The Moon Motion Basic Equation (modified)

IN THE ALMIGHTY GOD NAME
Through the Mother of God mediation
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Gerges Francis Tawadrous/
2nd
Course student – physics Faculty – People's Friendship University – Moscow –Russia..
mrwaheid1@yahoo.com mrwaheid@gmail.com +201022532292
1
The Moon Motion Basic Equation (modified)
The Author Authorized To Be Used By
Mr. Gerges Francis Tawdrous
A Student–Physics Department- Physics
& Mathematics Faculty –
Peoples' Friendship University of Russia
(RUDN University) – Moscow – Russia
Dr. Budochkina, Svetlana Aleksandrovna
Associate Professor (Mathematical Analysis
and Theory of Functions Department)
Peoples' Friendship University of Russia
(RUDN University) – Moscow – Russia
Phone +201022532292
E-Mail: mrwaheid@gmail.com
Curriculum Vitae http://vixra.org/abs/1902.0044
Phone +7 (495) 952-35-83
E-Mail: budochkina-sa@rudn.ru, sbudotchkina@yandex.ru
Website
http://web-local.rudn.ru/web-local/prep/rj/index.php?id=2944&p=19024
The Assumption Of S. Virgin Mary -Written in Cairo – Egypt – 16th
December 2020
Abstract
A Modification In
The Moon Orbital Motion Equation
The Old Form
θ1 (Per Solar Day) = θ0 (of Previous Day) + 0.98562 degrees
The Modified form
θ1 (Per Solar Day) = θ0 ( of Previous Day) + 1.5 degrees
- The Equation uses 1.5 degrees in place of the angle (0.98562 degrees) because the
moon axial tilt declines on the Earth Ecliptic line with 1.5 degrees.
- This paper tests the new modification on the equation accuracy
- The modified equation defines the moon position with an accuracy =96.12 %
(where the error is (3.88 %))
The Equation Concept
- The moon uses Pythagoras triangle to do the following job. While the moon moves
a daily displacement =88000 km, The moon real displacement (L) through its orbit
can be less than (88000 km) where (L =88000 Cos (θ))
- The moon needs to decrease its daily displacement (88000 km) through its orbit to
enable the moon to revolve around Earth in more near orbits to Earth
- The angle (θ) defines the moon real displacement and its distance to perigee radius
(r=0.363 mkm).
- For that reason the equation depends on the angle (θ).

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1- Introduction
- The moon moves daily (88000 km) on the right triangle hypotenuse (AC), but the
moon creates an angle (θ) between its motion direction and its orbital horizontal
level, by that the real displacement will be (L= 88000 km cos (θ)) through the
moon orbit, and by that, spite the moon moves 88000 km and the orbital horizontal
distance be less than (88000 km) and this is the objective for which the moon uses
Pythagoras triangle –
- As an example, if (θ) =28.63 degrees So the real displacement (L) = 77237 km, So,
if the moon real displacement daily be equal this value during 29.53 days the moon
will move a distance = 2.28 million km and this will be the moon orbital
circumference, BUT for what radius? 2.28 mkm = 2π x (0.363 mkm)
- The Moon Orbital Perigee Radius =0.363 mkm
- That means, the moon by a real displacement =77237 km can move around Earth
through the perigee orbit (radius =0.363 mkm), this is the useful result the moon
performs by using Pythagoras triangle,
- Now let's suppose the moon doesn't use Pythagoras triangle, what would happen?
- The moon daily displacement = 88000 km, during 29.53 days the moon moves a
distance = 2.598 mkm BUT for what radius? 2.598 mkm = 2π x (0.413 mkm)
- The Moon Orbital Apogee Radius =0.406 mkm
- So the moon will move along month revolving round Earth through its apogee
orbit (or even far from apogee orbit) because the total distance can't be passed
through any more near orbit around Earth…
- The data shows how Pythagoras triangle is so useful for the moon orbital motion.

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The Angle θ
- The angle (θ) needs to pay some attention for its specific effect…let's summarize
the idea in following
o The angle (θ) changes the real displacement (L = 88000 cos (θ)), through the
moon orbit..
o We know that, when the real displacement (L) be shorter the moon can
move through near orbits to Earth and that means the moon will be near or
at Perigee radius (0.363 mkm)
o When the real displacement (L) be greater the moon has to move through
orbits far from Earth and by that the moon will be near or at to apogee orbit
o That means, the angle (θ) does change the real displacement (L) and also
change the distance between the moon to perigee or to apogee, shortly, the
angle defines the moon position (as a ship) between 2 river banks….
- Let's analyze the angle (θ) in some deep
o We know that (363000)2
+ (86000)2
= (373000)2
o In Pythagoras triangle with the previous dimensions, what's the angle (θ)
value? (θ) = 13.33 degrees
o Also (396800)2
+ (86000)2
= (406000)2
the angle (θ) = 12.229 degrees
o I have used (363000 km and 406000 km) because they are the perigee and
apogee radiuses between which the moon moves.
o The difference between angles = 1.1 degrees
i.e.,
The angle (1.1 deg.) controls the moon motion from perigee to apogee.

