The original equation, using P as the center, is x^2/(228000000)^2 + y^2/(227030834.9)^2 = 1.
The foci, C, the sun, is 21,000,000.
What is the new equation using the sun as the center? (How do the units shift to create the new equation?)
Activity Lab Martian Math Applying conic sections Even though we discovered life haven on Mars, we know a lot of other things about the planet. Mars has a day about 25 hours a pattern of seasons similar to Earth's and long, icecaps Mars also has surface temperatures that rarely rise above freezing and almost no oxygen in its Mars is often called the atmosphere. Red Planet because red deserts cover its surface. Earth's orbit is Activity 1 almost circular Mars is 207,000,000 km eccent a. Mars travels in an elliptical orbit with the sun at one only 0.0167 from the sun at of its foci. Use the data from the diagram to calculate its closest point y a, b, and c of this elliptical orbit. its perihelion) b. Point P is the midpoint between Mars' closest and farthest distances to the sun. Use your values of a and b to write an equation of the elliptical orbit of Mars relative to a coordinate system drawn through point PO-axis in gray). Use distances in millions of kilometers. c. It is also useful to define Mars' motion relative to the sun. Imagine a new coordinate system y-axis in black) with its origin at the center of the sun. Rewrite your equation for the ellipse in this new coordinate system. d. Critical Thinking Explain how the eccentricity of a Not drawn to scale T Mars is 249,000, planet's orbit can affect its annual weather cycle. from the Sun at its The eccentricity farthest point (its of Mars' orbit is aphelion) 0.0934 artian sand dunes
Show transcribed image text Activity Lab Martian Math Applying conic sections Even though we discovered life haven on Mars, we know a lot of other things about the planet. Mars has a day about 25 hours a pattern of seasons similar to Earth's and long, icecaps Mars also has surface temperatures that rarely rise above freezing and almost no oxygen in its Mars is often called the atmosphere. Red Planet because red deserts cover its surface. Earth's orbit is Activity 1 almost circular Mars is 207,000,000 km eccent a. Mars travels in an elliptical orbit with the sun at one only 0.0167 from the sun at of its foci. Use the data from the diagram to calculate its closest point y a, b, and c of this elliptical orbit. its perihelion) b. Point P is the midpoint between Mars' closest and farthest distances to the sun. Use your values of a and b to write an equation of the elliptical orbit of Mars relative to a coordinate system drawn through point PO-axis in gray). Use distances in millions of kilometers. c. It is also useful to define Mars' motion relative to the sun. Imagine a new coordinate system y-axis in black) with its origin at the center of the sun. Rewrite your equation for the ellipse in this new coordinate system. d. Critical Thinking Explain how the eccentricity of a Not drawn to scale T Mars is 249,000, planet's orbit can affect its annual weather cycle. from the Sun at its The eccentricity farthest point (its of Mars' orbit is aphelion) 0.0934 artian sand dunes