקה מן המודיעים ולחוץ וכמדתה לכל רוח דברי רבי עקיבא רבי אליעזר אומר מאיסקופת העזרה ולחוץ אמר ליה רבי יוסי לפיכך נקוד על ה׳ לומר לא מפני שרחוק ודאי אלא מאיסקופת העזרה ולחוץ:

What is the definition of a distant journey that exempts one from observing the first Pesach? Anywhere from the city of Modi’im and beyond, and from anywhere located an equal distance from Jerusalem and beyond in every direction; this is the statement of Rabbi Akiva. Rabbi Eliezer says: From the threshold of the Temple courtyard and beyond is considered a distant journey; therefore, anyone located outside the courtyard at the time that the Paschal lamb is slaughtered is exempt from observing the first Pesacḥ. Rabbi Yosei said to him: Therefore, the word is dotted over the letter heh in the word “distant [rechoka]” to say that the meaning of the word should be qualified: It should be understood that it is not because he is really distant; rather, it includes anyone located from the threshold of the Temple courtyard and beyond.

Says the GREATEST commentary ever written on the Mishna - the Gemara!:

אמר עולא מן המודיעים לירושלים חמשה עשר מילין הויא סבר לה כי הא דאמר רבה בר בר חנה אמר רבי יוחנן כמה מהלך אדם ביום עשרה פרסאות מעלות השחר ועד הנץ החמה חמשת מילין משקיעת החמה ועד צאת הכוכבים חמשת מילין פשו לה תלתין חמיסר מצפרא לפלגא דיומא וחמיסר מפלגא דיומא לאורתא

Ulla said: The distance from the city of Modi’im to Jerusalem is fifteen mil. He held like this following opinion that Rabba bar bar Ḥana said that Rabbi Yochanan said: How far can an average person walk on an average day? One can walk ten parasangs [parsaos], which are forty mil. This is divided in the following way: From dawn until sunrise one can walk a distance of five mil, and from sunset until the emergence of the stars one can walk another five mil. There are thirty mil remaining that one can walk in a day: Fifteen from the morning until midday, and fifteen from midday until evening.

עולא לטעמיה דאמר עולא אי זה הוא דרך רחוקה כל שאין יכול ליכנס בשעת שחיטה. ורב יהודה אמר כל שאינו יכול ליכנס בשעת האכילה.

The Gemara explains that Ulla conforms to his standard line of reasoning below, as Ulla said: What is the definition of a distant journey? It is any distance from which one is unable to reach Jerusalem and enter the Temple by the time of the slaughter of the Pesach. 

And Rav Yehuda said: Any journey of a distance from which one is unable to reach Jerusalem, where the Pesach is eaten, and enter during the time of the eating, the following night.

Rashi says:

חמשה עשר מילין - וסבירא ליה לעולא דרך רחוקה כל שאינו יכול ליכנס בשעת שחיטה כל שעת שחיטה מהלך ואינו מגיע ושעת שחיטה מחצות היום ואילך דבין הערבים כתיב ביה כתמיד ותמיד אע"פ שנשחט בשש ומחצה זמנו מן התורה מתחלת שבע ואילך שמתחלת החמה להתעקם כלפי מערב קצת ומשחרי כותלי דהכי אמרינן ביומא בפ' שלישי (דף כח:) צלותיה דאברהם מכי משחרי כותלי והיינו מחצות היום ..... ומחצות ועד שקיעת החמה מהלך חמשה עשר מילין כי הא דר' יוחנן:

בשעת אכילה - כל שעת אכילה שרחוק מחצות היום כל כך שאינו יכול ליכנס כל הלילה אכילת הפסח כל הלילה ורבנן עבוד הרחקה ואמור עד חצות לר"ע ולר"א דאורייתא עד חצות בפרק בתרא (דף קכ:) ובברכות בפ"ק (דף ט.).

We see from Rashi that according to Ulla the definition of דרך רחוקה is that he is so far that he will not be able to arrive in Yerushalayim during the time of the slaughtering [i.e. until שקיעה - sundown] if he leaves at the beginning of the time of the slaughtering [i.e. midday]. That would be a place like מודיעין which is 15 mil away. 

Rav Yehuda says that he won't be able to arrive the entire of the eating of the Pesach, either until midnight or the morning. 

However the Rambam [Korban Pesach 5-8/9] learns differently:

ואי זו היא דרך רחוקה חמשה עשר מיל חוץ לחומת ירושלים:

מי שהיה בינו ובין ירושלים יום ארבעה עשר עם עליית השמש חמשה עשר מיל או יתר הרי זה דרך רחוקה היה בינו ובינה פחות מזה אינו בדרך רחוקה מפני שהוא יכול להגיע לירושלים אחר חצות כשיהלך ברגליו בנחת.

What is meant by the term "on a distant way" which exempts a person from bringing a Paschal sacrifice? Fifteen mil outside the walls of Jerusalem.

