Question

Halley's Comet has a mass estimated at 100 billion tons. Furthermore, it is estimated to lose about 100 million tons of material when its orbit brings it close to the Sun. If its orbital period is 76 years, calculate the maximum remaining life span of Halley's Comet.

Short answer

Halley's Comet may last approximately 76,000 more years.

Step-by-step solution

Convert Mass Units

Convert the mass of Halley's Comet from tons to metric tons. Since 1 ton is equal to 0.907 metric tons:\[ 100 ext{ billion tons} \times 0.907 = 90.7 ext{ billion metric tons} \]

Convert Mass Loss Units

Convert the mass loss of Halley's Comet from tons to metric tons as well. For 100 million tons:\[ 100 ext{ million tons} \times 0.907 = 90.7 ext{ million metric tons} \]

Calculate Mass Loss Per Orbit

Since the comet loses 90.7 million metric tons each orbit, express this in terms of the comet's mass:\[ ext{Mass loss per orbit} = 90.7 ext{ million metric tons} \]

Calculate Number of Orbits Until Depletion

Calculate how many orbits will pass before the comet is completely depleted:\[ ext{Number of orbits} = \frac{90.7 ext{ billion metric tons}}{90.7 ext{ million metric tons/orbit}} = 1000 ext{ orbits} \]

Calculate Maximum Remaining Life Span

Multiply the number of orbits by the comet's orbital period to find its remaining life span:\[ 1000 ext{ orbits} \times 76 ext{ years/orbit} = 76000 ext{ years} \]

Finalize the Calculation

The maximum remaining life span for Halley's Comet, assuming a linear mass loss with no other factors involved, is 76,000 years.

Key concepts

Orbital Period

An orbital period is the time it takes for a celestial object, like a comet, to complete one full orbit around a focal point such as the Sun. For Halley's Comet, this period is 76 years. This means that every 76 years, Halley's Comet travels all the way around the Sun.
The orbital period depends on the comet's speed and the shape of its path. If the path is more elongated, the journey takes longer, adjusting the speed accordingly. Halley's Comet is particularly famous because its predictable visits allow scientists and sky-watchers to study it closely during its recurrent solar journey.

Mass Loss

Mass loss for a comet occurs when it's near the Sun. At this time, solar energy heats the comet, causing it to release gas and dust. For Halley's Comet, the estimated mass loss is 100 million tons every time it completes an orbit.
The mass loss is significant because, over time, it affects the comet's size and lifespan. Each close encounter with the Sun strips away some of its material, as it transforms from a solid ice body to gaseous components that form its tail. This process isn't uniform as it relies on factors like surface area exposed and the material composition of the comet.

Comet Life Span

The life span of a comet like Halley's is determined by its orbital interactions and the rate of its mass loss. Halley's Comet is particularly interesting because of its long visible history; it has been observed for thousands of years.
In our calculations, assuming the comet loses 90.7 million metric tons per orbit from an original 90.7 billion metric tons, the comet could complete approximately 1,000 more orbits. Therefore, with its 76-year orbital period, this gives a potential lifespan of 76,000 more years. Of course, this is an ideal estimate, ignoring other disturbances it might encounter.

Metric Ton Conversion

Metric ton conversion is essential for consistency in scientific calculations. In this problem, both the mass and the mass loss of Halley's Comet are originally given in tons, a unit more commonly used in the US.
However, for scientific purposes, it's common to convert to metric tons (1 ton = 0.907 metric tons) because the metric system is used universally. This conversion standardizes measurements, ensuring clarity in communication and computation, which is crucial for calculations involving global scientific tasks like those concerning Halley's Comet.