Question

As its closest approach, the distance between the Mars and the Earth is found to be 60 million \(\mathrm{km}\). When the planets are at this closest distance, how long would it take to send a radio massage from a space probe of Mars of Earth? (a) \(5 \mathrm{~s}\) (b) \(200 \mathrm{~s}\) (c) \(0.2 \mathrm{~s}\) (d) \(20 \mathrm{~s}\)

Short answer

The time taken for a radio message to travel from Mars to Earth at the closest approach is approximately 200 seconds.

Step-by-step solution

Understand the Speed of Light

Radio waves travel at the speed of light in a vacuum, which is approximately 299,792 kilometers per second (km/s).

Convert Distance to Kilometers

The distance between Mars and Earth at the closest approach is already given in kilometers (60 million km), so no conversion is necessary.

Calculate the Time for Radio Transmission

To find out the time it takes for a radio message to travel from Mars to Earth, use the formula: Time = Distance / Speed. Here, the distance is 60 million km and the speed is the speed of light (299,792 km/s).

Key concepts

Radio Wave Transmission

Understanding the fundamentals of radio wave transmission is essential when considering the vast distances across our solar system. Radio waves are a type of electromagnetic radiation, similar to visible light but with longer wavelengths. These waves can travel through the vacuum of space at a constant speed, known as the speed of light. This speed is roughly \(299,792 \mathrm{km/s}\).

When we talk about radio wave transmission in the context of space communication, it's crucial to consider the medium they are passing through. In outer space, the lack of atmospheric interference allows radio waves to travel without significant attenuation or loss of strength. This makes them an ideal candidate for communication between distant objects like planets and spacecraft. Questions about radio wave transmission often involve calculating the time it takes for these waves to travel a certain distance. Using the simple formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\), we can easily determine that the time is directly proportional to the distance and inversely proportional to the speed. This is why, despite their incredible velocity, radio waves still take measurable amounts of time to cover astronomical distances.

Interplanetary Communication

Interplanetary communication, a thrilling frontier of human technology, relies on sending and receiving signals across the immense void between planets. It's a challenge that melds astrophysics with cutting-edge engineering. Initiatives like NASA's Deep Space Network (DSN) are pivotal for such communication. They maintain a network of giant antennas and communication facilities that support interplanetary spacecraft missions.

To grasp the complexity involved in these systems, it's paramount to acknowledge the effects of vast distances on transmission times. Even at the speed of light, signals from Mars to Earth require several minutes to travel. This delay necessitates advanced planning in spacecraft operations and data transmissions. The problem from the textbook exemplifies this concept, asking how long it would take for a radio message to traverse the 60 million kilometers separating Earth and Mars at their closest point. As we calculate the duration using the speed of light, we encounter a real-world application of the concepts of physics and orbital mechanics in managing these essential communications.

Physical Chemistry Problems

In the realm of physical chemistry, understanding the principles that govern the movement of electromagnetic radiation such as radio waves is of paramount importance. This branch of chemistry is concerned with the underlying physical principles that affect chemical systems, such as the interaction of matter with energy. Problems in physical chemistry often involve calculations related to the rates of reactions, energy transfer, and other dynamic processes.

Within these calculations, concepts from physics are commonly applied to chemical scenarios. For example, the speed of light may be used when considering the energy of various types of electromagnetic radiation, or calculating the time for a reaction to occur over a distance when radiation is involved. The speed of light is analogous to an ultimate speed limit, affecting not only how quickly information travels but also influencing the energetics of molecular-level events. In the case of radio wave transmission between planets, physical chemistry reminds us of the profound interconnectedness between physical laws and the transmission of energy across cosmic distances.