Johannes Kepler in his working with data together with Tycho Brahe, put forth three laws which described the motion of the planets across the sky.

The laws are:

- The Law of Orbits:
*The planets move in ellipses with the Sun at one focus*

^{11}mDistance from the Earth to the Sun when at its furthest (aphelion) = 1.521×10^{11}m - The Law of Areas:
*A line drawn from the planet to the Sun sweeps out equal areas in equal times.*This means that bodies move faster when closer to the Sun – the best example of this being the long period comets. They spend only a few months close to the Sun before moving off into deep space – not returning for maybe many hundreds of years. - The Law of Periods:
*The square of the period of any planet is directly proportional to the cube of the semi-major axis of its orbit.*The Earth is 150×10^{9}m from the Sun and it takes one year (3.16×10^{7}s) to orbit the Sun.Therefore Kepler’s constant (r^{3}/T^{2}) for the Solar System is (150×10^{9})^{3}/(3.16×10^{7})^{2}= 3.37×10^{18}m^{3}s^{-2}.

Kepler’s laws were derived for orbits around the sun, but they apply to satellite orbits as well.

**GENERAL EVALUATION (POST YOUR ANSWERS USING THE QUESTION BOX BELOW FOR EVALUATION AND DISCUSSION):**

- State the mathematical expression of Isaac Newton’s law of gravitation.
- What is the mathematical relationship between gravitational intensity and gravitational potential?
- State the Kepler’s laws.
- Considering a rocket launched from the earth’s surface, show that the velocity of escape V
_{0}is given by: V0=2gR−−−−√ - Estimate the possible gravitational force between the earth and the moon at 4 × 10
^{8}m apart if their masses are 6 ×10^{24}kg and 7 ×10^{22}

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