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2- The Modified Equation Test
The Modified form
2-1 The Equation Test (6-30 June 2020)
I-Data
Date The Earth Moon Distance
6-6-2020 369418
7-6-2020 373729
8-6-2020 378917
9-6-2020 384534
10-6-2020 390096
11-6-2020 395156
12-6-2020 399345
13-6-2020 402395
14-6-2020 404153
15-6-2020 404574
16-6-2020 403718
17-6-2020 401733
18-6-2020 398840
19-6-2020 395303
20-6-2020 391409
21-6-2020 387432
22-6-2020 383607
23-6-2020 380110
24-6-2020 377044
25-6-2020 374451
26-6-2020 372338
27-6-2020 370703
28-6-2020 369571
29-6-2020 369005
30-6-2020 369106
Data Reference is
https://www.timeanddate.com/moon/egypt/cairo?month=1
Note Please
- In the ascending motion from perigee to apogee the angle (1.5 deg) will be minus
- In the descending motion from apogee to perigee the angle (1.5 deg) will be
positive.

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II- The Equation Test
1st
The Ascending Motion
(1) 6 –June -2020
Jun 6 369418 km Jun 7 373729km (The Next Day)
On 6/6/2020 the moon Earth distance was 369418 km
So we need to know where the moon will be on the next day (7/6/2020)?
Let's try to do that….
- The radius =369418 km so C (orbital circumference) = 369418 x 2π=2.321 mkm
- The moon moves it during 29.53 days ( L0= 2.321 mkm/29.53) = 78602.1 km
- L0= 78602.1 km but L0 = 88000 km Cos θ0
- θ0= 26.721 degrees
- θ1= θ0- 1.5 = 26.721 – 1.5 = 25.221 degrees
- L1 = 88000 km (Cos 25.221 degrees) = 79611 km
- During 29.53 days = L1 x29.53 = 79611 km x 29.53 = 2.35 mkm
- 2.35 mkm = 2π x 374159.6 km
- i.e. The moon on next day (7/6/2020) should be on 374159.6 km
The registered value on 7/6/2020 (373729 km)
The difference = 373729 km – 374159.6 km = 430.6 km

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(2) 7 –June -2020
- L0= 79519.4 km but L0 = 88000 km Cos θ0
- θ1= θ0- 1.5 = 25.36 – 1.5 = 23.86 degrees
- L1 = 88000 km (Cos 23.86 degrees) = 80479.2 km
- During 29.53 days = L1 x29.53 = 80479.2 km x 29.53 = 2.376 mkm
- 2.376 mkm = 2π x 378239.9 km

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(3) 8 – June -2020
- L0= 80623.3 km but L0 = 88000 km Cos θ0
- θ1= θ0- 1.5 = 23. 627 – 1.5 = 22.127 degrees
- 2.407 mkm = 2π x 383126.2 km

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(4) 9 – June -2020
- L0= 81818.4 km but L0 = 88000 km Cos θ0
- θ1= θ0- 1.5 = 21. 60 -1.5 = 20.1 degrees
- 2.44 mkm = 2π x 388396.6 km
The difference = 390096 km – 388396.6 = 1700 km

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(5) 10 – June -2020
- The moon moves it during 29.53 days ( L0= 2.451 mkm/29.53) = 83002 km
- L0= 83002 km but L0 = 88000 km Cos θ0
- θ0= 19.4033 degrees
- θ1= θ0- 1.5 = 19.4033 – 1.5 = 17.9033 degrees
- 2.4728 mkm = 2π x 393559.18 km
The difference = 395156 km –393559.18 km = 1597 km

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(5) 11 – June -2020
Jun 11 395156 km Jun 12 399345 km (The Next Day)
- L0= 84078.5 km but L0 = 88000 km Cos θ0
- θ1= θ0- 1.5 = 17.169 – 1.5 = 15.669 degrees
- 2.502 mkm = 2π x 398216.7 km

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(6) 12 – June -2020
- L0= 84970 km but L0 = 88000 km Cos θ0
- θ0= 15.0794 degrees
- θ1= θ0-1.5 = 15.0794 – 1.5 = 13.5794 degrees
- 2.525 mkm = 2π x 402024 km
- i.e. The moon on next day (13/6/2020) should be on 402024 km
The difference = 402395 km –402024 km = 370.2 km

