Physics: kongity 6.2 - NEWTON'S LAW OF GRAVITATION

Kepler’s first law

**First law**: Planets move in elliptical orbits with the Sun at one focus.

Kepler’s second law

**Second law**: The line between the Sun and a planet sweeps out equal areas in equal time.

Kepler’s third law

**Third law**: The square of the period, ***T***, of a planet's orbital motion is proportional to the cube of the average distance it is away from the Sun, ***r***.

The **universal law of gravitation**

The **universal law of gravitation** states that the gravitational force, ***FG***, between two objects is attractive along the line joining them and equal to:

***FG=G*Mm/r(^2)***

Here, ***M*** and ***m*** are the masses of the two objects, ***r*** is the distance between their centres of mass, and ***G***=6.67×10^(−11)N⋅m2⋅kg^(−2) is Newton's constant of universal gravitation.

A force field

A **force field** is a region in space where a body will experience a force because of its properties such as mass (gravitational field) and charge (electric field). It is a model to describe non-contact forces.

The strength of the ability of an object to exert a gravitational pull at a point in space depends on two variables:

1. The size of its mass, ***M***
2. The distance between that point and the centre of mass of the object, ***r***

The gravitational field strength

The **gravitational field strength**, ***g***, is the gravitational force per unit mass at a point as experienced by a test mass at that point. A test mass is an object with a small mass compared to the mass(es) whose field strength is being determined: A large mass will have its own gravitational field that will affect the system.

If the test mass has a mass ***m***, then we have:

***g=F/m.***

When solving problem involving planets, you must watch for the following points:

* Units, such as radii expressed in kilometres rather than metres.


* Objects at a certain altitude, expressed in terms of ***h***, are a distance ***rplanet+h*** from the centre of the planet, where ***rplanet*** is the radius of the planet.
* The square of the distance from the centre of the gravitating mass, in particular when comparing to the Earth's surface gravitational field strength.

A **satellite**

A **satellite** is an object that is in orbit around another object.