1. The problem statement, all variables and given/known data Two satellites are orbiting around the Earth. One satellite has a period of 1.5 h and is 250 km above the Earth's surface. The second satellite has a period of 7.5 h. Using Kepler's Laws and the fact that the Earth's radius is 6.38x106 m determine the height of the second satellite above the Earth's surface. 2. Relevant equations Kepler's 3rd law: (Ta/Tb)2=(Ra/Rb)3 motion of planets must conform to circular motion equation: Fc=4∏2mR/T2 From Kepler's 3rd law: R3/T2=K or T2=R3/K Gravitational force of attraction between the sun and its orbiting planets: F=(4∏2Ks)*m/R2=Gmsm/R2 Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏2Ke)m/R2=Gmem/R2 Newton's Universal Law of Gravitation: F=Gm1m2/d2 value of universal gravitation constant is: G=6.67x10-11N*m2/kg2 weight of object on or near Earth: weight=Fg=mog, where g=9.8 N/kg Fg=Gmome/Re2 g=Gme/(Re)2 determine the mass of the Earth: me=g(Re)2/G speed of satellite as it orbits the Earth: v=√GMe/R, where R=Re+h period of the Earth-orbiting satellite: T=2∏√R3/GMe Field strength in units N/kg: g=F/m Determine mass of planet when given orbital period and mean orbital radius: Mp=4∏2Rp3/GTp2 3. The attempt at a solution So for satellite #1 we have, T1=1.5 hr h1=250 km above earth's surface For second satellite we have, T2=7.5hr h2=? We know that the earth's radius is RE=6.38x106 m so R1=250000m+ (6.38x106m)= 6630000m R2=RE+h2 I used (Ta/Tb)2=(Ra/Rb)3 to solve for R2=8.098x1010m Then I did, R2-RE=h2 h2=80 970 595 km Could someone please just verify that what I did here is correct? and if I made any mistakes if someone could please point them out to me that would be greatly appreciated! Thanks so much in advance !