Jupiter is the largest planet in the solar system, with a diameter of approximately 9 x 10^4 miles. Mercury is the smallest planet in the solar system, with a diameter of approximately 3 x 10^3 miles. How many times larger is Jupiter than Mercury?

1 Answer
Nov 29, 2016

Jupiter is 2.7 xx 10^4 times larger than Mercury

Explanation:

First we need to define 'times larger'. I will define this as the ratio of the approximate volumes of the planets.

Assuming both planets are perfect spheres:

Volume of Jupiter (V_j) ~= 4/3 pi (9/2xx10^4)^3

Volume of Mercury (V_m) ~= 4/3 pi (3/2xx10^3)^3

With the definition of 'times larger" above:

V_j/V_m = (4/3 pi (9/2xx10^4)^3) / (4/3 pi (3/2xx10^3)^3)

= ((9/2)^3xx10^12)/((3/2)^3xx10^9)

=9^3/2^3 * 2^3/3^3 xx 10^3

=3^6/3^3 xx 10^3

=3^3 xx 10^3

=27xx10^3 = 2.7xx10^4