#### Yerzhan Orymbetov

Solar System
mass distance
1,2/2⁰ = 1,2/1M🜨 = 1,2 (Earth 1AU)
1,2/2¹ = 0,6/0,8M🜨 = 0,7 (Venus 0,7 AU)
0,6/2² = 0,15/0,1M🜨 = 1,5 (Mars 1,5 AU)
0,15/2³ = 0,02/0,05M🜨= 0,4 (Mercury 0,4 AU)

MJ (Jupiter's mass), M🜨 (Earth's mass)

The NU2 Lupi planetary system
mass distance
3,74/2⁰ = 3,74/8,7M🜨 = 0,43 AU planet d
3,74/2¹ = 1,87/11,2M🜨= 0,17 AU planet c
1,87/2² = 0,47/4,7M🜨 = 0,1 AU planet b

8,7M🜨 × 0,43 = 3,74 ( planet d)

The HD 37124 planetary system
mass distance
2,2/2⁰ = 2,2/0,69MJ = 3,2 AU planet d
2,2/2¹ = 1,1/0,65MJ = 1,7 AU planet c
1,1/2² = 0,3/0,67MJ = 0,5 AU planet b

0,69M🜨 × 3,2AU = 2,2 AU ( planet d)

M
ass and density of giant planets

Earth mass
(M🜨) DENSITY (g/cm³)
423/318M🜨 = 1,33 (JUPITER 1,33 g/cm³)
423/(7×1)/95
M🜨 = 0,64 (SATURN 0,69 g/cm³)
423/(7×2)/17
M🜨 = 1,78 (NEPTUNE 1,64 g/cm³)
423/(7×3)/14,5
M🜨 =1,39 (URANUS 1,27 g/cm³)

a) 318M🜨×1,33= 423 (Jupiter's density 1,33 g/cm³)
b) 5,2 AU × 1,33 = 7 (Jupiter's distance 5,2AU)
c) Jupiter's mass (318M🜨), Saturn (95M🜨),
Neptune (17M🜨), Uranus (14,5M🜨)

423/(7×0)/318M🜨 (impossible)

RADIUS, MASS (M🜨) and DENSITY (ρ) of planets
19 × 2⁰= 19/14,5/1,27= 1,03 (Uranus1,03 )
19
× = 38/ 17 / 1,64 = 1,36 (Neptune1,00 )
38
× = 152/ 95 /0,69 = 2,32 (Saturn 2,36 )
152
× =1216/318/1,33= 2,87 (Jupiter 2,84 )

a) 14,5 M🜨 ×1,27 g/sm³×1,03 = 19 (Uranus)

Neptune 24,622 km =1,00 17 M🜨 1,64 g/sm³
Uranus 25,362 km (1,03) 14,5 M🜨 1,27 g/sm³
Saturn 58,232 km (2,36) 95 M🜨 0,69 g/sm³
Jupiter 69,911 km (2,84) 318 M🜨 1,33 g/sm³

Gravity and mass of giant planets

Earth mass (M🜨) Gravity (m/s²)
123×2⁰ = 123/14,5M🜨 = 8,5 (Uranus 8,5 m/s²)
123×2¹ = 246/17 M🜨 = 14,5 (Neptune 11,2 m/s²)
246×2² = 984/95 M🜨 = 10,4 (Saturn 10,4 m/s²)
984×2³ =7872/318M🜨 = 24,8 (Jupiter 24,8 m/s²)

a)14,5M🜨×8,5 m/s²=123 (Uranus's gravity 8,5 m/s²)
c) Uranus's mass (14,5 M🜨), Neptune (17 M🜨), Jupiter (318 M🜨), Saturn (95 M🜨)

Probable mass and distance of 9th planet
distance mass
0,55⁰*1653 / 5,2 AU = 318 M🜨 (Jupiter)
0,55¹*1653 / 9,54 AU = 95 M🜨 (Saturn)
0,55² * 1653 / 30 AU = 17 M🜨 (Neptune)
0,55³ * 1653 /19 AU = 14,5 M🜨 (Uranus)

