If the earth could be at one half of its present distance from the sun and maintain the same orbital speed the number of days in 1 year would be approximately?

Answer 1

If it had half the present distance from the Sun, then it WON'T have the same orbital speed - it will move faster (unless the Sun's mass decreases). Use Kepler's Third Law to do the calculations.

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The accuracy of the above notwithstanding, the questioner may be asking about the effect of one half the distance, disregarding for this question any impossible or catastrophic results. All things being equal, and also disregarding the slight eccentricity of earth's orbit, one half the distance from the sun would result in an orbit (circumference) of one half the length. Moving at the same orbital speed [which we know could not actually be the case] would create a year of one half the absolute length of a current year. So there would be roughly 182.6282 days per year.

Answer 2

Approximately 58 days. This is because the time it takes for one complete orbit (a year) is inversely proportional to the square root of the distance from the sun. Halving the distance would make the orbit faster by a factor of sqrt(2), resulting in a year being about 58 days long.