Kepler’s Laws provided early astronomers with a useful framework for understanding planetary motion.

Johannes Kepler described his laws of planetary motion between 1609 and 1619, he was one of the first people to like to the skies and encapsulate the behavior of stars, moons and planets into laws.

The **first law** described the orbits of planets to be elliptical where one of the foci were a sun. However, some orbits are not elliptical, rather they are circular. This is a special case where both foci of the elliptical orbit occur at the same spot.

The **second law** found a relationship between the movement of a planetary body. It’s speed is variable throughout its orbit – the area the radius sweeps is equal to the time it takes to sweep it for differing points along the elliptical path.

In the below diagram, area S_{1} is swept in the same time as area S_{2}.

The third law states for multiple bodies orbiting the same mass, the square of the period of revolution divided by the cube of the eclipse will be constant. Sometime this is referred to the semimajor axis of the ellipse being the same.

- r = the distance between the center of two bodies
- G = Universal gravitational constant, 6.67 * 10
^{-11}N m^{2}kg^{-2} - T = the period of rotation
- M = the mass of the object being orbited

What to Memorize for Kepler’s Laws.

Law 1: Planetary orbits are elliptical, the sun is a foci.

Law 2: radius vector for area from the sun to a planet sweeps equal areas in equal times.

Law 3:

HSC Questions for Kepler’s Laws.

**Question 1. [4 mark]**

Evaluate Kepler’s law’s contribution to our understanding of motion.

**Question 2. [4 marks]**

The mass of the sun is 1.989 × 10^30 kg and the radius between the centre of earth and the sun is 147.79 million km.

1.989 × 10^30 kg = mass of sun

148.97 * 10^9 m radius between sun to earth

a) What is the period of the earth around the sun

b) What is the average velocity of the earth around the sun

c) What is the average angular velocity of the earth around the sun

**Question 3.**

Two satellites orbit a distant earth like planet, one has a mass of 3 Ton and the other has a mass of 4 Ton, if the lighter satellite has a radius of 345 000 m from the planet and the heavier is 300 000 m from the surface and the planet has a 300 000 m radius. The lighter satellite takes 10. days to orbit the planet. How long does the heavier satellite take to orbit the other planet.

Answers.

Q2a) 3.14 *10^7 s

b) 9.44 * 10^5 m/s

c) 2*10^-7 rad/s

Q3) 8.1 days or 700595 sec

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