Based on the current value of the Earth's circumference (equatorial circumference of 40,075), calculate its radius. Observe the number of significant figures and the proper unit for your answer.
Answers
Answer:
Explanation:
For this problem, ignore the Earth's orbital motion around the Sun (and the Sun's orbital motion in the galaxy and the galaxies motion relative to other galaxies, etc.) We assume the Earth is a sphere and we live at the equator. As the Earth spins we are carried with the surface of the Earth in a big circle. The circle is the circumference of the Earth. The velocity is the distance traveled divided by the time needed to travel that distance.
We define the following algebraic quantities:
D = distance traveled = circumference [not area] of a circle
T = time
v = velocity = D/T
pi = 3.1415
R = radius of a circle (in this case the radius of the whole Earth since we live at the equator)
The circumference of a circle is found from the formula
D = distance traveled = 2 * pi * R
T = time to travel distance D
In this case, diameter of the Earth = 2R = 12,756 km, so D = 4.01 x 104 km
T = one day = 1 [day] x 24 [hr/day] x 60 [min/hr] x 60 [sec/min] = 86,400 seconds
v = D/T = 4.01 x 104 km / 8.64 x 104 sec = 0.46 km /sec