1. The earth moves round the sun.

2. The Earth moves round the sun.
3. Earth moves round the sun.
4. The earth moves round the Sun.
[Which ones are okay? Do we have to use 'the' in #2 or #3? What about #4? "the Sun?"]

All are acceptable, with or without "the" Earth. Capitalization is inconsistent, though. Earth and Sun are always capitalized when referring to the planet and the star. They are proper nouns. Note that generic uses, as in sunshine or digging in the earth (dirt, soil) they are not capitalized, not proper nouns as in the names of the astronomical bodies.

All four statements are grammatically acceptable, but they have slightly different meanings and usage conventions.

1. "The earth moves round the sun." - This statement is grammatically correct and usually used when we are making a general statement about an ongoing or habitual action. It implies that the Earth, as a specific planet, continually orbits the Sun.

2. "The Earth moves round the sun." - In this sentence, 'Earth' is capitalized as it refers to our specific planet. Here, 'the' is used before 'Earth' to refer to our planet as a unique entity. We generally use this capitalization and article when referring to Earth in scientific or astronomical contexts.

3. "Earth moves round the sun." - In this statement, 'Earth' is not capitalized, and 'the' is not used before 'Earth'. This usage treats 'earth' as a common noun, representing any planet, including Earth. It is commonly used when discussing astronomical facts or making general statements.

4. "The earth moves round the Sun." - In this sentence, 'earth' is not capitalized, and 'the' is used before 'earth' and 'Sun'. This usage treats 'earth' and 'Sun' as generic nouns rather than specific entities. It can be used when making general statements about any planet moving around any star, not necessarily meaning Earth and the Sun.

In summary, the usage of capitalization and 'the' in these statements depends on the specific context and how we want to convey the meaning.