0,55⁴* 1653 / 60 AU = 2,5 M🜨 (9th planet)
0,55⁴* 1653 / 79 AU = 1,9 M🜨 (9th planet)

Perihelion Aphelion
2⁰×0,31=0,31
0,31AU MERCURY 0,47AU 2⁰×0,47=0,47
2¹×0,31=0,62 0,72 AU VENUS
2²×0,31=1,24 EARTH 1,02AU 2¹×0,47=0,94
2³×0,31=2,48 MARS 1,67 AU 2²×0,47=1,88
2⁴×0,31=4,96 4,95 AU JUPITER
2⁵×0,31=9,92 9,05 AU SATURN
2⁶×0,31=19,8 18,4 AU URANUS
2⁷×0,31=39,68 (Eris 38,3 AU)
2⁸×0,31= 79,36 (Sedna 76,2 AU)

9th planet 79 AU
NEPTUNE 30,4 AU
2⁶ *0,47=30,1
9th planet 60 AU 2⁷*0,47= 60

AXIAL TILT

3⁰ = 1 Mercury (0,03⁰)
3¹ = 3 Jupiter (3⁰)
Venus (2,7⁰/177⁰)
3² = 9 Sun (7,25 ⁰)
3³ = 27 Saturn (27⁰)
Neptune (28⁰)
Mars (25⁰)
Earth (23⁰)
3⁴ = 81 Uranus (82⁰/98⁰)

PLANETARY MASS (M🜨)

318/3⁰ = 318 (Jupiter 318
M🜨)
318/3¹ = 106 (Saturn 95,2
M🜨)
318/3² = 35,3 (Neptune 17,1
M🜨)
318/3³ = 11,8 (Uranus 14,5
M🜨)
318/3⁴ = 3,9 (9th planet 3,9
M🜨??)
318/3⁵ = 1,3 (Earth 1
M🜨)
318/3⁶ = 0,5 (Venus 0,81
M🜨)
318/3⁷ = 0,14 (Mars 0,11
M🜨)
318/3⁸ = 0,05 (Mercury 0,05
M🜨)
318/3⁹ = 0,02 (Ganymede 0,02
M🜨)
318/3¹⁰ = 0,01 (Moon 0,01
M🜨)

Yerzhan Orymbetov, 2022

#### Yerzhan Orymbetov

Radius, mass and distance of the planets

284×2⁰/14,5M🜨 /19AU = 1,03 (Uranus 1,03)
284×2¹/ 17M🜨 /30 AU = 1,1 (Neptune 1,0)
284×2² (9th planet)
284×2³/ 95 M🜨 /9,5 AU = 2,5 (Saturn 2,37)
284×2⁴/ 318M🜨 /5,2 AU =2,8 (Jupiter 2,84)

a) Uranus (25,362 km) 1,03 × 14,5 M🜨 ×19 AU = 284
b) Uranus (25,362 km) /Neptune (24,622 km) =1,03
c) If the 9th planet is like Uranus (radius 1,03 and mass 14,5 M🜨) then: Distance = 284×2²/14,5/1,03 = 76 AU.

Neptune 24,622 km (1) 17 M🜨 30 AU
Uranus 25,362 km (1,03) 14,5 M🜨 19 AU
Saturn 58,232 km (2,37) 95 M🜨 9,5 AU
Jupiter 69,911 km (2,84) 318 M🜨 5,2 AU

Yerzhan Orymbetov

#### Yerzhan Orymbetov

Distance and mass of planets

mass distance

1653 / 1,82⁰/ 318 M🜨 = 5,2 AU (Jupiter)
1653 / 1,82¹/ 95 M🜨 = 9,5 AU (Saturn)
1653 / 1,82²/ 17 M🜨 = 29,5 AU (Neptune)
1653 / 1,82³/ 14,5 M🜨= 19 AU (Uranus)

