What would happen if the earth did not revolve round the sun?

Answer 1

If the earth was not round and was cubical, all the places on will experience temperate weather while there would be no place with equatorial weather. However, that will happen if it rotates on the corners of the cube.

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A strange concept, a cubic planet; but it's a more profound question than you might think because it is a throw-back to the early days of the science of geology.

When late-18C to 19C geologists started to try to understand the planet's internal structure and how mountain ranges form, they had realised the Earth had started as a ball of molten rock and gas so treated the problem as one of straightforward cooling by radiating heat into Space. Therefore, they thought, folds, faults and mountains were effects of contraction simply straining the Crust, whose structure was not yet really known. (Radioactivity was not yet discovered so they did not yet know the Earth has an internal heat source, let alone know its nature.)

One accompanying, early, idea was that contraction would eventually pull the globe into a rough polyhedron: certainly not a cube, but still facetted, perhaps a dodecahedron. This far-fetched notion might have been related to observing how some liquids freeze into polyhedral plates or prisms. (E.g. sun-baked mud-flats, basalt columns.)

Answer 2

The earth revolves around the sun because it is travelling at some speed on a tangent to the sun, and the gravity from the sun pulls the earth toward itself.

If the earth did not revolve around the sun, then it would be pulled by the sun's gravity, directly into the sun, leading to the death of all life on earth.