Comet Halley has a mass of approximately \(2.2 \times 10^{14}\) kg. It loses about \(3 \times 10^{11} \mathrm{kg}\) each time it passes the Sun. a. The first confirmed observation of the comet was made in 230 BCE. Assuming a constant period of 76.4 years, how many times has it reappeared since that early sighting? b. How much mass has the comet lost since 230 BCE? c. What percentage of the comet's total mass does this amount represent?

Mass loss is a crucial concept in understanding astronomical objects, especially comets like Halley's Comet. When Comet Halley passes near the Sun, it loses a portion of its mass due to the Sun's heat. The heat causes the comet's ices to sublimate (turn directly from solid to gas), releasing dust and gas into space. This process forms the comet's glowing coma and tail.
In this exercise, we calculate the mass loss by multiplying the amount of mass lost per passage by the number of passages (29 in this case). The comet loses \(3 \times 10^{11}\) kg each time it orbits the Sun. Multiplying this by 29, we find the total mass loss to be \(8.7 \times 10^{12}\) kg. Understanding mass loss helps us predict how a comet will evolve over time and informs us about the longevity of such celestial bodies.

Astronomy calculations involve understanding and applying mathematical principles to determine various properties and behaviors of celestial objects. In this case, we used simple arithmetic and algebra to derive the needed values.
First, we calculated the number of years from the first confirmed observation of Comet Halley (230 BCE) to the present year (2023 CE). This was done by adding the years before the common era (BCE) to the years in the common era (CE): 230 + 2023 = 2253 years.
Next, to find how many times the comet has reappeared, we divided this time span by the comet's period of 76.4 years: \(\frac{2253}{76.4} = 29.48\). We rounded down to 29, as we consider complete cycles only.
These calculations are fundamental in astronomy for predicting celestial events, understanding the history and future of cosmic objects, and for planning observational activities. Mastering these basic calculations can help tackle more complex astronomical problems.

Comet Halley, also known as Halley's Comet, is one of the most famous and well-studied comets. Its periodic appearances every 76.4 years have been recorded since ancient times. The comet's regular timeline allows scientists to study its physical characteristics and behavior over many centuries.

• First observed: 230 BCE.
• Periodicity: Approximately every 76.4 years.
• Current mass: \(2.2 \times 10^{14}\) kg (prior to calculated mass loss).
• Mass loss per passage: \(3 \times 10^{11}\) kg.
• Significance: Provides insights into the composition and longevity of comets.

By knowing the period and the mass loss per orbit, scientists can estimate how much mass the comet has lost since its first recorded appearance and predict its future. For instance, from our exercise, we found that Comet Halley has lost around \(8.7 \times 10^{12}\) kg of its mass, which is roughly 3.95% of its original mass.
Understanding Comet Halley’s mass loss and orbital dynamics contribute to our broader knowledge of comets, the solar system, and the processes that shape these celestial bodies over time.