Solar Eclipse on Mars (Refer to Exercise 69.) The sun's distance from the surface of Mars is approximately 142,000,000 mi. One of Mars' two moons, Phobos, has a maximum diameter of 17.4 mi. (Data fromThe World Almanac and Book of Facts.) b. Phobos is approximately 5800 mi from Mars. Is it possible for Phobos to cause a total eclipse on Mars?

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insert step 1: Understand the concept of a total eclipse, which occurs when the moon completely covers the sun as seen from a particular point.

insert step 2: Use the formula for angular diameter to compare the apparent sizes of the sun and Phobos as seen from Mars. The formula is: Angular Diameter = (Diameter / Distance) * (180/π) degrees.

insert step 3: Calculate the angular diameter of the sun as seen from Mars using its diameter and distance from Mars.

insert step 4: Calculate the angular diameter of Phobos as seen from Mars using its diameter and distance from Mars.

insert step 5: Compare the angular diameters of the sun and Phobos. If Phobos' angular diameter is greater than or equal to the sun's, a total eclipse is possible.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Angular Size

Angular size refers to the apparent size of an object as seen from a specific point, measured in degrees. It is determined by the object's actual size and its distance from the observer. In the context of eclipses, both the sun and the moon's angular sizes must be compared to determine if one can completely cover the other during an eclipse.

Eclipse Geometry

Eclipse geometry involves the spatial arrangement of the sun, moon, and planet during an eclipse. For a total eclipse to occur, the moon must be positioned directly between the sun and the planet, with the moon's angular size being equal to or greater than that of the sun as viewed from the planet's surface. Understanding this geometry is crucial for determining the possibility of an eclipse.

Distance and Scale

Distance and scale are essential in evaluating the potential for an eclipse. The distance from Mars to Phobos and the sun must be considered to calculate the relative sizes and positions of these celestial bodies. This helps in assessing whether Phobos can block the sun's light completely when viewed from Mars, which is necessary for a total eclipse.