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(7) 13 – June -2020
- L0= 85618.8 km but L0 = 88000 km Cos θ0
- θ0= 13.3592 degrees
- θ1= θ0- 1.5 = 13.3592 – 1.5 = 11.8592 degrees
- 2.543 mkm = 2π x 404758.6 km
Note Please
- This day is the last day in the moon ascending motion from Perigee to apogee, on
the next day the moon will stay on apogee for one more day (404574 km) on (15th
- 6-2020), and then on (16th
-6-2020) will start its descending motion (403718
km). So we will start the descending motion analysis in next page, and because it's
a descending motion we will add the value 0.985 degrees to the angle (θ)

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1st
The Descending Motion
(8) 15 – June -2020
- L0= 86082.4 km but L0 = 88000 km Cos θ0
- θ1= θ0+ 1.5 = 11.983 +1.5 = 13.483 degrees
- 2.527 mkm = 2π x 402187.6 km

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(9) 16 – June -2020
- L0= 85900 km but L0 = 88000 km Cos θ0
- θ0= 12.5413 degrees
- θ1= θ0+ 1.5 = 12.5413 +1.5 = 14.0413 degrees
- 2.5209 mkm = 2π x 401228.8 km

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(10) 17 – June -2020
- L0= 85478 km but L0 = 88000 km Cos θ0
- θ1= θ0+ 1.5 = 13.75 +1.5 = 15.25 degrees
- 2.507 mkm = 2π x 399023 km
The difference = 398840 km –399023 km = 183 km

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(11) 18 – June -2020
- L0= 84862.36 km but L0 = 88000 km Cos θ0
- θ1= θ0+ 1.5 = 15.346 +1.5 = 16.846 degrees
- 2.487 mkm = 2π x 395838.2 km

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(12) 19 – June -2020
- L0= 84109.8 km but L0 = 88000 km Cos θ0
- θ0= 17.1 degrees
- θ1= θ0+ 1.5 = 17.1 +1.5 = 18.6 degrees
- During 29.53 days = L1 x29.53 =83403.6 km x 29.53 = 2.463 mkm
- 2.463 mkm = 2π x 391984.1 km
The difference = 391409 km – 391984.1 km =575.1 km

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(13) 20 – June -2020
- L0= 83281.3 km but L0 = 88000 km Cos θ0
- θ1= θ0+ 1.5 = 18.848 +1.5 = 20.348 degrees
- 2.436 mkm = 2π x 387778 km
The difference = 387432 km – 387778 km =345.76 km

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(14) 21 – June -2020
- L0= 82435 km but L0 = 88000 km Cos θ0
- θ1= θ0+ 1.5 = 20.485 +1.5 = 21.985 degrees
- 2.409 mkm = 2π x 383511.1 km
The difference = 383607 km – 383511.1 km =96 km

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(15) 22 – June -2020
- L0= 81621.2 km but L0 = 88000 km Cos θ0
- θ0= 21.9495 degrees
- θ1= θ0+ 1.5 = 21.9495 +1.5 =23.4495 degrees
- 2.384 mkm = 2π x 379428.8 km
The difference = 380110 km – 379428.8 km =681.2 km

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(16) 23 – June -2020
- L0= 80877 km but L0 = 88000 km Cos θ0
- θ0= 23.2112 degrees
- θ1= θ0+ 1.5 = 23.2112 +1.5 = 24.7112 degrees
- 2.360 mkm = 2π x 375712.8 km

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(17) 24 – June -2020
- L0= 80224.8 km but L0 = 88000 km Cos θ0
- θ1= θ0+ 1.5 = 24.266 +1.5 = 25.766 degrees
- 2.340 mkm = 2π x 372466.3 km

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(18) 25 – June -2020
- L0= 79673 km but L0 = 88000 km Cos θ0
- θ1= θ0+ 1.5 = 25.126 +1.5 = 26.626 degrees
- 2.323 mkm = 2π x 369725.9 km
The difference = 372338 km – 369725.9 =2612 km

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(19) 26 – June -2020
- L0= 79223.4 km but L0 = 88000 km Cos θ0
- θ0= 25.8 degrees
- θ1= θ0+ 1.5 = 25.8 +1.5 = 27.3 degrees
- 2.309 mkm = 2π x 367520 km
The difference = 370703 km –367520 =3183 km
Note Please
- This day is the last day in the moon descending motion, after it the moon stay in
perigee 3 days!! (28-6-2020 369571 km), (29-6-2020 369005 km), (30-6-2020
369106 km) –
- That tells, when the moon changes its motion from ascending to descending and
vice versa, the moon consumes long time in this process which causes great error
for the calculations…
- So,
- we will analyze the equation test results for 20 days only