If one was fifteen mil or more outside of Jerusalem at the appearance of the sun on the fourteenth Nisan, he is considered to be "on a distant way." If he was closer than this, he is not considered to be "on a distant way," because he could reach Jerusalem after midday while walking comfortably by foot.

The Kesef Mishna writes that the Rambam explains the words of Ulla "כל שאינו יכול ליכנס בשעת שחיטה" as meaning the BEGINNING of the time of שחיטה i.e. by חצות [as opposed to Rashi who learns that he is talking about arriving by the END of the time of שחיטה].  

We have to understand:

1] What compelled the Rambam to that שעת השחיטה means the BEGINNING of the time of שחיטה and automatically it emerges that the שיעור of דרך רחוקה depends on a person's whereabouts at sunrise and didn't explain like Rashi that it depends on the person's whereabouts at midday?

2] We also have to understand  - מהיכי תיתי [from whence a source or rationale] that the דין of דרך רחוקה would depend on a person's whereabouts at sunrise?? I understand that it should depend on his whereabouts at חצות - that is when the time for שחיטה starts, so it makes sense that at that point he has an obligation to go to ירושלים. But what happens at sunrise?? And if it starts at the beginning of the day then the time would be DAWN - עמוד השחר, like other mitzvos, as the Mishna says [Megilla 20b]. Also, as the Shaagas Aryeh [סי' י"ז] roared, if a person must go to ירושלים before the time of the שחיטה, then why not a few days before?

To answer the second question - The Yerushalmi [Shabbos 19-5] asks whether a baby on his 8th day at nightfall [after day 7] is considered fit for the mitzva of  Milah even though in practice it may not be performed until the next day. The Gemara resolves the question by pointing to the דין that already on the 8th night an animal may be put in the pen to be separated as מעשר [and it says in the Mishna that if an animal is מחוסר זמן - not having reached the required time, it may not enter the pen], so we see that ליל שמיני כשמיני - the 8th night is like the 8th day. That would mean that in principle the 8th night is already considered the time to perform the Bris Milah, even though in practice it may not be performed until the next morning. We see this notion in various other place, such as the Rashi in Sukkah [33b] who says that already at night the time for the mitzva of taking the Arba Minim has arrived [in theory but not practice]. Based on this we can answer the question of the Rosh ['סוכה פ"ד סי' ב] on the Behag who says that the שהחיינו at Kiddush covers the Arba Minim as well. Asked the Rosh - There is a night in between the bracha of שהחיינו and the obligation of the Arba Minim the next day, so how does that work? There is a הפסק?? But now we understand, that in principle the obligation already begins at night, even though in practice it is only taken the next day, so the bracha at night can cover the mitzva done [in practice] the next day.

So now we can say that the same applies to the mitzva of sacrificing the Pesach - namely that it already begins at the night of the 14th. If so, he should really have to leave his house at night but he can't because Rav Yehuda [Pesachim 2a and see also Taanis 10a, Bava Kamma 60b] derives from psukim that one shouldn't leave his house to travel at night, nor may he enter the new city at night - "לעולם יכנס אדם בכי טוב ויצא בכי טוב". The earliest time one may leave is at sunrise, as Rashi says [Pesachim 2a]. In line with this the Rambam rules that one must leave at sunrise and if he cannot arrive in ירושלים by חצות היום he is considered בדרך רחוקה and not that he must leave at עמוד השחר because that is too early. That is the opinion of Ulla. [Question #2 resolved].  

Now to answer Question #1: Rav Yehuda holds that the Torah required that the person leave his house at the time of the EATING of the Pesach. So in principle, he should not have to leave until the NIGHT of the 15th. But since Rav Yehuda said [Pesachim 2a] that one must leave his city "בכי טוב", that means that he can't leave at night. The best option then is to say that he should leave at חצות היום because that is the time of the שחיטה which is הכשר האכילה - enables the eating. This way he will enter the city "בכי טוב" before nightfall. Now if R' Yehuda holds that he must be able to arrive at the BEGINNING of the time for eating, then his בר פלוגתא [interlocuter] Ulla must hold that he must be able to arrive at the BEGINNING of the time of שחיטה i.e. חצות היום. Also, if Ulla holds that he may arrive at the END of the time of שחיטה then he will be holding EXACTLY like R' Yehuda and that can't be! [Question #1 resolved]

How does Rashi say according to R' Yehuda that he may arrive all night? What about R' Yehuda's rule that one may not enter a city when it is dark [Pesachim 2a]? 

There are 2 reasons offered by Tosfos why only enter or exit "בכי טוב". Either because of mystical מזיקין or physical minefields and pitfalls. Maybe Rashi holds issue with night time is מזיקין but on Pesach night which is ליל שימורים from מזיקין there is nothing to worry about. While the Rambam can hold like the other opinion that the issue is one of physical danger which one is not necessarily protected from on ליל פסח, so he may not arrive or leave at night. 

[עפ"י תורת הגר"נ געשטטנר זצ"ל]