Pretend you discover another planet in our solar system, and that this planet orbits the sun in a circular orb?

one astronomical unit is roughly the distance from the sun to the earth, which is approximately 93 million miles. if this new planet has an orbital radius of one au, it would be approximately the same as the earth's.  the distance of earth to the sun is a straight line, so it would be the radius in relation to its entire orbit.  A and C would seem correct to me, but most likely C.

A/. The planets will collide eventually, orbits are not perfect,
B/. The two planets have the same mass since they orbit at the same point,
......and have not hit each other, therefore the same period.
C/. Orbital period will be the same under the acceleration towards the sun,
......otherwise they collide.
D/. Possibly, it may not have the same atmosphere or any atmosphere,
E/. Same as D/.

This was a favourite of sci-fi writers, a second earth opposite ours which we could not see.

GL>

if i discovered another planet in our solar system that would mean that it has been around for billions of years, so its likelihood of colliding with earth would be practically nil, so A is out.

you cannot tell the mass of a planet based on its orbital radius, you would need to know how fast it is moving as well, so B is out

C well unless the planet has the same mass as the earth it's orbital period could be different, so technically c is out.

D finally is true in theory assuming that the atmospheric composition is the same as earth's its surface temperature would also likely be very similar. however since we are not told about its atmosphere it could have a very different temperature. so far this one is the best though.

E based on orbital radius alone there is no evidence for life E is out.

so yeah D seems to be the most likely one but it still has flaws to. any of them would require more information, we could make guesses about orbital period and planetary mass, but not enough information is given to make a true choice.

sort of a bad question really.

While it is an interesting discussion, try to disguise your homework questions a bit more, a bit of a buzzkill doing someone's homework.