Week 6 - Kepler's Laws and Retrograde Motion

Please solve and show solution. Please include ILLUSTRATION TOO. Thanks

What would be the answer for 7 8 and 9

What’s the answer the the three 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…

The dwarf planet Pluto has an elliptical orbit with a semi-major axis of 5.91×10^12 m and eccentricity 0.249. Calculate Pluto's orbital period. Express your answer in seconds.   Calculate Pluto's orbital period. Express your answer in earth years.   During Pluto's orbit around the sun, what is its closest distance from the sun? Express your answer with the appropriate units.   During Pluto's orbit around the sun, what is its farthest distance from the sun? Express your answer with the appropriate units.

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).

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.

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.

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.

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

Mars is 1.53 times as far from the Sun as Earth is. Use Keller’s third law to predict the required for Mars to orbit the sun in Earth days.

Use the diagram and the fact that Planet A has a nearly circular orbit while Planet B has a highly elliptical orbit to answer the following questions. Use examples of Newton’s and Kepler’s laws in your answers. a. Does Planet B travel faster or slower when it is closest to the Sun than at other times? Explain your answer. b. Which planet takes longer to orbit the Sun? Explain your answer. c. Does the gravitational attraction between these planets increase or decrease as their orbits move them closer together? Explain your answer.  d. Which planet has the highest average orbital speed? Explain your answer. e. Which planet travels at about the same speed throughout its orbit? Explain your answer.

In an elliptical orbit, the furthest point of the planet from the Sun is called “aphelion”, the closest point is called “perihelion”.  Watch the planet orbit the Sun, see how the force is not always perpendicular to the velocity. For half the orbit the planet speeds up, going fastest at perihelion; slowing for the other half with aphelion being the slowest point in the orbit. Q . Comet NEOWISE (which made a bright appearance in Earth’s skies in July 2020) has a perihelion distance of 0.295 AU and an aphelion distance of 715.14 AU. If its speed was 65 km/s at perihelion, what will be its speed at aphelion? Please, show the process of reaching the answer step by step.

The planet Mercury takes 0.24 sidereal years to go around the sun. What is the distance from the center of Mercury to the center of the sun? (Remember 1 sidereal year = 1 revolution) * Your answer The Planet Jupiter's mean orbital radius is 5.2025 AU's. What is the period of Jupiter in Earth years? Your answer There is belt of asteroids between Mars and Jupiter which circles the "inside" of our solar system. This "Asteroid Belt" has a mean radius from the Sun of 2.6 AU's. How long does it take for one asteroid in the belt to travel around the Sun once? * Your answer

Suppose we launch a satellite in a circular orbit, and want it to revolve once around every 2 hours? How far above the surface of the Earth should this satellite be placed? Report your answer in Earth radii. (Neglect the presence of the moon).

Write 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 expect

Write down an expression for the gravitational filed strength of a planet of radius R and density p. 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 p and use rho and pi. Please use the "Display response" button to check you entered the answer you expect. Display response

From Kepler’s law of orbit, we can infer that the sun is located _____ of the planet’s orbit. a) at the centre b) at one of the foci c) at both foci d) anywhere along the semi-minor axis

Define the kepler's laws of planetary motion in short?

Measure 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.)

Ma years, what is 2. Saturn has an orbital period of 29.46 years, and its average distance to the sun is 9.54 A.U. If Venus has an orbital period of 0.62 its average distance to the sun in astronomical units (A.U.)? M stance A.U., Conceptual Physics Reading and Study Workbook Chapter 14

Suppose you're in a circular orbit around Saturn (M = 5.683 x 1026 kg) with a semi-major axis of a = 237,948 km. a. What is your orbital velocity? b. Using the "Vis-viva" equation (which can be derived from the total energy) v = GM What is the delta-V you would need to get from your current orbit, into an elliptical orbit that has an apoapsis near Titan (a = 1,221,870 km)?

number 4 please

Henry claims that you can cut the force of gravity in half if you double your distance from the center of the planet. Is Henry correct? Explain why or why not. What will happen to the force of attraction when distance is quadrupled (multiplied by four)? Explain how you know.

Illustrate then show complete solutions. Thank you.