The Trojan asteroids share Jupiter's orbit around the Sun: approximately circular with a mean radius 5.2...

Transcribed Image Text:

The Trojan asteroids share Jupiter's orbit around the Sun: approximately circular with a mean radius 5.2 AU (1 AU= 1.5 x 10¹¹ m is the mean radius of the Earth's orbit around the Sun). The Trojans are clustered around two points labelled L4 and L5, where the L4 point is 60° ahead of Jupiter in its orbit and the L5 point is 60° behind Jupiter in its orbit. (a) Determine the mean distance between the asteroids 588 Achilles (at the L4 point) and 617 Patroclus (at the L5 point). (b) A spacecraft travels in a straight line between the two asteroids, accelerating at 10 ms2 until the half-way point between the asteroids, and decelerating at 10 ms from there to the end-point. Assuming that the asteroids are approxi- mately stationary on the timescale of the journey, and neglecting any gravitational effects of Jupiter or the Sun, find the total travel time. (e) Explain why the assumption that the asteroids are approximately stationary dur- ing the journey is well-justified. [2] [3] [1] The Trojan asteroids share Jupiter's orbit around the Sun: approximately circular with a mean radius 5.2 AU (1 AU= 1.5 x 10¹¹ m is the mean radius of the Earth's orbit around the Sun). The Trojans are clustered around two points labelled L4 and L5, where the L4 point is 60° ahead of Jupiter in its orbit and the L5 point is 60° behind Jupiter in its orbit. (a) Determine the mean distance between the asteroids 588 Achilles (at the L4 point) and 617 Patroclus (at the L5 point). (b) A spacecraft travels in a straight line between the two asteroids, accelerating at 10 ms2 until the half-way point between the asteroids, and decelerating at 10 ms from there to the end-point. Assuming that the asteroids are approxi- mately stationary on the timescale of the journey, and neglecting any gravitational effects of Jupiter or the Sun, find the total travel time. (e) Explain why the assumption that the asteroids are approximately stationary dur- ing the journey is well-justified. [2] [3] [1]

Answer rating: 100% (QA)

a The mean distance between the asteroids 588 Achilles at the L4 point and 617 Patroclus at the L5 p... View the full answer