Question

In January 2006, the New Horizons space probe was launched from Earth with the mission to perform a flyby study of Pluto. The arrival at the dwarf planet was estimated to happen after nine years, in 2015 . The distance between Earth and Pluto varies depending on the location of the planets in their orbits, but at their closest, the distance is 4.2 billion kilometers \((2.6\) billion miles). Calculate the minimum amount of time it takes for a transmitted signal from Pluto to reach the Earth.

Short answer

The minimum amount of time it takes for a transmitted signal from Pluto to reach the Earth is approximately 3.89 hours.

Step-by-step solution

Find the speed of light in space

The speed of a transmitted signal in space is equal to the speed of light, which is approximately \(3.0 \times 10^8\) meters per second (m/s).

Convert distance to meters

The distance between Earth and Pluto at their closest is given as 4.2 billion kilometers. To use this value in our calculations, we need to convert it to meters. There are 1,000 meters in a kilometer, so we can find the distance in meters by multiplying the given distance by 1,000: \(4.2 \times 10^9\) kilometers × 1,000 meters/kilometer = \(4.2 \times 10^{12}\) meters.

Use the speed, distance, and time relationship

We know that the distance (d) traveled by an object can be expressed as the product of its speed (v) and the time (t) it takes to travel that distance: \(d = vt\). In this case, we want to find the time (t) taken for a signal to travel from Pluto to Earth, so we can rearrange the equation to solve for time: \(t = \frac{d}{v}\).

Plug in values and calculate time

Now we know the distance between Earth and Pluto (\(4.2 \times 10^{12}\) meters) and the speed of light (\(3.0 \times 10^8\) meters per second), so we can plug these values into the formula we derived above: \(t = \frac{4.2 \times 10^{12}\,\text{meters}}{3.0 \times 10^8\,\text{meters/s}}\).

Simplify and find the answer

Divide the given values to find the time: \(t = \frac{4.2 \times 10^{12}}{3.0 \times 10^8} = 14 \times 10^3\) seconds. Now, we could convert this to minutes by dividing by 60 seconds per minute: \(14 \times 10^3\,\text{seconds} ÷ 60\,\text{seconds/minute} \approx 233.33\) minutes. To get a more intuitive value, we can convert this to hours by dividing by 60 minutes per hour: \(233.33\,\text{minutes} ÷ 60\,\text{minutes/hour} \approx 3.89\) hours. So, the minimum amount of time it takes for a transmitted signal from Pluto to reach the Earth is approximately 3.89 hours.

Key concepts

Signal Transmission

Signal transmission through space is an amazing process, especially when considering distances like that between Pluto and Earth. In space, signals often travel as electromagnetic waves, primarily at the speed of light, which is approximately \(3.0 \times 10^8\) meters per second. This speed is fundamental in calculating how long it takes for information to travel across vast distances in the universe.

The speed of light is incredibly fast when compared to everyday speeds on Earth. However, when dealing with astronomical distances, even this speed results in significant delays.

To understand how these signals travel, it's important to remember that they move straight through the vacuum of space without any atmospheric interference, unlike on Earth where signals can be slowed or scattered by the atmosphere. This allows for relatively direct travel of data transmissions, like those from spacecraft such as the New Horizons mission.

Distance Conversion

Distance conversion plays a critical role in calculating travel times for signals in space. As seen in the example of the space probe New Horizons, converting the units of distance from kilometers to meters is essential. This is because the speed of light is usually given in meters per second.

To convert kilometers into meters, you need to multiply the number of kilometers by 1,000 because there are 1,000 meters in a kilometer. For instance, the distance from Earth to Pluto at its closest is 4.2 billion kilometers, equating to \(4.2 \times 10^9\) kilometers.

By converting, you get \(4.2 \times 10^{12}\) meters, making it easier to use in formulas involving the speed of light to find out how long a signal would take to travel such a vast distance.

Time Calculation

Time calculation is crucial in understanding how long a signal takes to travel from one point to another in space. Using distance and speed, time can be determined using the basic formula of motion: \(d = vt\), which can be rearranged to \(t = \frac{d}{v}\).

In this formula, \(d\) represents the distance traveled, \(v\) is the speed, and \(t\) is the time. By knowing the distance between Earth and Pluto as \(4.2 \times 10^{12}\) meters and the speed of light as \(3.0 \times 10^8\) m/s, the time \(t\) for the signal's travel can be calculated.

Once the values are plugged into the equation, you find that it takes approximately 14,000 seconds, or about 3.89 hours, for a signal to travel from Pluto to Earth. This illustrates how even the fastest speeds can result in long travel times over astronomical distances.

Pluto

Pluto, once considered the ninth planet in our solar system, was reclassified as a "dwarf planet" in 2006 by the International Astronomical Union. It resides in the Kuiper Belt, a region of the solar system beyond the major well-known planets.

The distance from Earth to Pluto varies significantly as both planets orbit around the Sun. At its closest approach, Pluto lies about 4.2 billion kilometers from Earth, a distance covered by the New Horizons mission to perform its scientific objectives.

Understanding extraterrestrial worlds like Pluto requires careful planning and significant time considerations, given its great distance from us.

New Horizons Mission

The New Horizons mission is a landmark project by NASA, aiming to explore Pluto, its moons, and other objects in the Kuiper Belt. Launched in 2006, the spacecraft reached Pluto in July 2015 after a journey spanning nine years.

This mission extended our knowledge about Pluto by sending back spectacular images and valuable data regarding its atmosphere, surface, geology, and moons, all of which contribute to our understanding of the outer regions of our solar system.

• One of the major achievements of New Horizons was capturing detailed images of Pluto's surface.
• The data it collected has helped scientists understand more about this mysterious dwarf planet and its place in the solar system.
• New Horizons remains important as it continues on its journey, gathering data from other distant celestial bodies.

The mission further demonstrated the challenges and triumphs of deep space exploration, showcasing the harsh reality of time demands for interplanetary travel.