Welcome to the article You observe a comet 0 90 AU from Earth with a tail that is 1 0 degrees long 1 How long is the tail in. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
The tail of the comet is approximately 0.015 au long, which corresponds to approximately 2.24 million kilometers. The length of the tail is equivalent to about 520 times the width of the United States.
When observing a comet from Earth, the apparent length of its tail can be measured in degrees. In this case, the tail is observed to be 1.0 degrees long. To find the actual length of the tail in astronomical units (au), we need to use the concept of angular diameter. One degree of angular diameter is equal to 1/360th of the circumference of a circle, which corresponds to 1/360th of the comet's orbital path around the Sun.
Given that the comet is observed at a distance of 0.90 au from Earth, we can set up a proportion to find the actual length of the tail in au:
1 degree / 360 degrees = actual length of the tail / 0.90 au
Solving for the actual length of the tail gives us approximately 0.015 au.
To convert this length to kilometers, we need to know the average distance between the Earth and the Sun, which is approximately 149.6 million kilometers. We can set up another proportion:
1 au / 149.6 million km = 0.015 au / x km
Solving for x gives us approximately 2.24 million kilometers.
Finally, to find out how many times the United States could fit along the length of the tail, we divide the length of the tail (2.24 million km) by the width of the United States (4,313 km). The result is approximately 520 times.
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