Global gravity

Содержание и основные понятия

Any body with a mass attracts. The force of gravity grows with the work of mass and loses proportionally to the square of the distance between the centres.
GEF · Grade 9
PIF · Baseline
Interactive model
Gravity
gravity
weight
weightlessness
Satellite
01
The physical picture
What happens and what boundaries the model has.
Main message
Any body with a mass attracts. The force of gravity grows with the work of mass and loses proportionally to the square of the distance between the centres.
Weight is the force of the body's action on a support or suspension, and gravity affects the body itself.
The acceleration g is reduced with altitude and depends on the mass and radius of the planet.
Inweightlessness means no weight, but not no gravity.
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.
F
=
G
m
1
m
2
r
2
F=G\frac{m_1m_2}{r^2}
F
=
G
r
2
m
1
​
m
2
​
​
The law of gravity
g
=
G
M
R
2
g=G\frac{M}{R^2}
g
=
G
R
2
M
​
acceleration at surface
Review of the situation
The cosmonauts in orbit are unweighing because the ship and people together fall freely around the Earth.
04
Links and application
In the real world
The cosmonauts in orbit are unweighing because the ship and people together fall freely around 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 topic "World gravity" through a model, not just a formula.
Outcome 2
To distinguish and correctly use terms: gravity, gravity, weight.
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.
Gravity
The universal attraction of all bodies with energy and mass.
gravity
The power of gravitational gravity of the body of Earth or of another celestial body.
weight
The power with which the body acts as a result of interaction on a support or suspension.
weightlessness
The state in which the body does not act on the support or suspension is usually in the case of a joint free fall.
Satellite
A body orbiting a more massive body under the influence of gravity.
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.
F
=
G
m
1
m
2
r
2
F=G\frac{m_1m_2}{r^2}
F
=
G
r
2
m
1
​
m
2
​
​
empirical law
The law of gravity.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
∝
m
1
m
2
F\propto m_1m_2
F
∝
m
1
​
m
2
​
A comparison of body movements shows that gravitational action is proportional to each of the interacting masses.
F
∝
1
r
2
F\propto\frac{1}{r^2}
F
∝
r
2
1
​
The laws of planetary motion and force measurements are consistent with the inverse proportionality of the distance square.
F
=
G
m
1
m
2
r
2
F=G\frac{m_1m_2}{r^2}
F
=
G
r
2
m
1
​
m
2
​
​
The G coefficient is determined experimentally; the law of world gravity is established by experience and observation, not by algebraic proof.
Conditions:
Material points or spherical-symmetric bodies, distance r between their centres; Newtonian approach of weak field and low speeds.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
g
=
G
M
R
2
g=G\frac{M}{R^2}
g
=
G
R
2
M
​
model effect
Acceleration at the surface.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
=
G
M
m
R
2
F=G\frac{Mm}{R^2}
F
=
G
R
2
M
m
​
The body of the mass m at the surface of the spherical planet is affected by the gravity of the planet M mass.
F
=
m
g
F=mg
F
=
m
g
Under Newton's second law, the same power tells the free body acceleration g.
m
g
=
G
M
m
R
2
⇒
g
=
G
M
R
2
mg=G\frac{Mm}{R^2}\Rightarrow g=G\frac{M}{R^2}
m
g
=
G
R
2
M
m
​
⇒
g
=
G
R
2
M
​
The reduction in the mass of the test body shows why the acceleration of the free fall does not depend on its mass.
Conditions:
The point is at the surface of the spherical-symmetric body of the radius R; rotation of the planet, altitude and resistance of the atmosphere are not taken into account.
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 the weight is the force of the body's action on the support or the suspension, and the gravity is acting on the body itself.
How to Check the Mind
The acceleration g is reduced with the height and depends on the mass and radius of the planet. Then check the units, vector direction and behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Global gravity
Any body with a mass attracts. The force of gravity grows with the work of mass and loses proportionally to the square of the distance between the centres.
Weight is the force of the body's action on a support or suspension, and gravity affects the body itself.
The acceleration g is reduced with altitude and depends on the mass and radius of the planet.
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.