Kepler 3rd law: M1 + M2 = P2/D3 Jupiter’s moon Callisto orbits the planet at a distance of 1.88 X 106 km in about 16.7 days. If one year is 365 days, and if 1 AU is 1.5 X 108 km, calculate the mass of Jupiter in solar mass units. (Show your work)

Kepler 3rd law: M1 + M2 = P2/D3 Jupiter’s moon Callisto orbits the planet at a distance of 1.88 X 106 km in about 16.7 days. If one year is 365 days, and if 1 AU is 1.5 X 108 km, calculate the mass of Jupiter in solar mass units. (Show your work)

Astronomy

1st Edition

ISBN:9781938168284

Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Publisher:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Chapter21: The Birth Of Stars And The Discovery Of Planets Outside The Solar System

Section: Chapter Questions

Problem 24E: Kepler’s third law says that the orbital period (in years) is proportional to the square root of the...

See similar textbooks

Similar questions

The table below presents the semi-major axis (a) and Actual orbital period for all of the major planets in the solar system. Cube for each planet the semi-major axis in Astronomical Units. Then take the square root of this number to get the Calculated orbital period of each planet. Fill in the final row of data for each planet. Table of Data for Kepler’s Third Law: Table of Data for Kepler’s Third Law: Planet aau = Semi-Major Axis (AU) Actual Planet Calculated Planet Period (Yr) Period (Yr) __________ ______________________ ___________ ________________ Mercury 0.39 0.24 Venus 0.72 0.62 Earth 1.00 1.00 Mars 1.52 1.88 Jupiter…
Using Kepler’s Third Law (r3 = MT2 where M is the mass of the central star) find the orbital radius in astronomical units of this planet. M = 1.5 times the mass of the sun. Remember to convert days to years using 365.25 as the length of a year in days. Key Points to know: - The semimajor axis of the planet in AU is r = 0.0379 AU - The circumference of the orbit is l = 3.562 x 10^10 m - The orbital velocity in m/s is v = 1.874 x 10^5 m/s Questions that need to be answered: - With that orbital velocity, the radius of the orbit in meters, find the centripetal acceleration of our exoplanet: - Knowing the acceleration that our planet experiences, calculate the force that the host star exerts on the planet: - Knowing the force on the planet, the orbital radius, and the mass of the parent star, use the equation for gravitational force to find the mass of our planet (m2). (To get m1 in kg multiply the mass of the star in solar masses by 1.98 x 1030).
lo Europa Ganymede Callisto Orbital Period (Days) 2 3.57 7.12 16.43 Mass Calculation Amplitude (Jupiter Diameters) 0.00311048 0.00460952 0.2087671 Average: 0.01285714 Mass of Jupiter as determined by Orbital Period (Years) a3 P2 lo: Con vert ↓ Europa: Ganymede: Callisto: 0.00547345 0.00978082 0.01950685 All values should be 3 significant figures! Examples: 6.44x104 or 5.78 or 0.00752 0.0450137 You now have P (period) and a (semi major axis) for each moon orbiting Jupiter. Using the following equation, calculate the mass of Jupiter as measured by each moon. Then average. M≈ Semi Major Axis (AU) 3.266 (This is a modified Kepler's 3rd law which only works if units of AU, Years, and Solar mass are used) 4.84 7.62 13.5 Solar Masses Solar Masses Solar Masses Solar Masses Solar Masses
From the data measured read off the period, P and the orbital radius, a from thegraph for the moon Ganymede . These values will have units of hours for the period P, and Jupiter Diameters (J.D.) for a. Enter your results here:P (period) = _________ hours a (orbital radius) = ________ J.D. After,In order to use Kepler's Third Law, you need to convert the period into years, using: 1 day = 24 hours and 1 year = 365.25 days. The orbital radius must be converted to A.U., using 1050 J.D. = 1 A.U. Enter your converted values here: P (period) = _________ years a (orbital radius) = ________ A.U.
A planet's speed in orbit is given by V = (30 km/s)[(2/r)-(1/a)]0.5 where V is the planet's velocity, r is the distance in AU's from the Sun at that instant, and a is the semimajor axis of its orbit. Calculate the Earth's velocity in its orbit (assume it is circular): What is the velocity of Mars at a distance of 1.41 AU from the Sun? What is the spacecraft's velocity when it is 1 AU from the Sun (after launch from the Earth)? What additional velocity does the launch burn have to give to the spacecraft? (i.e. What is the difference between the Earth's velocity and the velocity the spacecraft needs to have?) How fast will the spacecraft be traveling when it reaches Mars? Does the spacecraft need to gain or lose velocity to go into the same orbit as Mars?
