How Long Does It Take for Radio Transmissions Between Earth and Jupiter?

[kokenwa]

Suppose some astronauts have landed on Jupiter.
(a) When Jupiter and Earth are on the same side of the Sun and as close as they can be to one another, how long does it take for radio transmissions to travel one way between the two planets?




Suppose the astronauts ask a question of mission control personnel on Earth. What is the shortest possible time they have to wait for a response? The average distance from Jupiter to the Sun is 7.78 E11 m.


- i figured the the answer to a) would be distance divided by the speed of light but that isn't getting me anywhere
-i don't even know where to begin on the second one

 

[G01]

You are correct that the answer to part a) is:

t=d_min/c

HINTS:

For part a) You need to know how far apart Jupiter and Earth are for this case. How far is the Earth from the sun? How far is Jupiter from the sun? Can you now find how far apart the two planets are when they are on the same side of the sun? It may help to draw a picture.

For part b) Remember that the astronauts have to wait for their radio message to get to earth, and then they have to wait for the response to travel back to them. Using what you know from part a), how long does this whole process take?

 

[Moetasim]

I would first clarify that radio transmissions are a type of electromagnetic wave, which is a form of energy that can travel through space. Electromagnetic waves are characterized by their wavelength and frequency, and they include various forms such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.

To answer the first question, we need to calculate the distance between Jupiter and Earth when they are on the same side of the Sun and at their closest point. This distance can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the hypotenuse (c) is the distance between Jupiter and the Sun, and the other two sides (a and b) are the distances between Earth and the Sun and between Jupiter and the Sun, respectively.

Using the given average distance of Jupiter from the Sun (7.78 E11 m), we can calculate the distance between Earth and Jupiter at their closest point. This distance is approximately 6.18 E11 m.

Next, we need to know the speed of radio transmissions, which is the speed of light (c). The speed of light in a vacuum is approximately 3 E8 m/s.

Therefore, using the formula distance/speed = time, we can calculate the time it takes for radio transmissions to travel one way between Jupiter and Earth when they are on the same side of the Sun and at their closest point.

Time = (6.18 E11 m)/(3 E8 m/s) = 2.06 E3 seconds = 34.4 minutes.

This means that it takes approximately 34.4 minutes for radio transmissions to travel one way between Jupiter and Earth when they are at their closest point.

For the second question, the shortest possible time for the astronauts to receive a response from mission control on Earth would be the time it takes for the radio transmissions to travel from Earth to Jupiter and back. This is known as the round-trip time.

Using the same formula as before, we can calculate the round-trip time as follows:

Round-trip time = 2 x (6.18 E11 m)/(3 E8 m/s) = 4.12 E3 seconds = 68.8 minutes.

Therefore, the shortest possible time for