(Jupiter) 318M🜨 × 5,2 AU = 1653

The Gliese 876 planetary system

mass distance

0,5/ 5⁰ / 2,36 MJ = 0,21 (planet b 0,21 AU)
0,5/ 5¹ / 0,74MJ = 0,13 (planet c 0,13 AU)
0,5/ 5² / 0,05MJ = 0,4 (planet e 0,34 AU)
0,5/ 5³ / 0,02 MJ = 0,2 (planet d 0,02 AU)

(Planet b) 2,36 MJ × 0,21 AU = 0,5

MJ (Jupiter's mass), M🜨 (Earth's mass)
Yerzhan Orymbetov

#### Yerzhan Orymbetov

Distance, orbital and rotation period of planets

distance sidereal rotation period
3300/3⁰/30AU/ 165yr/= 0,67 (Neptune 0,67days)
3300/3¹/19AU/ 84yr/ = 0,7 (Uranus 0,72 days)
3300/3² (9th planet)
3300/3³/9,5AU/29,4yr/ = 0,44 (Saturn 0,44 days)
3300/3⁴/5,2AU/11,9yr/ = 0,6 (Jupiter 0,41 days)

(Neptune) 30AU × 164,8yr × 0,67days =~3300

Eccentricity, mass and distance of planets
distance mass eccentricity
83/2⁰/ 5,2AU /318M🜨= 0,05 (Jupiter e=0,05)
83/2¹/ 9,5AU /95 M🜨 = 0,05 (Saturn e=0,056)
83/2² (9th planet)
83/2³/ 19AU /14,5M🜨= 0,04 (Uranus e=0,047)
83/2⁴/ 30AU /17 M🜨 = 0,01 (Neptune e=0,01)

a)(Jupiter) 5,2 AU × 318 M🜨 × 0,05 e = 83
B) If the 9th planet is like Neptune (e= 0,01 and mass 17M🜨) then: Distance = 83/2²/17/0,01 = 122 AU

Yerzhan Orymbetov

#### Yerzhan Orymbetov

Orbital speed and period, distance of planets

distance sidereal orbital speed
26700/3⁰/30AU/ 165yr/= 5,4 (Neptune 5,4 km/s)
26700/3¹/19AU/ 84yr/ = 6 (Uranus 6,8 km/s)
26700/3²/9,5AU/29,4yr/= 10 (Saturn 9,7 km/s)
26700/3³/5,2AU/12yr/= 15,8 (Jupiter 13,1 km/s)

(Neptune) 30AU × 164,8yr × 5,4 km/s =~26700

Yerzhan Orymbetov

#### Yerzhan Orymbetov

Perihelion, orbital speed and period
of inner planets

perihelion sidereal orbital speed
62/2⁰/1,38AU /1,88 yr = 24 (Mars 24 km/s)
62/2¹/0,98AU /1,00 yr = 31 (Earth 30 km/s)
62/2²/0,72AU /0,61 yr = 35 (Venus 35 km/s)
62/2³/ (9 th planet)
62/2⁴/0,31AU/0,24 yr = 52 (Mercury 47 km/s)

(Mars) 1,38 AU × 1,88 yr × 24 km/s =~ 62

Yerzhan Orymbetov

#### Yerzhan Orymbetov

Eccentricity and orbital speed
of inner planets

orbital speed eccentricity
9,7/4⁰/47 km/s = 0,206 (Mercury e=0,206)
9,7/4¹/24 km/s = 0,101 (Mars e=0,093)
9,7/4²/30 km/s = 0,020 (Earth e=0,017)
9,7/4³/35 кm/s = 0,0043 (Venus e=0,0068)

