(a) Calculate the time necessary for Kepler shear to spread rings with the following parameters over 360° in longitude: Width 1 km, orbit 80 000 km from Saturn. Width 100 km, orbit 80 000 km from Saturn. Width 1 km, orbit 120 000 km from Saturn. Width 2 km, orbit 63 000 km from Neptune.
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- Use the small-angle formula to calculate the angular diameter (in degrees) of Saturn (including its rings) (diameter = 9.64 ✕ 105 km) as seen from Earth if Saturn were at the location of the Moon (distance = 384,000 km).How does the dynamo effect take place in Neptune?Venus can be as bright as apparent magnitude −4.7 when at a distance of about 1 AU. How many times fainter would Venus look from a distance of 7 pc? Assume Venus has the same illumination phase from your new vantage point. (Hints: Recall the inverse square law; also, review the definition of apparent visual magnitudes. Note: 1 pc = 2.1 ✕ 105 AU). [fill in the blank] times fainter What would its apparent magnitude be?
- 4) Science fiction movies often portray asteroid belts as crowded, dense regions that require spaceships to maneuver quickly to get through them. In this problem, we will calculate the fraction of volume in an asteroid belt that is actually occupied by asteroids. a) If there are 300,000 large asteroids between 2 and 3 AU from the Sun, and each asteroid is assumed to be spherical with a radius of 100 km, determine the total volume occupied by asteroids in this region. Recall that the volume of a sphere is given by the equation V = 4TR³ /3. b) Let's assume the region in which these asteroids orbit is an annulus with an inner radius of 2 AU, an outer radius of 3 AU, and a thickness of 2Ro. Determine the volume of this region. Recall that the area of a circle is given by the equation A = TR². Here are two conversions that you'll need: 1 AU = 1.496 × 108 km and 1 Ro = 6.955 × 105 km. c) What is the ratio of the volume occupied by asteroids to the volume of the asteroid belt (i.e., the…What is necessary for differentiation to occur in a planet? (A) It must be a mixture of materials with different densities (B) The materials inside the planet must be able to flow (C) The planet must have metal and rock in it O (B) Just A & B A, B and C (A)The innermost rings of Saturn orbit in a circle with a radius of 67,000 km at a speed of 23.8 km/s. Use the orbital velocity law to compute the mass contained within the orbit of those rings.
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