Calculating Time for a Radio Pulse to Travel between Earth and Venus

[DrnBrn]

Hi

I'm a bit confused, I hope you can help.

The question is -

In the course of their orbits, the distance between the Earth and Venus changes. The radii of the orbits of the two planets are 1.5 x 10e8 km and 1.1 x 10e8 km. If a radio pulse is transmitted from Earth towards Venus, calculate the greatest and least times that would be measured before the return pulse was detected.

This is what I think I'm supposed to do:

a) Calculate the maximum radius of the Earth's orbit and Venus' orbit. Also, calculate the minimum radius of each planet's orbit.

I'm not sure how to do this. It's not mentioned in the question but as far as I know both those values of r (radius) given in the question are mean radii for each planets orbit around the Sun. I'm guessing I need a max and min value of r for each planetary orbit but I don't know how to work it out. I think it may involve using Kepler's Third Law but I have been unsuccessful with my attempts so far.

b) With my max and min values of r for each planet I can work out the max and min distance between Earth and Venus, then I can calculate the time a radio pulse travels between the two using time = distance/speed, speed being the speed of light 3 x 10e8 m/s.

I appreciate your help.

Thanks
Darren

 

[Mark44]

My take on this is that you are to assume that the orbits of the Earth and Venus are circular, with radii as given. The orbits are actually ellipses, which makes the problem harder, but the assumption of circular orbits makes for a simpler solution.

When are the two planets closest together? The farthest apart?

 

[collinsmark]

Hello DrnBrn,

Welcome to Physics Forums!

This is what I think I'm supposed to do:

a) Calculate the maximum radius of the Earth's orbit and Venus' orbit. Also, calculate the minimum radius of each planet's orbit.

I'm not sure how to do this. It's not mentioned in the question but as far as I know both those values of r (radius) given in the question are mean radii for each planets orbit around the Sun. I'm guessing I need a max and min value of r for each planetary orbit but I don't know how to work it out. I think it may involve using Kepler's Third Law but I have been unsuccessful with my attempts so far.

If you really wanted to do that you would need a lot more information than what's given to you in the problem statement, such as each orbit's
o Eccentricity
o Inclination
o Longitude of the ascending node
o Argument of periapsis
o etc.
Not only are the orbits elliptical, but they are also each oriented in 3-dimensions (they're not exactly on the same plane).

My point is that if you really wanted to be perfect, this could be a very complicated exercise. But I'm guessing that you're not supposed to get that detailed.

I'm guessing you're supposed to just assume that both orbits are circles, and on the same plane.

b) With my max and min values of r for each planet I can work out the max and min distance between Earth and Venus, then I can calculate the time a radio pulse travels between the two using time = distance/speed, speed being the speed of light 3 x 10e8 m/s.

Sounds reasonable. And it will be a lot easier if you assume circular, co-planar obits too.

 

[DrnBrn]

Thanks. Assuming the orbits are circular makes a lot more sense.

So, I suppose the distance when the planets are closest is 1.5 x 10e8 (radius Earth's orbit) - 1.1 x 10e8 (radius venus' orbit). And when they're farthest apart the distance is the difference calculated above + the diameter of venus' orbit. Am I on the right track?

 

[collinsmark]

So, I suppose the distance when the planets are closest is 1.5 x 10e8 (radius Earth's orbit) - 1.1 x 10e8 (radius venus' orbit).

Yes. That's what I would do.

And when they're farthest apart the distance is the difference calculated above + the diameter of venus' orbit. Am I on the right track?

Uh, not quite, the way you've worded it. The way you worded it, you would just get back the radius of Earth's orbit.

If you draw the concentric circles out on a piece of paper (with the sun in the middle) it might help. The farthest distance is when Venus is on the opposite side of the sun as Earth.

 

[DrnBrn]

I've drawn out the circular orbits and worked it out. Thanks for your help.