# Math Help - word problem help

1. ## word problem help

Hi there...just can't do this problem because I have always had problems with translations.
Problem: A result of Keplers harmonic law is that the mass of a planet (M) with a satellite is directly proportional to the cube of the mean distance(d) from the satellite to the planet and inversely proportional to the square of the period of revolution (p). Early astronomers estimated the mass of the earth to be 5.976 x 10 to the 24th power kg and obseved that the moon orbited the earth with a period of 27.322 days at a mean distance of 384.4 x 10 cubed km.
1.) Write a formula for the mass of a planet according to Kepler. 2.)Find the proportionality constant using the observation and estimates for the earth and moon. 3.)Extend your knowledge across the solar system to find the mass of Mars based on observations that Phobos orbits Mars in 7.65 hours at a mean distance of 9330 km. 4.)What is the approximate ratio of the mass of the earth to the mass of Mars? 5.)Explain steps taken to solve this problem.

2. Originally Posted by mnavarro21467@hotmail.com
Hi there...just can't do this problem because I have always had problems with translations.
Problem: A result of Keplers harmonic law is that the mass of a planet (M) with a satellite is directly proportional to the cube of the mean distance(d) from the satellite to the planet and inversely proportional to the square of the period of revolution (p). Early astronomers estimated the mass of the earth to be 5.976 x 10 to the 24th power kg and obseved that the moon orbited the earth with a period of 27.322 days at a mean distance of 384.4 x 10 cubed km.
1.) Write a formula for the mass of a planet according to Kepler. 2.)Find the proportionality constant using the observation and estimates for the earth and moon. 3.)Extend your knowledge across the solar system to find the mass of Mars based on observations that Phobos orbits Mars in 7.65 hours at a mean distance of 9330 km. 4.)What is the approximate ratio of the mass of the earth to the mass of Mars? 5.)Explain steps taken to solve this problem.
$M=\frac{kd^3}{p^2}$

$5.976\times10^{24}=\frac{k(384.4\times10^3)^3}{(27 .322)^2}$

Solve for k. (proprotionality constant) Use that to solve part 3.