Question

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

Short answer

Halley's Comet will last approximately 76,000 years.

Step-by-step solution

Convert Mass and Loss to the Same Unit

First, we need to convert the mass of Halley's Comet from billions of tons to tons: $$\text{Mass of Halley's Comet}=100\times {10}^9\text{ tons}={10}^{11}\text{ tons}$$and the mass loss per orbit from million tons to tons:$$\text{Mass loss per orbit}=100\times {10}^6\text{ tons}={10}^8\text{ tons}$$

Calculate Total Orbits Before Complete Disintegration

Next, we calculate the total number of orbits Halley's Comet can complete before it loses all its mass:$$\text{Total orbits}=\frac{\text{Total mass}}{\text{Mass loss per orbit}}=\frac{{10}^{11}}{{10}^8}={10}^3$$

Calculate Maximum Remaining Life Span

Now, we find the maximum remaining life span by multiplying the total orbits by the orbital period:$$\text{Maximum life span}={10}^3\times 76\text{ years}=76000\text{ years}$$

Conclude the Calculation

Concluding the calculation, we determined that Halley's Comet can last approximately 76,000 years before it loses all its mass due to orbital passages close to the Sun.

Key concepts

Orbital Period

The orbital period of an object, like Halley's Comet, is the time it takes to make one full orbit around another object, typically a star. For Halley's Comet, it takes approximately 76 years to complete one orbit around the Sun. This period is significant because it helps us predict when the comet will be visible from Earth again. Every time Halley's Comet returns, its characteristics deeply fascinate astronomers and enthusiasts alike. The 76-year cycle plays a major role in understanding the potential lifespan and activity of the comet. This is because each return marks an occasion where the comet undergoes substantial change while interacting with the Sun.
In scientific terms, the orbit of a comet around the Sun is usually highly elliptical, meaning it has a stretched oval shape, as opposed to being circular. This contributes to the variation in speed and position of Halley’s Comet throughout its journey. As it approaches the Sun (called perihelion), the comet speeds up and the gravitational forces intensify. Understanding these orbital mechanics is key to predicting the potential lifespan of Halley’s Comet as discussed in the textbook problem.

Mass Loss

As Halley's Comet orbits the Sun, it loses mass due to factors such as solar wind and radiation. This process is intense when the comet is close to the Sun, which causes the ice and other volatile substances within the comet's core to vaporize, forming a glowing coma and tail.
The exercise estimates a mass loss of 100 million tons per orbit, calculated from the data that the comet's initial mass is about 100 billion tons. This degree of mass loss significantly affects the comet’s structure and future visibility. Each pass depletes the resources within the comet, reducing its overall mass. By converting the initial mass ( 10^{11} tons) and mass loss per orbit ( 10^{8} tons) to a common unit, we can predict how many orbits Halley’s Comet could make before its resources are completely exhausted.
Understanding this concept helps us comprehend how the beautiful tails of comets are formed and the inevitable cycle of mass reduction that these fascinating celestial objects undergo during their lifespan.

Comet Lifespan

A comet’s lifespan corresponds to the total number of orbits it can complete before disintegrating entirely. For Halley's Comet, this lifespan is calculated by dividing the initial mass by the mass lost in each orbit. Using the initial mass of 10^{11} tons and mass loss per orbit of 10^{8} tons, Halley's Comet can theoretically complete 1,000 orbits.
This is expressed mathematically as:
$$\text{Total orbits}=\frac{{10}^{11}}{{10}^8}={10}^3$$
By multiplying the total number of possible orbits (1000) by the orbital period (76 years), we find that the comet has an estimated remaining lifespan of about 76,000 years.
Thus, if current estimates and conditions remain unchanged, Halley’s Comet will cease to exist once it completes these orbits. However, external factors like collisions or changes in the solar environment could impact this predicted lifespan, making it a fascinating topic for ongoing research.

Sun Proximity Effects

The proximity of Halley's Comet to the Sun has profound effects on its physical state and orbital characteristics. This is primarily because the Sun's immense energy and gravitational forces influence the comet when it is closest during its orbit.
At its closest approach, known as perihelion, the solar radiation causes significant heating of the comet's nucleus. This heating leads to the sublimation of ice within the comet, forming a glowing coma and a spectacular tail that are characteristic features of comets.
The interacting solar wind and magnetic fields can also cause changes in the comet's trajectory over time. The heat and radiation not only cause mass loss, but can alter surface chemistry and structure. This process essentially limits the comet’s ability to survive its journey around the solar system.
These phenomena showcase the dynamic and ever-changing nature of comets like Halley, providing valuable insights into the forces that govern comet evolution and the transient beauty witnessed from Earth.