Problem 3. Physical Features of the Giant Planets: Size of Uranus (Palen, et. al. 1st Ed. Chapter 8 Problems 56) Uranus occults (Links to an external site.) a star at a time when the relative motion between Uranus and Earth is 23.0 km/s. An observer on Earth sees the star disappear for 37 minutes and 2 seconds and notes that the center of Uranus passes directly in front of the star. Based on these observations, what value would the observer calculate for the diameter of Uranus? (SHOW YOUR ALGEBRA) What could you conclude about the planet’s diameter if its center did not pass directly
Problem 3. Physical Features of the Giant Planets: Size of Uranus (Palen, et. al. 1st Ed. Chapter 8 Problems 56)
Uranus occults (Links to an external site.) a star at a time when the relative motion between Uranus and Earth is 23.0 km/s. An observer on Earth sees the star disappear for 37 minutes and 2 seconds and notes that the center of Uranus passes directly in front of the star.
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Based on these observations, what value would the observer calculate for the diameter of Uranus? (SHOW YOUR ALGEBRA)
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What could you conclude about the planet’s diameter if its center did not pass directly in front of the star?
Relative motion between earth and Uranus= 23km/s
The star disappears for 37 minutes 2 seconds i.e. (37 x 60 + 2) seconds = 2222 seconds
As the centre of Uranus passes directly in front of the star, therefore, diameter Uranus= relative motion between earth and Uranus × time of disappearance of the star
= 23km/s x 2222 s
= 51,106 km
Therefore the diameter of Uranus is 51,106 km.
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