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Astro 104- HW 4

Astro 104- HW 4 - Karen Sanchez Astronomy 104 Professor...

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Karen Sanchez Astronomy 104 Professor Wilcots DIS 404 21 November 2010 Homework 4 1. a) Uranus rings within Roche limit: DR= 2.44 (pplanet/pmoon) 1/3 R planet Uranus density: 1.270 Uranus radius: 25,559 km Uranus average moon density: 1.477 (taken from pg. A-12) Work shown: The Roche Limit of Uranus is 59,302.74 km and since Uranus’ farthest rings are 51,00 km away from the planets center (as shown in the book), all of Uranus’ rings reside within the Uranus Roche limit. b) Mars Roche Limit: The density of the moon of Mars is 1.75 realtive to water because it is the average of Mars’ two moons- Phobos and Deimos who have densities of 2.0 and 1.5, respectively. Mars Roche Limit is 10,857 km Work shown: Phobos lies within the Red Planet’s Roche limit. Since it has a semi-major axis of 9,380 km but Deimos does not due to its semi-major axis of 23,500 km. If their semi-major axes get smaller by 20%, Phobos would have a semi-major axis of 7504 km (9380 * .2= 1876, 9380-18760= 7504) which is still within the Roche limit. However, Demois would then have a semi-major axis of 18,800 km which is still outside the Roche limit. In 5 Myr, if the moons of Mars decay by up to 20%, both Phobos and Deimos would reside inside and outside of the Roche limit, respectively. 2. a) Gravitational force exerted on a 1kilogram rock by the Moon when the rock is located at: i) Center of Earth- ii) The side of the Earth facing the Moon- iii) The side of the Earth that is opposite the moon- We experience tides because the moon’s tidal stresses stretch Earth into an elongated shape- tidal bulge. Due to friction, Earth’s rotation drags its tidal bulge around, out of perfect alignment with the Moon and ocean tides arise and fall as the rotation of

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the Earth carries us through the ocean’s tidal bulges. In this instance, the tidal force
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Astro 104- HW 4 - Karen Sanchez Astronomy 104 Professor...

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