An asteroid orbits the sun with a very elliptical orbit. a. If the period of rot

Question

An asteroid orbits the sun with a very elliptical orbit.
a. If the period of rotation of the asteroid is 8 Earth years what is its average distance from the sun? (Hint: Set up a proportionality and answer in terms of AU. 1AU = the distance between the Earth and the Sun.) (10 points)
b. If its closest approach to the sun (perihelion) is 1.5 AU, what is its greatest distance from the sun (aphelion)? (5 points)
c. What is the gravitational potential energy of the asteroid at its greatest distance (aphelion). (In this case, set PE=0 at r = infinity). (5 points)

Explanation / Answer

(b) First you find the length of the semi-major axis (half of the total long axis of the elliptical orbit): Sm(AU) = P(yr)^(2/3) Sm(AU) = 8^(2/3) Sm = 4 AU So you can double that to get the full length of the long axis (the major axis): M = Sm * 2 M = (4 AU) * 2 M = 8 AU Since the Sun is one of the foci, you simply subtract the perihelion distance from the total major axis to get distance to aphelion: D = (8 AU) - (1.5 AU) D = 6.5 AU

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.