Solar system

Содержание и основные понятия

The solar system is formed by the Sun, planets, satellites and small bodies associated with gravity, and the laws of mechanics explain orbits and space flights.
GEF · Grade 9
PIF · Baseline
Interactive model
orbit
Kepler's laws
planet
Satellite
phases of the Moon
01
The physical picture
What happens and what boundaries the model has.
Main message
The solar system is formed by the Sun, planets, satellites and small bodies associated with gravity, and the laws of mechanics explain orbits and space flights.
The planets are moving along the ellipses, one of the tricks the sun is in.
The orbital period increases.
The phases of the Moon are determined by the mutual position of the Sun, the Earth, and the Moon, not by the shadow of the Earth.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
T
2
a
3
=
c
o
n
s
t
\frac{T^2}{a^3}=\mathrm{const}
a
3
T
2
​
=
const
Kepler's Third Law
v
≈
G
M
r
v\approx\sqrt{\frac{GM}{r}}
v
≈
r
GM
​
​
circular orbit
Review of the situation
Mars is further from the Sun, so its orbital velocity is lower and one year longer than the Earth.
04
Links and application
In the real world
Mars is further from the Sun, so its orbital velocity is lower and one year longer than the Earth.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the theme "Sun System" through a model, not just a formula.
Outcome 2
Distinguish and correctly use terms: orbit, Kepler's laws, planet.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
orbit
The trajectory of the body in the field of gravity relative to the chosen central body.
Kepler's laws
Three empirical laws describing orbits, areas observed by the radius-vector and planetary orbital periods.
planet
A massive, almost charred, celestial body orbiting the star and clearing the surrounding area of its orbit.
Satellite
A body orbiting a more massive body under the influence of gravity.
phases of the Moon
The observed shapes of the lighted part of the moon, depending on the mutual position of the sun, the Earth, and the moon.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
T
2
a
3
=
c
o
n
s
t
\frac{T^2}{a^3}=\mathrm{const}
a
3
T
2
​
=
const
empirical law
The third kepler law.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
T
2
∝
a
3
T^2\propto a^3
T
2
∝
a
3
Kepler has established from astronomical tables that the squares of planetary periods are proportional to the cubes of the large hemispheres of their orbits.
T
1
2
a
1
3
=
T
2
2
a
2
3
\frac{T_1^2}{a_1^3}=\frac{T_2^2}{a_2^3}
a
1
3
​
T
1
2
​
​
=
a
2
3
​
T
2
2
​
​
For bodies orbiting one central body, the ratio is the same and allows for a comparison of orbits.
T
2
a
3
=
c
o
n
s
t
\frac{T^2}{a^3}=\mathrm{const}
a
3
T
2
​
=
const
The formula is Kepler ' s empirical law; later the Newtonian model explained the constant as approximately 4pi2/(GM).
Conditions:
Orbits of bodies around one dominant central body; a is a large crescent, mutual outrage, and the mass of satellites are small.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
v
≈
G
M
r
v\approx\sqrt{\frac{GM}{r}}
v
≈
r
GM
​
​
model effect
It's a circular orbit.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
гр
=
G
M
m
r
2
F_{\mathrm{гр}}=G\frac{Mm}{r^2}
F
Gr.
​
=
G
r
2
M
m
​
The mass satellite m is drawn by the central mass body M at a distance r from the centre.
F
ц
=
m
v
2
r
F_{\mathrm{ц}}=m\frac{v^2}{r}
F
c/
​
=
m
r
v
2
​
For a circular orbit, gravity completely creates the necessary centrifugal acceleration.
G
M
m
r
2
=
m
v
2
r
⇒
v
=
G
M
r
G\frac{Mm}{r^2}=m\frac{v^2}{r}\Rightarrow v=\sqrt{\frac{GM}{r}}
G
r
2
M
m
​
=
m
r
v
2
​
⇒
v
=
r
GM
​
​
The equalization of forces and the reduction of the mass of the satellite give a circular orbital velocity; the E.E. mark reminds us of idealization.
Conditions:
The circular orbit around the spherical-symmetrical body, møM; the atmosphere, thrust and influence of the other bodies are negligible.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
You can't move the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that planets are moving along the ellipses, one of which is the sun's tricks.
How to Check the Mind
The orbital conversion period increases with the orbit size. Then check the units, vector direction, and behavior of the result at zero or very large parameter.
Σ
Conclusion on the topic
Solar system
The solar system is formed by the Sun, planets, satellites and small bodies associated with gravity, and the laws of mechanics explain orbits and space flights.
The planets are moving along the ellipses, one of the tricks the sun is in.
The orbital period increases.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.