Kepler's First Law

All planets orbit the sun on elliptical paths. The Sun is always in one focus of that ellipse.

Ellipses might be something you haven’t studied yet, so here are the basics:

• Ellipse is defined by two points - foci (F1 and F2). The sum of distances from any point on the ellipse to each of the foci is constant.
• The ellipse has two axes - the major axis (S1S2, usually written as “a”) and the minor axis (S3S4, usually written as “b”). Semi-major and semi-minor axis is half of that length.
• The eccentricity of the ellipse is the measure of its deviation from the circle (which has both foci at the same point) and is expressed as the ratio of the distance between the origin and foci and major axis: MF1/S1S2.
• If the centre of a coordinate system is placed at the origin (M), each point of the ellipse fulfils the equation of a standard ellipse:

\(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\)

Kepler's Second Law

Radius-vector of the planet (line star-planet) sweeps out equal areas during equal time intervals - sector-speed of the planet is constant.

This basically says that when the planet is close to the star it moves faster than when it is further.

Kepler's Third Law

Ratio of the square of planet’s orbital period and the cube of semi-major axis is constant.

\(\frac{T^2}{a^3} = const\)

In our solar system, this ratio is equal to exactly 1 (when the period is expressed in Earth years and the length of the semi-major axis is expressed in astronomical units).

Newton’s Law of Gravity

Newton’s law of gravity applies on every pair of particles in the universe, and says that the force with which they attract is proportional to the product of their masses and inversely proportional to the square of the distance between them:

\(F = \frac{GMm}{r^2}\)

Coefficient G is called gravitational constant and its value is \(G = 6.67\times 10^{-11} \: Nm^2kg^{-2}\)

Written by Pavle Ignjatovic