posted by Faith on .
How would the speed of Earth’s orbit around the sun change if Earth’s distance from the sun increased by 4 times?
The velocity required to keep the earth in a circulor orbit of radius 4 x(93,000,000) miles derives from
V = sqrt[µ/r] where µ = the Sun's gravitational constant = 4.68772x10^21 ft.^3/sec.^2 and r = the radius of the increased orbit in feet = 4.9104x10^11 feet.
Therefore, the orbital velocity becomes
V = sqrt[4.68772x10^21ft.^3/sec.^2/4.901x10^11] = 48,853 ft./sec. = mph. = 9.25 mph. compared to 97,706fps and 18.5 mph in its existing orbit
More symplictically, V = 97,700sqrt[r/4r] = 97,706[1/4) = 97,706/2 = 48,853 fps or 9.25 mph.