Kepler's lawsplanetary motion

Johannes Kepler's primary contributionastronomy/astrophysics werethree lawsplanetary motion. Kepler derived these laws,part, by studyingobservationsBrahe. Isaac Newton would later verify these lawshis lawsmotionuniversal gravity. The generic terman orbiting object"satellite".

Tablecontents

1 Kepler's LawsPlanetary Motion 2 Kepler's First Law 3 Kepler's Second Law 4 Kepler's Third Law (Harmonic Law) 5 Not Just ApplicablePlanets 6 Kepler's UnderstandingSaid Laws 7 Newton's FormKepler's Third Law

Kepler's LawsPlanetary Motion

• Kepler's First Law (1609): The orbit, ofplanet aboutstar,an ellipse withstar at one focus.

• Kepler's Second Law (1609): A line joiningplanetits star, sweeps out equal areas during equal intervalstime.

• Kepler's Third Law (1618): The square ofsidereal period,an orbiting planet,directly proportional tocube oforbit's semimajor axis.

Kepler's First Law

• Kepler's First Law (1609): The orbit, ofplanet aboutstar,an ellipse withstar at one focus.

Thereno object atother focus ofplanet's orbit. The semimajor axis, a, isaverage distance betweenplanetits star.

Kepler's Second Law

• Kepler's Second Law (1609): A line joiningplanetits star, sweeps out equal areas during equal intervalstime.

Thisalso known aslawequal areas. Supposeplanet takes 1 daytravel from points AB. During this time, an imaginary line, fromSun toplanet, will sweep out a, roughly, triangular area. This same amountarea will be swept every day.

Asplanet travelsits elliptical orbit; its distance, fromSun, will vary. As an equal areaswept, during any periodtime;since,distance fromplanetit's orbiting star varies; one can conclude thatorder forarea being sweptremain constant; that,planet must varyvelocity. Planets move most rapidly when at perihelionmore slowly when at aphelion.

This law was developed,part, fromobservationsBrahe; which, indicated thatvelocity,planets, was not constant.

Kepler's Third Law (Harmonic Law)

• Kepler's Third Law (1618): The square ofsidereal period,an orbiting planet,directly proportional tocube oforbit's semimajor axis.
  • P² ∝ a³
  • P = object's sidereal periodyears
  • a = object's semimajor axis,AU

The largerdistance (betweenplanetits sun), a,longersidereal period. By understanding this, andsecond law, one can determine; that,larger an orbit--sloweraverage velocity,an orbiting object, will be (assatellite will be consistently farther fromobject being orbited).

Newton would modify this third law, noting thatperiodalso affected bysatellite's mass.

Not Just ApplicablePlanets

The lawsapplicable whenevercomparatively light object revolves aroundmuch heavier one becausegravitational attraction. Itassumed thatgravitational effect oflighter object onheavier onenegligible. An example iscase ofsatellite revolving around Earth.

Kepler's UnderstandingSaid Laws

Kepler did not understand why his laws were correct,was Isaac Newton who discoveredanswerthis.

Newton's FormKepler's Third Law

Newton, understanding that his third lawmotion was relatedKepler's third lawplanetary motion, devisedfollowing:

where:

• P = object's sidereal periodyears
• a = object's semimajor axis,AU
• G = Gravitational constant
• m₁ = massobject 1
• m₂ = massobject 2