Using Appendix G, complete the following table that describes the characteristics of the Galilean moons of Jupiter, starting from Jupiter and moving outward in distance. Table A This system has often been described as a mini solar system. Why might this be so? If Jupiter were to represent the Sun and the Galilean moons represented planets, which moons could be considered more terrestrial in nature and which ones more like gas/ice giants? Why? (Hint: Use the values in your table to help explain your categorization.)
Kepler’s third law says that the orbital period (in years) is proportional to the square root of the cube of the mean distance (in AU) from the Sun (Pa1.5) . For mean distances from 0.1 to 32 AU, calculate and plot a curve showing the expected Keplerian period. For each planet in our solar system, look up the mean distance from the Sun in AU and the orbital period in years and overplot these data on the theoretical Keplerian curve.
An asteroid is observed to be on a superior orbit with a synodic period of 466.6 days. What are the sidereal orbital period and semi-major axis of this asteroid? Choose the option below that most closely matches your answers. Select one: O a. Sidereal period = 1683 days and %3D semi-major = 2.7 AU O b. Sidereal period = 1683 days and semi-major axis = 4.8 AU O c. Sidereal period = 865 days and semi- major axis = 1.8 AU O d. Sidereal period = 426 day and semi- %3D major axis = 2.7 AU O e. Sidereal period = 1727 days and е. semi-major axis = 0.8 AU
ure This image is taken from the course content (Lessons or Readings). Select the words from the drop-down controls which best describe the image. Eris Pluto Neptune Saturn Uranus Jupiter Mars Earth Sun Venus The image shows the sun, the planets, and the • The objects are Mercury • largest known +
1- MODIS is an Earth Observation sensor onboard TERRA spacecraft flying in a near-polar circular orbit with an orbital period of 98.8 minutes. The width of the swath imaged by MODIS is 2330 km. A- How many orbits does TERRA trace in one day? B- Assuming that the Earth rotates around its polar axis at a rate of 0.2618 rd/hr and that the equatorial radius is 6378 km, do two consecutive swaths of MODIS overlap at the equator? (hint: the length of an arc = angle in rd * radius) C- The radius of the latitude circle at 35 deg is 5224.5 km. Do two consecutive swaths of MODIS overlap at latitude 35 deg? 2- An aerostationary orbit for Mars is equivalent to a geostationary orbit for Earth. It is designed to enable a satellite in that orbit to image always the same surface of Mars. Calculate the altitude of an aerostationary orbit assuming that Mars is spherical, that its sidereal rotational period is 1.02595676 Earth days, its equatorial radius is 3389.50 km and its mass is…
Comet Halley has a semi-major axis of 17.7 AU. (The AU, or Astronomical Unit, is the distance from the Sun to the Earth. 1 AU = 1.50x1011 m.) The eccentricity of Comet Halley is 0.967. a. How far is Comet Halley from the sun at Aphelion, the farthest position from the sun? (Give your answer in AU.)? b. What is comet Halley's orbital time? (Give your answer in years.) Note: Using Kepler's third law in the form: P2 = a3 is convenient. This equation works for any object orbiting the sun when the orbital period is in years and the semi major axis is in AU. The reason this works is because this equation is normalized to earth. The AU and year are both 1 for Earth. c. In what year will Comet Halley start to move back toward the sun?
I. Directions: Complete the given table by finding the ratio of the planet's time of revolution to its radius. Average Radius of Orbit Times of Planet R3 T2 T?/R3 Revolution Mercury 5.7869 x 1010 7.605 x 106 Venus 1.081 x 1011 1.941 x 107 Earth 1.496 x 1011 3.156 x 107 1. What pattern do you observe in the last column of data? Which law of Kepler's does this seem to support? II. Solve the given problems. Write your solution on the space provided before each number. 1. You wish to put a 1000-kg satellite into a circular orbit 300 km above the earth's surface. Find the following: a) Speed b) Period c) Radial Acceleration Given: Unknown: Formula: Solution: Answer: Given: Unknown: Formula: Solution: Answer: Given: Unknown: Formula: Solution: Answer: