The year would be longer if it moved away from the Sun and shorter if nearer. The amount of the Sun's heat per square metre would also change bringing back an Ice Age if further away or creating global deserts like Mars if it moved closer.
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No, earth's orbit around the sun did not change as result of the earthquake/ Tsunami in Japan, which was actually updated to a magnitude 9.0 earthquake. The length of a day, though, did change, and it changed by 1.8 millionths of a second. For earth's orbit to change, something would have to hit earth from outer space.
It would need to be launched into a tangent plane parellel to that of the earth's orbit around the sun, with the same speed of rotation around the sun
It appears that geosynchronous orbit (orbit that appears stationary from earth's surface) is more or less equal to the circumference of the earth (around 27,000 miles). The moon which orbits the earth reaches the same point every 29 or so days. So it would appear that the moon is around 29 times the distance for geosynchronous orbit or about 783,000 miles.
False. Why would it slow down? There is no friction in a high orbit; a satellite can orbit indefinitely. Only in low orbits will satellites slow down and fall from orbit, and the cause is the friction of the extremely tenuous final traces of Earth's atmosphere.
Not really. If there was an observer between the moon and Earth during this mission, if they were orientated properly, they could have seen the Apollo 11 CSM and LM pass in front of the sun, but no one was there to see this. The moon is in orbit around the Earth. The space craft simply went from low Earth orbit to a higher orbit that intersected the moon's orbit. At no time did they travel further than 260,000 miles. The sun is 93,000,000 from the Earth. There would be no reason for the Apollo 11 craft to "pass the sun" to get to the moon.