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 isnt getting me anywhere
-i dont even know where to begin on the second one

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a) The orbits of the planets are elliptical and not circular, that is to say, the distance between them varies periodically over time. When one planet is at its closest to another, it's said to be at its "perihelion" distance between the two. Likewise, the "aphelion" distance is the distance at which one planet is furthest from the other.

What we are therefore interested in is the perihelion distance between Earth and Jupiter, not the Semi-Major axis distance that is given.

Perihelion distance: 740,742,598,000m

If we assume a vacuum between the two planets, then the speed of EM radiation is
~ 3 x 10^8 m/s.

You are correct in your logic of dividing the distance by the speed of light.

b) What we've calculated in a) is the time it takes for a signal to travel from Jupiter to Earth, now in b) we require a signal back from Earth to Jupiter. So whatever answer you get from a), all you need to do is multiply it by two:

a) Jupiter > signal > Earth
b) Jupiter > signal > Earth > signal > Jupiter

Regards,
Rob.