Finding the distance of a space shuttle using radio wave transmissions

[OnceKnown]

Homework Statement

Mission control sends a brief wake-up call to astronauts in a far away spaceship. 2.4 seconds after the call is sent, Mission Control can hear the groans of the astronauts. How far away (at most) from Earth is the spaceship?

Homework Equations

Have yet to find a suitable equation for this problem.

The Attempt at a Solution

I do believe that this problem has to do with light properties and/or radio waves, but I'm unsure which one. I'm also wondering would the mediums (air and vacuum of space) that these waves travel through would severely affect the possible velocity of the waves?

So far, I can assume that we need to know how fast these radio waves are traveling, since we are given the time only, and from there we can calculate the distance that the space shuttle is away. But I'm just lacking the other variables, so do I go online and apply real world data for this one?

thank you!

 

[voko]

The question says "at most". So you can assume the fastest possible speed of radio transmission.

 

[lep11]

Electromagnetic waves travel at the speed of light.

 

[OnceKnown]

Hi, Voko and lep11, thank you for your replies.

Okay, so I tried the wave speed of the EM-wave as 299,792,458 m/s and I figured that 2.4 seconds would be the total time that the EM-wave takes to go to the spaceship and back to mission control.

So to find the distance of the spaceship away from Earth, I reduced the time by a half and multiplied that by the EM-wave speed and got the right answer!

Thanks once again!

 

[Nickie]

I can provide a response to this content by first acknowledging that this is a common problem in the field of astrophysics, known as the "time delay problem." To solve this problem, we need to use the equation d = vt, where d is the distance, v is the velocity, and t is the time. In this case, we are given the time (2.4 seconds) and we need to find the distance (d).

To determine the velocity (v), we need to consider the medium through which the radio waves are traveling. In this case, it is a vacuum of space, which means that the velocity of the radio waves is equal to the speed of light, c = 3 x 10^8 m/s. We can now substitute this value into our equation, d = (3 x 10^8 m/s)(2.4 s), and we get a distance of 7.2 x 10^8 meters.

However, we must note that this distance is the total distance traveled by the radio waves, which includes the distance from Earth to the space shuttle and back to Earth. Therefore, we need to divide this distance by two to get the distance from Earth to the space shuttle, which is approximately 3.6 x 10^8 meters.

In conclusion, the maximum distance that the space shuttle can be from Earth is approximately 3.6 x 10^8 meters, assuming that the radio waves travel at the speed of light and there are no other factors affecting their velocity.