Download Astronomy Assignment: Spacecraft Orbits and Gravity Effects on Weight and more Quizzes Astronomy in PDF only on Docsity! PTYS/ASTR 206 – Section 1 – Spring 2009 Activity #3: 1/27/09 NAME:_________________________________________________________________ # 1. The NASA mission STEREO, launched in October, 2006, is two separate spacecraft designed to orbit the Sun nearly along a same orbital path as the Earth, with one spacecraft (A) moving slightly faster that the Earth and the other (B) slightly slower. While both spacecraft, and the Earth, move nearly along the same orbital path around the Sun, in order for them to move at different speeds, they cannot exactly move along the same path. Which spacecraft would you expect to be farther away from the Sun and which would you expect to be closer to the Sun? Explain your reasoning. Spacecraft A must be slightly closer to the Sun in order to move faster along nearly the same path as Earth (it has a slightly smaller orbit, and hence, a shorter orbital period according to Kepler’s 3rd law). It will orbit the Sun in slightly under a year. Spacecraft B must orbit slightly farther away from the Sun than Earth to move slower (it has a slightly larger orbit, and hence, a longer orbital period according to Kepler’s 3rd law). It will orbit the Sun in slightly more than a year. #2. How would your weight change if: A) the Earth were twice as massive, but had the same radius that it currently has? If the Earth’s mass is doubled, the force is doubled (i.e replace Mearth with 2Mearth in the force due to gravity, and you find that the force is just 2 times bigger). B) the Earth was half its present size (1/2 the radius), but the same mass? If the Earth’s radius is halved, the force is 4 times bigger. (i.e replace Rearth with (1/2)Rearth in the force due to gravity, and you find that the force is just 4 times bigger). It is bigger because with the Earth being smaller, you are closer to the center of the Earth, and hence, experience a larger force. #3. In terms of the relationship between the period P and semi-major axis, a, of their orbits around the planet, how do the moons of Jupiter behave? (circle one and provide a brief reason for your answer) A) The moons do not obey the Keplerian relation P2 = ka3, because they orbit Jupiter and not the Sun. B) They obey the relation, P2 = ka3, in which k is the same for planetary motion around the Sun, because it is a universal constant. C) They follow the relationship, P2 = ka3, where k is a constant that is different from the relation governing planetary motion around the Sun. D) The moons do not obey the relation P2 = ka3, because their motion about Jupiter is affected by Jupiter's motion about the Sun. REASON FOR YOUR ANSWER: The orbits are indeed Keplerian. The constant, k, depends on the mass of the two bodies in question (for instance, a planet and the Sun; or a moon and its parent planet, etc.). Since the mass of Jupiter and the mass of the Sun are different, the constant, k, is different.