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2-2 The Test Results Discussion And Analysis
Let's take a look on the different distances between the equation results and the
registered data in following
Day Registered Data Equation Results Difference
6-6-2020 369418 km --------------- --
7-6-2020 373729 km 374159.6 km 431
8-6-2020 378917 km 378239.9km 677
9-6-2020 384534 km 383126.2km 1408
10-6-2020 390096 km 388396.6km 1700
11-6-2020 395156 km 393559.18km 1597
12-6-2020 399345 km 398216.7 km 1129
13-6-2020 402395 km 402024 km 370
14-6-2020 404153 km 404758.6 km 606
15-6-2020 404574 km --------------- --
16-6-2020 403718 km 402187.6 km 1531
17-6-2020 401733 km 401228.8 km 504
18-6-2020 398840 km 399023 km 183
19-6-2020 395303 km 395838.2 km 535
20-6-2020 391409 km 391984.1 km 575
21-6-2020 387432 km 387778 km 346
22-6-2020 383607 km 383511.1 km 96
23-6-2020 380110 km 379428.8 km 681
24-6-2020 377044 km 375712.8 km 1331
25-6-2020 374451 km 372466.3 km 1985
26-6-2020 372338 km 369725.9 km 2612
27-6-2020 370703 km 367520 km 3183
369571 km ----------------
369005 km -----------
369106 km --------------
[

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The Test Results Analysis:
- The Total Results Are 20 Values
(1st
Category)
o 12 values, defines the moon position in range 1280 km (Error 3%)
(2nd
Category)
o 6 values, defines the moon position in range 1300-2000 km (Error 4.6 %)
(3rd
Category)
o 2 values, defines the moon position in range 2000-3200 km (Error 7.4 %)
- The Results Explanation
- The distance from perigee to apogee =43000 km, and the equation defines the
moon position with a range of error (1280 km),
- So this 1280 km is considered an error (1280 km/43000 km) = (Error 3%)
- Means, when the moon position defined by the equation with a distance 1280 km
from the registered moon position, so the error is 3%
- In the 1st
category, the greatest distance is 1280 km, and so the greatest error in this
category =3%
- By this same rule, the 2nd
Category error 4.6 % and the 3r Category error 7.4%
- The Equation Accuracy
o 12 Values their error 3% the total 36
o 6 Values their error 4.6% the total 27.6
o 2 Values their error 7.4 % the total 14.8
o The general total = 78.4 for 20 Values
o Each Value 3.92 %
o The Equation accuracy = 96.1 %
o The general error = 3.92%
The Conclusion
The Equation Is correct and trustee

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References
The Moon Motion Trajectory Analysis (II)
https://www.academia.edu/44368860/The_Moon_Motion_Trajectory_Analysis_II_
The Moon Motion Basic Equation (III) (Test No.2)
https://www.academia.edu/s/e493aec33a
or
https://www.slideshare.net/Gergesfrancis/the-moon-motion-basic-equation-iii-test-no2
Light Motion Features Are Discovered in Planet Motion
https://www.slideshare.net/Gergesfrancis/light-motion-features-are-discovered-in-planet-motion
or
https://www.academia.edu/44286772/Light_Motion_Features_Are_Discovered_in_Planet_Motion
Can Different Rates Of Time Be Found In The Solar System Motion?(II)
https://www.academia.edu/44334645/Can_Different_Rates_Of_Time_Be_Found_In_The_Solar_System_Motion_II_
Dr. Budochkina, Svetlana Aleksandrovna
Associate professor - Candidate of physico-mathematical sciences (2005)
http://www.mathnet.ru/eng/person22119
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/757317
http://elibrary.ru/author_items.asp?spin=6087-3245
http://orcid.org/0000-0003-3447-0425
http://www.researcherid.com/rid/G-7453-2014
http://www.scopus.com/authid/detail.url?authorId=6507007003
https://www.researchgate.net/profile/Svetlana_Budochkina
Full list of
publications:
http://web-local.rudn.ru/web-
local/prep/rj/index.php?id=2944&p=15209
Mr.Gerges Francis Tawdrous +201022532292
Physics Department- Physics & Mathematics Faculty
Gerges Francis Tawdrous +201022532292
Curriculum Vitae http://vixra.org/abs/1902.0044
E-mail mrwaheid@gmail.com
Linkedln https://eg.linkedin.com/in/gerges-francis-86a351a1
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Quora https://www.quora.com/profile/Gerges-F-Tawdrous
Google https://scholar.google.com/citations?user=2Y4ZdTUAAAAJ&hl=en
Academia https://rudn.academia.edu/GergesTawadrous
List of publications http://vixra.org/author/gerges_francis_tawdrous

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