21st Century Astronomy (fifth Edition)
5th Edition
ISBN: 9780393603330
Author: Laura Kay, Stacy Palen, George Blumenthal
Publisher: W. W. Norton & Company
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 3, Problem 31QP
To determine
Find the given graph is linear or logarithmic and find the value semimajor axis and period of Saturn.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Using Kepler's 3rd law solve the following problem. Show your work and highlight your answer.
In a distant star system there are many inhabitable planets. One of these planets is named Qomar. Qomar is 3.2 AU's from its star and takes 6.5 Earth years to go around its star once. There is another planet in the same star system called Ferenginar. Ferenginar is 0.9 AUs from the star. What is the length of a Ferengi year (on Ferenginar) in terms of Earth years?
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 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).
Chapter 3 Solutions
21st Century Astronomy (fifth Edition)
Ch. 3.1 - Prob. 3.1CYUCh. 3.1 - Prob. 3.2CYUCh. 3.2 - Prob. 3.3CYUCh. 3.2 - Prob. 3.4CYUCh. 3.3 - Prob. 3.5CYUCh. 3.4 - Prob. 3.6CYUCh. 3 - Prob. 1QPCh. 3 - Prob. 2QPCh. 3 - Prob. 3QPCh. 3 - Prob. 4QP
Ch. 3 - Prob. 5QPCh. 3 - Prob. 6QPCh. 3 - Prob. 7QPCh. 3 - Prob. 8QPCh. 3 - Prob. 9QPCh. 3 - Prob. 10QPCh. 3 - Prob. 11QPCh. 3 - Prob. 12QPCh. 3 - Prob. 13QPCh. 3 - Prob. 14QPCh. 3 - Prob. 15QPCh. 3 - Prob. 16QPCh. 3 - Prob. 17QPCh. 3 - Prob. 18QPCh. 3 - Prob. 19QPCh. 3 - Prob. 20QPCh. 3 - Prob. 21QPCh. 3 - Prob. 22QPCh. 3 - Prob. 23QPCh. 3 - Prob. 24QPCh. 3 - Prob. 25QPCh. 3 - Prob. 26QPCh. 3 - Prob. 27QPCh. 3 - Prob. 28QPCh. 3 - Prob. 29QPCh. 3 - Prob. 30QPCh. 3 - Prob. 31QPCh. 3 - Prob. 32QPCh. 3 - Prob. 33QPCh. 3 - Prob. 34QPCh. 3 - Prob. 35QPCh. 3 - Prob. 36QPCh. 3 - Prob. 37QPCh. 3 - Prob. 38QPCh. 3 - Prob. 39QPCh. 3 - Prob. 40QPCh. 3 - Prob. 41QPCh. 3 - Prob. 42QPCh. 3 - Prob. 43QPCh. 3 - Prob. 44QPCh. 3 - Prob. 45QP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Show your complete solution and box your answers.arrow_forwardAs discussed in class, the moon is receding from the Earth due to tides at a rate of ~4 cm/year. Let’s assume that rate has been constant throughout time (it wasn’t, but we can use it to illustrate some key points). Its current semi-major axis is 384,400 km.a) If the moon formed 4.5 billion years ago and has been receding from the Earth ever since, what was its original semi-major axis? What was its original orbital period?b) What would the apparent size of the Moon have been in the sky as viewed from Earth? That is, in Hmwk 2, you were told the diameter of the Moon spans about 0.5o when viewed from Earth today. What would it have been when the Moon first formed? Reletive Numbers Relevant Numbers1 AU = 150,000,000 km = 1.5x108 kmEccentricity of Earth’s Orbit: 0.0167Radius of Earth: 6371 kmMass of Earth: 5.96x1024 kgRadius of the Moon: 1737 kmMass of Moon: 7.34x1022 kgRadius of Mars: 3390 kmMass of Mars: 6.4x1023 kgRadius of the Sun: R⦿=696,300 kmMass of the Sun: M⦿=2x1030…arrow_forward1 1 |.. 2 . 1.. What is the eccentricity of this orbit? SHOW YOUR WORK. st1 4. 3. 14 -5- 6. Using Kepler's Third Law, fill in the blanks for this data table. Show your work on the right. Planet Distance from Sun (AU) Period of Revolution (in Earth Years) Mercury 0.387 0.241 Venusarrow_forward
