The sun heats earth mainly through a) fusion. eliminate b) radiation. c) conduction. d) convection.

B. radiation is your answer hope this helps

For heat transfer, there's basically only convection, conduction, and radiation. So first we eliminated A.
Next, we need to know that the space between the sun and the earth is mainly vacuum, not air. Therefore, there's no fluid flow happening and convection may not be the right choice.
Then, we also need to know that vacuum is the worst conductor of heat in conduction, which is also the best insulator or heat in another way. Therefore the rate of conduction is so low that we can also eliminate choice C.
Now only remain B, radiation. Radiation is possible in vacuum and it is always happening even if we don't see it.

An  atom  (ours, not carroll's) consists of a positively charged  nucleus, surrounded by one or more negatively charged particles called  electrons. the positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. most of an atom's mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. although the nucleus is heavy, it is quite small compared with the overall size of an atom. the radius of a typical atom is around 0.1 to 0.25 nanometres (nm), whereas the radius of a nucleus is about 10-6  nm.  *  if an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily rest inside a small football stadium.read more on -