Astronomy Class Question

Question

Estimate the maximum and minimum time it takes a radar signal to make the round trip between Earth and Venus, which has a semi major axis of 0.72 AU.

 

This is for Astronomy Class?

Answer 1

The planetary orbits are nearly circular, so we can approximate the radius as equal to the semi-major axis.

 

Minimum time occurs when the Earth, Venus, and Sun are colinear, and the Earth and Venus are on the same side of the Sun.

 

c = speed of light

 

radius of Earth orbit ≅ 1 AU

 

round trip time = 2(1 AU - 0.72 AU)/c = (0.56 AU)/c

 

Theoretically, maximum time occurs when the Earth, Venus, and Sun are colinear, and the Earth and Venus are on opposite sides of the Sun (ignoring the fact that the Sun is blocking any signal between the Earth and Venus).

 

round trip time = 2(1 AU + 0.72 AU)/c = (3.44 AU)/c

 

c = 3 x 10⁸ m/s

 

You can convert AU to meters and finish from here.