- Say you have designed a machine that will allow you to become to first human to visit the center of the Earth. The journey straight down from your home to the center of the planet's core will take you 10 hours (at constant speed). Use this information and your own research to determine about how long it will take you to pass through the Earth's crust. PLEASE SHOW YOUR WORK.arrow_forwardDrag the moon to various locations in order to determine the quantitative effect of distance upon the gravitational force. Examine the effect of doubling, tripling and quadrupling the distance of separation (as measured from planet'scenter). Consider the planet'ssurface to be a distance of one Earth-radius (1 Rplanet). Use the table at the right to record data for whole-number multiples of Rplanet.Use your data to complete the following sentences.If the separation distancebetween the moonand the planetis ... a. ... increased by a factor of 2, then the Fgravis ______________ by a factor of _______.b. ... increased by a factor of 3, then the Fgravis ______________ by a factor of _______.c. ... increased by a factor of 4, then the Fgravis ______________ by a factor of _______arrow_forwardWrite down an expression for the gravitational filed strength of a planet of radius R and density ρ. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate without the quotes). For Greek letters such as ?ρ and ?π use rho and pi. Please use the "Display response" button to check you entered the answer you expectarrow_forward
- 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…arrow_forwardMeasure the periods for each planet. Measure the orbital radius of each planet. Calculate the ratios of square of the periods and cubed of the radii for the planets. Compare the results and comment if your result confirms Kepler's Third Law. (Pic1 has the yellow and bluw planets points plotted. Pic2 has the grey and red planet plots listed.)arrow_forwardDetermine what the period of revolution of the Earth would be if its distance from the sun would be 4 AU rather than 1 AU. Assume that the mass of the Sun remains the same. State the law that you use to figure this out, and show your calculation.arrow_forward
- Directions: Use GRESA method. note: please thoroughly explain your answer and do not forget to follow the GRESA (Given, Required, Equation, Solution, Answer)! thank you solve LAST three subparts ill give thumbs uparrow_forwardJust need help with questions d, e and f A mini satellite weighing 50 kg is going to be launched into an orbit around earth by arocket. One sidereal day (period of earth’s self-orbit) is 23 hours, 56 minutes and 4.1seconds. (a) The rocket is to be launched from a platform in the Mongolian Plateau with a heightof 3.5 km above earth surface. Calculate the acceleration due to earth’s gravity atthis elevation.(b) The satellite shall complete 10 orbits in precisely 1 sidereal day. Calculate theorbital height and orbital velocity of the satellite.(c) Once the satellite is in this orbit, what is the acceleration due to earth’s gravityexperienced by the satellite?(d) Referring to your answer in part (c), explain why the satellite does not fall towardsearth as a result of earth’s gravitational pull?(e) Calculate the total energy of the satellite in orbit, using infinity as frame ofreference.(f) Calculate the escape velocity to leave earth’s gravitational well.arrow_forwardPlease show the formula you used. 1. What is the force exerted by the Sun on Earth? (Mass of Earth: mE = 5.97 × 1024 [kg] , Mass of Sun: mS = 1.99 × 1030 [kg]) answer format: F(SE) =___ E=____ choose one direction: a) +i b) +j c) +k 2. What is the force exerted by the Moon on Earth? (Mass of Moon: mM = 7.34 × 1022 [kg] ) answer format: F(ME) =___ E=____ choose one direction: a) +i b) +j c) +karrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Stars and Galaxies (MindTap Course List)PhysicsISBN:9781337399944Author:Michael A. SeedsPublisher:Cengage Learning
Foundations of Astronomy (MindTap Course List)PhysicsISBN:9781337399920Author:Michael A. Seeds, Dana BackmanPublisher:Cengage Learning
Stars and Galaxies (MindTap Course List)
Physics
ISBN:9781337399944
Author:Michael A. Seeds
Publisher:Cengage Learning
Foundations of Astronomy (MindTap Course List)
Physics
ISBN:9781337399920
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning
Kepler's Three Laws Explained; Author: PhysicsHigh;https://www.youtube.com/watch?v=kyR6EO_RMKE;License: Standard YouTube License, CC-BY