Does anybody know approximately how many minor planets, like Vesta, could fit inside Earth
(A) 120
(B) 600
(C) 1,200
(D) 6,000
(E) 12,000
look up the radii of the two bodies.
If the radius ratio earth/vesta = x, then the volume ratio will be x^3
That is how many Vestas will fit in one Earth.
so its e?
To determine how many minor planets like Vesta can fit inside Earth, we need to calculate the volume of Earth and divide it by the volume of Vesta.
First, let's find the volume of Earth:
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
The average radius of Earth is approximately 6,371 kilometers, or 6,371,000 meters.
Plugging the value of r into the volume formula:
V(Earth) = (4/3)π(6,371,000)^3
Next, let's find the volume of Vesta:
The approximate dimensions of Vesta are 525 kilometers in diameter, which gives it a radius of 262.5 kilometers, or 262,500 meters.
Using the volume formula:
V(Vesta) = (4/3)π(262,500)^3
Now, we can calculate the number of Vesta-like planets that can fit inside Earth:
Divide the volume of Earth (V(Earth)) by the volume of Vesta (V(Vesta)):
N = V(Earth) / V(Vesta)
Finally, let's calculate the answer by comparing it to the options provided:
(A) 120
(B) 600
(C) 1,200
(D) 6,000
(E) 12,000
Given the calculations above, we can substitute the values into the formula to determine the answer.