An asteroid in our Solar System has an eccentricity of 0.550 and a perihelion (closest to Sun) distance of 0.800 AU (Astronomical Units). a)What is its semimajor axis in AU? b)What is its orbital period in Earth years? (Hint: use the simpler form of Kepler’s law for orbitsaround our Sun. You do not need to know 1AU in m). c)What is the ratio of its maximum to minimum speedduring its orbit, vmax/vmin (3 sig figs)? (Hint: use a conservation law)
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An asteroid in our Solar System has an eccentricity of 0.550 and a perihelion (closest to Sun) distance of 0.800 AU (Astronomical Units).
a)What is its semimajor axis in AU?
b)What is its orbital period in Earth years? (Hint: use the simpler form of Kepler’s law for orbitsaround our Sun. You do not need to know 1AU in m).
c)What is the ratio of its maximum to minimum speedduring its orbit, vmax/vmin (3 sig figs)? (Hint: use a conservation law)
d)Choose one: The asteroid’s total mechanical energy is: i) positive, ii) zero iii) negative, iv) any of theaboveare possible.
e) The Earth’s orbit is very close to circular and draw it as acircle of radius 1AU (OK to trace sometime at least the size of a quarter or draw by hand). Label an “S” where the Sunis. Carefully mark theperihelion of the asteroid to the left of the Sun with a “P” and aphelion with an “A” to the right of the Sunto scale (use your ruler to measure it). Show the extent of the asteroid’s semimajor axis andlabel it “SMA”. Then draw the asteroid’s orbit around the Sun on the same drawing (note that the minor axis just has to be smaller than the major axis).
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