Two bodies with equal masses orbit the Sun in a circular orbit. If the radii of the two orbits are the same then following is true:

a) The orbital period of the two bodies is the same because their masses are the same.
b) Their orbital period of the two cannot be the same because their orbital planes are
perpendicular to each other
c) Their orbital periods are the same because the radii is the same
d) none of the above.

I want to say the answer is c) because isn't period only dependent on radii?

The source of internal heat within the Earth is:
Geothermal energy
Radioactivity.
Earthquakes
Electromagnetic Energy

Is it radioactivity?

c) Kepler's third law. The square of the orbital period of a planet (time taken for a complete orbit) is directly proportional to the cube of the semi-major axis of its orbit (the average distance from the sun).

And, yes, radioactivity (from the uranium decay series).

Residual heat left over from the formation of the earth is also important. Much of the interior remains molten. Friction from tectonic plate motion and tidal forces (mainly due to the Moon) also generates heat.

See http://pubs.usgs.gov/gip/dynamic/unanswered.html

For the first question, the correct answer is c) Their orbital periods are the same because the radii are the same.

The period of an orbiting object is determined by its distance from the central body (in this case, the Sun) and the mass of the central body. In this scenario, we are told that the two bodies have equal masses and the radii of their orbits are the same. The mass of the bodies does not affect the period in this situation because the mass of the central body (the Sun) remains the same. Therefore, the only factor that determines the orbital period is the radius of the orbit, which is the same for both bodies. Thus, their orbital periods are the same.

For the second question, the correct answer is b) Radioactivity.

The source of internal heat within the Earth is mainly attributed to radioactivity. Radioactive elements such as uranium, thorium, and potassium exist within the Earth's core and decay over time, releasing heat energy. This process is a fundamental source of the Earth's internal heat. While geothermal energy is also utilized as a form of renewable energy, it refers to the harnessing of heat stored within the Earth's crust, primarily originating from the transfer of heat from the core and radioactive decay. Earthquakes and electromagnetic energy are not considered as the primary sources of internal heat within the Earth.