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?

Question

2534 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-29T12:58:58

Jupiter is #2.7 xx 10^4# times larger than Mercury

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#