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- 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?Let us imagine that the spectrum of a star is collected and we find the absorption line of Hydrogen-Alpha (the deepest absorption line of hydrogen in the visible part of the electromagnetic spectrum) to be observed at 656.5 nm instead of 656.3 nm as measured in a lab here on Earth. What is the velocity of this star in m/s? (Hint: speed of light is 3*10^8 m/s; leave the units off of your answer) Question 4 of 7 A Moving to another question will save this response. 1 6:59 & backs4) 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…
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