The Gravity of the SituationThe Gravity of the SituationPTYS206-24 Mar 2008Upcoming EventsUpcoming Events• Exam 1 next Tuesday, March 11.• Essays due next Thursday, March 13.• Review session, Thursday, March 6.• New Homework will be posted today,due next Tuesday.• Come to office hours this week!!!!Exam 1Exam 1• Will cover everything so far• Bring your calculator!• You are allowed 1 side of an 8.5x11” paperwith your own notes.• You will be given any numerical values thatyou need, but not equations.• The exam is a mix of multiple choice, shortanswer and long answer questions.EssayEssay• You must pass in an essay nextThursday.• It will be assigned a provisional grade.• I will make comments on it and you willget to revise it to improve the grade.• If you do not pass in the essay yourgrade will be an E and you will not beable to improve it.List of SymbolsList of Symbols• F, force• a, acceleration (not semi-major axis in thislecture)• v, velocity• M, mass of Sun• m, mass of planet• d, general distance• r,radius of circle, semi-major axis of orbit• R, radius of EarthMass andMass and WeightWeightMass - an intrinsic property of matter. Formally, the m inF=ma. The amount of “stuff” in an object.Weight - the force experienced by an object in agravitational field. Weight is equal to mass multiplied bygravitational acceleration, W=mg.Mass and weight are often confused because thegravitational acceleration is the same everywhere on thesurface of the Earth and so mass and weight are directlyproportional.However,Mass and Weight ContinuedMass and Weight ContinuedIn deep space an object still has mass but no weightbecause there is no gravity.Lonely object, a zillionAU from anything, experiencing negligiblegravitational attraction.This is almost true weightlessness.Mass and Weight ContinuedMass and Weight ContinuedThere is a feeling of weightlessness when falling, but onlybecause the acceleration is equal to the gravitationalacceleration. This is not true weightlessness becausethere is still a gravitational force.AccelerationForceShe’s Falling TooWeight on the MoonWeight on the MoonAn astronaut weighs less on the moon than on Earth,but has the same mass.Mass of Moon =7.35×1022 kgRadius of Moon = 1.74×106 mGravity on Moong = GM/R2g = (6.67×10-11) (7.35×1022)(1.74×106)2g = 1.6 m s-2This is 1/6 th the value on Earth.Units for Mass and WeightUnits for Mass and WeightSI: Mass - kilograms, Force - Newtons (kg m s-2)English: Mass - slugs, Force - poundsTechnically, it is incorrect to say that someone weights Xkilograms (that’s a mass) or to say that someone has amass of Y pounds (that’s a weight).In Europe (metric system) kilograms are incorrectly usedto describe weight. In the US pounds are incorrectlyused to describe mass.Escape VelocityEscape VelocityThe velocity neededto escape thegravitational pull f aplanet or star isVesc = (2GM/R)1/2Escape VelocityEscape VelocityNotice, that Vesc does not depend on direction. A rocket fired at45˚ will escape a planet just as well as a rocket fired vertically.(Of course, firing a rocket downward doesn’t work.)Apollo 7Don’t Try ThisEscape VelocityEscape VelocityNotice, that Vescdepends on R, thedistance from thecenter of the planet orstar. Thus, smallervelocities are neededfor escape, the furtherone is from theattracting body.Escape Velocity on EarthVesc = (2GM/R)1/2Vesc = (2•6.67×10-11•5.97×1024 /6.37×106 )1/2Vesc = 1.12×104 m/s = 11.2 km/sOr roughly 25,000 miles per hourApproachApproachUsing algebra put the unknown quantity on the left handside of the equation and all the known quantities on theright hand side.Write down an algebraic expression before insertingany numbers.If you are given quantities as ratios (ratio of stars massto sun’s mass, etc.) then use them as such. It’ll makethe math easier.Think about the solution before you calculate it. Whatdo you expect the answer to be, big or small, fast orslow?Using NewtonUsing Newton’’s Form of s Form of KeplerKepler’’s s Third Law:Third Law:Example 1Example 1Planet Gabrielle orbitsstar Xena. The semimajor axis of Gabrielle'sorbit is 1 AU. Theperiod of its orbit is 6months. What is themass of Xena relative tothe Sun?Using NewtonUsing Newton’’s Form of s Form of KeplerKepler’’s s Third Law:Third Law:ExampleExample 22Planet Linus orbits starLucy. The mass of Lucy istwice the mass of the Sun.The semi-major axis ofLinus' orbit is 8 AU. Whatis the orbital period forLinus?Using NewtonUsing Newton’’s Form of s Form of KeplerKepler’’s s Third Law:Third Law:ExampleExample 33Planet Osiris orbits star Isis.The mass of Isis is half themass of the Sun. Theperiod of Osirisʼ orbit is 16years. What is the semi-major axis of Osirisʼ orbit?Using NewtonUsing Newton’’s Form of s Form of KeplerKepler’’s s Third Law:Third Law:ExampleExample 44Jupiter's satellite (moon)Io has an orbital period of1.8 days and a semi-majoraxis of 421,700 km. Whatis the mass of Jupiter?Using NewtonUsing Newton’’s Form of s Form of KeplerKepler’’s s Third Law:Third Law:ExampleExample 55The moon has an orbit witha semi-major axis of384,400 km and a period of27.32 days. What is themass of the
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