Question

During a certain 5-day time period, the line connecting a comet with the sun changes angle by about 3.2°. Assume that the comet’s distance from the sun is roughly 130 million km during this time. During a 5-day time period some time later, the angle of this line changes by 0.80°. How far is the comet from the sun now? Explain.

Answer 1

We calculated that the comet is currently approximately 32.5 million kilometers from the sun.

Step-by-step explanation:

To determine the distance of the comet from the sun now, we can use the concept of apparent motion.

The change in angle of the line connecting the comet with the sun represents the apparent change in position of the comet.

We can set up a proportion using the change in angle and the change in distance to find the current distance of the comet from the sun. Let's say x represents the current distance of the comet from the sun:

Let's say x represents the current distance of the comet from the sun:

(3.2° / 130 million km) = (0.80° / x)

Cross multiplying, we get:

3.2°x = 0.80° * 130 million km

Simplifying, we find:

x = (0.80° * 130 million km) / 3.2°

Calculating this, the current distance of the comet from the sun is approximately 32.5 million km.