Challenge - A problem in astronomy

[Messiah]

Given -
1) Twin earth-sized planets rotate about each other in a solar system.
2) The plane of their mutual orbit is the same plane in which they rotate about their star
3) Their star provides (on average) the same amount of energy as our sun

Questions -
1) What is the size and nature of their star?
2) What is the average distance from the center of their orbit to the star?
3) What is the distance between the planets at mutual apogee and perigee?
4) What is the period of rotation about each other?
5) What is the period of rotation about the star?
6) What is the likely period of their individual revolution?

BONUS POINTS -
Would a moon orbit around both planets
a) in an elipse
b) in a figure '8'?

PS: The winner gets to name the planets

 

[enigma]

It seems to me that you haven't given enough information.

Q2, 3, 4, 5, & 6 all depend on the semimajor axis, either of the planet to the CM or the planets' CM to the star.

For the bonus question, it would depend on the initial conditions. If the moon started off at either L4 or L5, it would stay in an elliptical orbit, following the rotation of the planets about each other. Other initial locations and velocities would result in different orbits, including a possibility of an alternating posigrade/retrograde orbit about one of the planets, but not the other (passes close to L1, but doesn't reach it, then turns around).

EDIT: Q1 would be the same stellar class as our sun, but I'll be danged if I can remember what that is... G5?

 

[axeeonn]

Originally posted by enigma

EDIT: Q1 would be the same stellar class as our sun, but I'll be danged if I can remember what that is... G5?

G2 V.

 

[enigma]

Originally posted by axeeonn
G2 V.

Thanks. I was sure there was a 5 in there SOMEwhere.

 

[Messiah]

Originally posted by enigma
It seems to me that you haven't given enough information.

Q2, 3, 4, 5, & 6 all depend on the semimajor axis, either of the planet to the CM or the planets' CM to the star.

For the bonus question, it would depend on the initial conditions. If the moon started off at either L4 or L5, it would stay in an elliptical orbit, following the rotation of the planets about each other. Other initial locations and velocities would result in different orbits, including a possibility of an alternating posigrade/retrograde orbit about one of the planets, but not the other (passes close to L1, but doesn't reach it, then turns around).

EDIT: Q1 would be the same stellar class as our sun, but I'll be danged if I can remember what that is... G5?

CM of both planets is same as Earth - revolving @ 24 hours (earth time). Rotation about the star - as close to earthly as possible. With the double mass, wouldn't its orbit be further from the star?