(Mercury) 47 km/s × 0,206 (e) = 9,7

#### Yerzhan Orymbetov

The probable rotation period of Venus and Mercury before the collision

Distance Rotation

1AU/1,52AU (Mars) = 0,5 1,026/1,52² = ~0,5
1AU/1,00AU (Earth) = 1,0 0,977/1² = 1
1AU/0,72AU (Venus) = 1,4 (?) 0,73/0,72² = 1,4
1AU/0,39AU (Mercury)= 2,5 (?)0,387/0,39² = 2,5

Orbital period
1yr/1,88yr (Mars) = 0,5 1,026/1,52/1,88 =~ 0,5
1yr/1,0 yr (Earth) = 1 0,977/1,00/1 = 1
1yr/0,615yr(Venus) = 1,6 0,73/0,615/0,72 = 1,6
1yr/0,241yr(Mercury)=4,1 0,387/0,241/0,39= 4,1

Earth distance 1AU, orbital period 1yr

Distance Orbital period Rotation
2,932/3⁰/1,52AU/1,88 yr = 1,026 (Mars 1,026 days)
2,932/3¹/ 1 AU /1,00 yr = 0,977 (Earth 0,977 days)
2,932/3²/0,72AU/0,615yr = 0,73 (Venus 243 days)
2,932/3³ (9th planet)
2,932/3⁴/0,39 AU/0,24 yr= 0,387 (Mercury 58,6days)

(Mars) 1,52AU × 1,88 yr × 1,026 = 2,932

Yerzhan Orymbetov

#### Yerzhan Orymbetov

Orbital period

1,88/0,39⁰ = 1,88 (Mars 1,88 yr)
1,88/0,39¹ = 4,8 (Ceres 4,6 yr)
1,88/0,39² = 12 (Jupiter 11,86 yr)
1,88/0,39³ = 31 (Saturn 29,5 yr)
1,88/0,39⁴ = 81 (Uranus 84 yr)
1,88/0,39⁵ = 208 (Neptune 165 yr
Pluto 248 yr)
(165+248)/2 =207yr
1,88/0,39⁶ = 534 (Eris 559 yr)

1,88×0,39⁰ = 1,88 (Mars 1,88yr)
1,88×0,39¹ = 0,7 (Venus 0,62 yr)
1,88×0,39² = 0,28 (Mercury 0,24 yr)

0,39 AU (Mercury, distance)
1,88 yr (Mars, orbital period)

Yerzhan Orymbetov

#### Yerzhan Orymbetov

Distance and mass of Sun and planets
mass distance
3000 / 1,81⁰/ 332,950 M🜨 = 0,009 AU (Sun)
3000 / 1,81¹/ 318 M🜨 = 5,2 AU (Jupiter)
3000 / 1,81²/ 95,2 M🜨 = 9,5 AU (Saturn)
3000 / 1,81³/ 17 M🜨 = 30 AU (Neptune)
3000 / 1,81⁴/ 14,5 M🜨= 19,2 AU (Uranus)

Sun's diameter 1,392,000 km / 1 AU = 0,009 AU
Sun's mass 332,950 M🜨 × 0,009 AU = ~3000

Aphelion and mass of giant planets
mass aphelion
1735 / 1,81⁰ / 317,8 M🜨 = 5,46 AU (Jupiter)
1735 / 1,81¹ / 95,16 M🜨 = 10,1 AU (Saturn)
1735 / 1,81² / 17,2 M🜨 = 30,5 AU (Neptune)
1735 / 1,81³ /14,54 M🜨 = 20,1 AU (Uranus)

(Jupiter) 317,8 M🜨 × 5,46 AU = 1735

The distance of the inner planets

88/58,6 × 0,31 AU = 0,47 AU (Mercury)
88/58,6 × 0,47 AU = 0,71 AU (Venus)
88/58,6 × 0,71 AU = 1 AU (Earth)
88/58,6 × 1,00 AU = 1,5 AU (Mars)

88 days (Mercury, orbital period)
58,6 days (Mercury, rotation period)
0,31 AU (Mercury, aphelion)
0,47 AU (Mercury, perihelion)

Yerzhan Orymbetov

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