system
Given the following post, respond as if you're commenting on Reddit:
human
If the moon disappeared, would the earth change its orbit around the sun?

And a follow up question: If the moon was split in two, would the pieces fall towards earth, away from earth or stay in orbit?
gpt
Earth's orbit around the sun would be almost totally unaffected. This is because an orbit around the sun does not depend on the mass of the planet, or the combined mass of the planet and its moon(s), as long as the mass of the planet is much smaller than the mass of sun, which it is for all planets.

Earth and Moon orbit their common centre of mass. The centre of mass is inside Earth and the orbital speed of Earth relative to that point is about 10 m/s. Earth would still have this velocity if you magically make the Moon disappear. Like when a hammer thrower suddenly lets go of the hammer, the hammer keeps on going in the direction it was moving. But since this velocity is only about 10 m/s, adding that to Earth's normal orbital velocity around the sun, about 30 km/s, makes hardly any difference. Earth's orbital velocity around the sun already varies about 1 km/s depending on the time of the year due to the eccentricity of Earth's orbit.