Kepler’s Laws of Orbital Motion

KEPLER’S LAWS OF ORBITAL MOTION

Reporter:

Mante Cros G. Nalzaro

FIRST LAW : LAW OF ORBITS

All planets move in elliptical orbits with the Sun at one focus.

SECOND LAW: LAW OF AREAS

A line that connects a planet to the sun sweeps out equal areas in equal times.

THIRD LAW : LAW OF PERIODS

NEWTON’S LAW OF GRAVITATION

Every object in the universe attracts every object with a force directly proportional to the product of their masses and inversely proportional to the square of the center-to-center distance separating them.

THE GRAVITATIONAL CONSTANT

It is impossible to determine the gravitational constant G from astronomical data alone, as Newton realized. A direct measurement of gravitational force between two known masses a known distance apart is needed. The difficulty here, as the example illustrates, is that gravitational forces are extremely small between objects of laboratory size.

The value of G was finally established in 1798, more than a century after Newton’s work, by Henry Cavendish. He used an instrument called a Torsion Balance. The forces exerted on the small sphere in Cavendish’s experiment could be found from the resulting twist in the fine suspending thread.

THE GRAVITATIONAL EQUATION

So, our equation for Newton’s Law of Gravitation is complete. For two bodies with masses m1 and m2 with center distance r, the force F.

F = G

Where F is in NG is in N-m2/kg2

m1, m2 are in kg

r is in m

REMEMBER

For Gravity Makes Masses Over-React and React

Or

False Gods Make Man Over-Righteous and Rebellious

EXAMPLE

A grocer puts a 100-kg lead block under the pan of his scale. By how much does this increase the reading of the scale when 1 kg bag of mangoes are on the pan, if the center of mass of lead and mangoes are 0.3 m apart?

SOLUTION