Let's use Kepler's laws for the inner planets. Use the following distances from the sun to calculate the orbital period for each of these planets. Express your answer in terms of Earth years to two significant figures. Note: Use Kepler's law directly. Don't just Google the answers, as they will be a little bit different. When you have calculated them, only submit the value for Mercury. Planet Distance from the sun Period of orbit around the sun Earth 150 million km ___ Earth years Mercury 58 million km ___ Earth years Venus 108 million km ___ Earth years Mars 228 million km ___ Earth years

Let's use Kepler's laws for the inner planets. Use the following distances from the sun to calculate the orbital period for each of these planets. Express your answer in terms of Earth years to two significant figures. Note: Use Kepler's law directly. Don't just Google the answers, as they will be a little bit different. When you have calculated them, only submit the value for Mercury. Planet Distance from the sun Period of orbit around the sun Earth 150 million km _ Earth years Mercury 58 million km _ Earth years Venus 108 million km _ Earth years Mars 228 million km _ Earth years

Stars and Galaxies

9th Edition

ISBN:9781305120785

Author:Michael A. Seeds, Dana Backman

Publisher:Michael A. Seeds, Dana Backman

Chapter4: Origins Of Modern Astronomy

Section: Chapter Questions

Problem 3DQ

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Let's use Kepler's laws for the inner planets. Use the following distances from the sun to calculate the orbital period for each of these planets. Express your answer in terms of Earth years to two significant figures. Answer for the highlighted planet in each question. Note: Use Kepler's law directly. Don't just Google the answers, as they will be a little bit different. When you have calculated them, only submit the value for Earth. Planet Distance from the sun Period of orbit around the sun Earth 150 million km ___ Earth years Mercury 58 million km ___ Earth years Venus 108 million km ___ Earth years Mars 228 million km ___ Earth years
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…
Kepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion. Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU. Does this make physical sense? Explain why or why not.
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).
How long (in Earth-Years) does it take Saturn to orbit the Sun? Use these values of (average) distance to the Sun. Venus: .72 A.U. Saturn: 9.5 A.U. Give your answer in (Earth) years to the correct number of significant figures.
Show your complete and detailed solution. Round off your answers to 4 decimal digits and box your final answers.
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:
In your own words, describe the meaning of Kepler's Third Law of Planetary Motion. Do not use any equations, do not describe the equations in words, just tell me the conceptual meaning.
A newly discovered planet orbits a distant star with the same mass as the Sun at an average distance of 122 million kilometers. Its orbital eccentricity is 0.5. 1. Find the planet's orbital period. Express your answer in years to three significant figures. 2. Find the planet's nearest and farthest orbital distances from its star. Express your answers in millions of kilometers to three significant figures separated by a comma.
You are given the following data from observations of an exoplanet: 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. What is the semimajor axis of this planet in AU? - Knowing the orbital radius in both kn and AU, use the value in km to find the circumference of the orbit, then convert that to meters. (Assume the orbit is a perfect circle). - Knowing the orbital circumference and the period in days, convert the days to seconds (multiply by 86,400) and find the orbital velocity in m/s - 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…
We need to create a scale model of the solar system (by shrinking the sun down to the size of a basketball or ~30cm). First, we will need to scale down actual solar system dimensions (planet diameters and average orbital radiuses) by converting our units. There are two blank spaces in the table below. We will effectively fill in the missing data in the next set of questions. Use the example below to help you. Example: What is the scaled diameter of Mercury if the Sun is scaled to the size of a basketball (30 cm)? The actual diameter of Mercury is 4879 km The Sun's diameter is 1392000 km If the Sun is to be reduced to the size of a basketball, then the conversion we need for this equation will be: 30cm1392000km Here is how we run the conversion: 4879km×30cm1392000km=0.105cm or 0.11cm if we were to round our answer. This means that if the sun in our model is the size of a basketball, Mercury is the size of a grain of sand. We can also see by looking at the table, that we would…
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?

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Planet	Distance from the sun	Period of orbit around the sun
Earth	150 million km	___ Earth years
Mercury	58 million km	___ Earth years
Venus	108 million km	___ Earth years
Mars	228 million km	___ Earth years