# Planetary phase angle of Hohmann transfer

This is Question 23 from USAAAO First Round 2015. The answer is D. Can someone show how to get the answer?

Calculate the planetary phase angle (counterclockwise from Earth, a = 1.0 AU) that a probe may correctly complete a Hohmann transfer orbit to Venus (a = 0.7 AU)

• a. 141 degrees
• b. 17.5 degrees
• c. 121 degrees
• d. 241 degrees
• e. 343 degrees

What I tried:

• Semimajor axis of Hohmann orbit: 0.85 AU
• Period of Hohmann orbit: 0.7836 yr
• Time of flight: 0.3918 yr
• Period of Venus: 0.5856 yr
• Angular distance travelled by Venus during flight: 241°

The last one looks suspiciously similar to the answer, but using that angular distance the phase angle should be 61°. Feel free to correct me anywhere that I’m wrong

• I'm not sure what you are asking. It seems to be "Here is a test question. The answer is D. I did some working and I got D. Please tell me what I did right." That is sort of an odd question to ask. Could you clarify. – James K Mar 23 at 20:26
• I think the question here is why is the angular distance Venus travelled in that time the answer – Tosic Mar 23 at 20:29
• @DavidHammen Thanks for replying. It would be great if you can show us the correct diagram. – Je Qin Chooi Mar 24 at 8:01
• @DavidHammen - I think the fourth object is supposed to be Venus at the initial time (given it's the same colour as the labelled Venus) – antispinwards Mar 24 at 11:32
• I edited the images just for readability (I couldn't read them easily as they were so huge) - if you think it causes issues please revert. – Rory Alsop Mar 24 at 17:47