Questions from General Calculus

Q: Jupiter’s orbit has eccentricity 0.048 and the length of the

Jupiter’s orbit has eccentricity 0.048 and the length of the major axis is 1.56 × 109 km. Find a polar equation for the orbit

Q: The orbit of Halley’s comet, last seen in 1986 and due

The orbit of Halley’s comet, last seen in 1986 and due to return in 2061, is an ellipse with eccentricity 0.97 and one focus at the sun. The length of its major axis is 36.18 AU. [An astronomical unit...

Q: Comet Hale-Bopp, discovered in 1995, has an elliptical

Comet Hale-Bopp, discovered in 1995, has an elliptical orbit with eccentricity 0.9951. The length of the orbit’s major axis is 356.5 AU. Find a polar equation for the orbit of this c...

Q: The planet Mercury travels in an elliptical orbit with eccentricity 0.

The planet Mercury travels in an elliptical orbit with eccentricity 0.206. Its minimum distance from the sun is 4.6 × 107 km. Find its maximum distance from the sun.

Q: The distance from the dwarf planet Pluto to the sun is 4

The distance from the dwarf planet Pluto to the sun is 4.43 × 109 km at perihelion and 7.37 × 109 km at aphelion. Find the eccentricity of Pluto’s orbit.

Q: Using the data from Exercise 29, find the distance traveled by

Using the data from Exercise 29, find the distance traveled by the planet Mercury during one complete orbit around the sun. (If your calculator or computer algebra system evaluates definite integrals,...

Q: Plot the point whose polar coordinates are given. Then find two

Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r

Q: Find the vertex, focus, and directrix of the parabola and

Find the vertex, focus, and directrix of the parabola and sketch its graph. x2 = 6y

Q: Test the series for convergence or divergence. /

Test the series for convergence or divergence.

Q: Find the vertex, focus, and directrix of the parabola and

Find the vertex, focus, and directrix of the parabola and sketch its graph. 2y2 = 5x