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
- 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 150×109 m from the Sun and it takes one year (3.16×107 s) to orbit the Sun.Therefore Kepler’s constant (r3/T2) for the Solar System is (150×109)3/(3.16×107)2 = 3.37×1018m3s-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 V0is given by: V0=2gR−−−−√
- Estimate the possible gravitational force between the earth and the moon at 4 × 108m apart if their masses are 6 ×1024kg and 7 ×1022