Help Needed: Solving Kepler's Third Law for a Solar Elliptical Orbit

[nick227]

Homework Statement

I have this problem for homework and I don't know how to even start. Can someone help? Thanks in advance.A neat and exploitive use of the sun would be to put a space probe into a solar elliptical orbit from the Earth on one side of the sun headed towards a rendezvous with Venus on the other side. Since Venus is a moving object, it would actually meet the space probe at the other end of the ellipse. So, employing Kepler's third law determine how many days are required for the space probe to travel to Venus. Consider both Venus and the Earth to have circular orbits. Also use this information:
Period(yr) Radius(AU) Eccentricity

Venus .615 .723 .007
Earth 1.000 1.000 .017

Homework Equations

t^2=((4pi^2)/(GM))a^3
t =period
G=universal gravity
M=mass of sun...?
a=semimajor axis or radius for a circle

The Attempt at a Solution

i don't really know how to start this. can anyone get me started?

 

[Dick]

The farthest point from the sun in the orbit is at the radius of the Earth's orbit. The closest is at the radius of Venus' orbit on the opposite side of the sun from the first point. Draw a picture. You can use that info to find the semimajor axis of the ellipse since the distance between those two points is twice the semimajor axis.

 

[nick227]

so...
1.723=2a
a=.8615

t=(.8615)^(3/2)=.800yr

.800*365 = 292 days

292 is the answer. thanks a lot.