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Newton's law of gravitation review

Review the key concepts, equations, and skills for Newton's law of gravity, including how to find the gravitational field strength.

Pojęcia kluczowe

Term (symbol)Meaning
Gravitational force (Fg)Attractive force between two objects with mass.
Gravitational fieldA model explaining the influence an object extends to produce a force on other objects.
Gravitational field strength (g)The numerical value of the gravitational field at a point in space. SI units of ms2 or Nkg.
Inertial mass (m)Two objects have the same inertial mass if they experience the same acceleration given the same force. This is the same mass used in Newton’s second law. Experimentally equivalent to gravitational mass. Has SI units of kg.
Gravitational mass (m)The property of matter that causes it to experience a force in a gravitational field. Two objects that balance each other on a scale have the same gravitational mass. Experimentally equivalent to inertial mass. Has SI units of kg.

Równania

EquationSymbolsMeaning in words
Fg=Gm1m2r2Fg is gravitational force, G is the gravitational constant, m1 and m2 are the point-like masses, and r is the distance between the massesThe gravitational force between point-like masses m1 and m2 is directly proportional to their masses and inversely proportional to the square of the distance between them.
g=Fgm2=Gm1r2g is the gravitational field strengthThe gravitational field strength is directly proportional to mass creating the field and inversely proportional to the square of the distance.

Newton's universal law of gravitation

Gravitational force Fg is always attractive, and it depends only on the masses involved and the distance between them. Every object in the universe attracts every other object with a force along a line joining them.
The equation for Newton’s law of gravitation is:
Fg=Gm1m2r2
Gdzie:
Fg is the gravitational force between m1 and m2,
G is the gravitational constant equal to 6.67×1011m3kgs2,
i
m1 and m2 are masses
The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass. This is called an inverse-square law.
For example, if we double the distance between the Earth and the Moon, the attractive force between them would go down (because it is inverse), and it would go down by a factor of 4 instead of 2 (because of the square).
It describes both objects falling down and those in a circular orbit, such as a satellite around Earth.

How to find the gravitational field strength

All objects attract other objects by producing a gravitational field g, which is defined by the gravitational force per unit mass. We find the strength of this gravitational field of mass m1 on any object with mass m2 by dividing our above equation by mass m2.
g=Fgm2=Gm1m2r2m2=Gm1r2

Często spotykane błędy i nieporozumienia

  1. Some people forget that gravity causes attraction between all objects. Every mass attracts every other mass. That means you are even gravitationally attracted to your friend, your pet, and even your pizza.
  2. People forget that the force of gravity is inversely proportional to r2 instead of just r. As the distance increases, the force of gravity decreases by a factor of 1r2.
  3. Sometimes people forget that r is the distance between the centers of mass. We measure the distance between objects from their centers, not their surfaces.

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