A satellite is placed in synchronous orbit around an exoplanet of mass 44⨯10^24 kg and radius 18⨯10^6 m. If the planet's day is 87.8 hours, at what altitude should you place the satellite?

1 Answer
A08
May 10, 2018

I have made slight editing of the question. I have changed Geosynchronous to synchronous orbit, as Geo refers to the Earth.

Explanation:

Newton's form of Kepler's third law states that the period #T# of a satellite having average distance of orbit #R# measured from the center of central body having mass #M_"cen"# are related by the equation

#T^2/R^3=(4pi^2)/(GM_"cen")#
where #T# is the period of the satellite, and #G# is Universal Gravitational Constant and# = 6.67 xx 10^-11\ N m^2kg^-2#.

Inserting given values we get

#R^3=(6.67 xx 10^-11xx44⨯10^24xx(87.8xx3600)^2)/(4pi^2)#
#=>R=3.09711691xx10^8\ m#

Now altitude of the satellite

#h=R-r#
where #r# is radius of exoplanet

#:.h=3.097xx10^8-1.8xx10^7=2.917xx10^8\ m#

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