Question

keplers laws starry night lab questions

Kepler EAND DATE Name: Class/Section: and let Xohie. hen it has gone TOwing Eart iginal croing e up X with Sous step. Write Noht Student Exercise-Answer Sheet Keplers Laws hatis the orbital period of asteroid X as calculated from Kepler's law? ete an orbit? Does mitation in at aphelion to a planet's question s agee 2 Describe how the period of the orbit depends on the orbital eccentricity, e. Lebad created an orbit with a4 AU, what would the period be? UTSIDE X crosses Ears hen it crosses 4 How lang did it take for X to complete an orbit? Does your answer agree with your computation in question 1? nside Earth's crbite rutside Earth's sXmoving faster at perihelion or at aphelion? OND LAW A Mpteri second law as applied toa planet's orbitalspeed. Does your answer for question s agree with this law? left of X under the ct SHOW INFO the display for the time flow rihelion. Write or aphelion 1How many months does X spend inside Earth's orbit? How many months does it spend outside Earth's orbit? What is the distance from the Sun at perihelion and at aphelion? at perihelion and what is the length with the numlers tentially hazandour ss Earth's orbit plar System are yo ven timelHow hal search for such ler's second law l the semimajor axis for X is I AU, what is the length of the major axis? Does this agree with the numbers you meanured in question 8? . 1 you wanted to find all of the potentially hazardous asteroids that have orbits that cross Earth's orbit, such as your observational search for such objects? (Hint: Think of what Kepler's second law says about elliptical orbits) wtenoid X, where in the Solar System are you most likely to find them at any given time? How would you focus

Answer 1

another object f applies orleita Solution (1) The orbital period is time agien astronomical object takes to complete one orleict around in astronomy usually to planets, asteroids olluting sun, stars, binary slars etc. The orbital period of Asteroid X can therefore be stated with the help of kepler's lave (Third Law) en The square of orlital period of a planch/ asteroid derectly proportional to cube of semimajor ares of its P24a3 where P = orlutel period of Asteroid x a = seminaj or ares of orbit. (2) The eccentricity defines the shape of Ellipse. exiuen the semi-major axes distance a & the eccentricity osecl Osecl then then the the perihelie perihelian distance is a cl-e) 8 aphelian distance is acite) The increase en excentricity increases the semi-major anus distance & hence the period ie otledel period a = 6= @=0 e = 0.7 e = 1 semimajor ares semi minor anis circular orbit Mliptic orbit parabolic orbit ; e = 1.3 hyperbolic orbit

allo (3) of hence sememajor anes & eccentricity of sem-ma semi major aus & otlintal period a= 4 AU so (period) & (semi major axis) i period a semi-major aris) & [Cuau? xr 64 AU period x 8 AU The time required by x to complete an orbit depends on velocity of x as well as the distance The time required therefore can be given as- - circumference of orbit velocity of a The answer es in good agreement with that of question (1) because eccentricity & uelocity (5) x is moving faster at perihelion.