A satellite that goes around the earth once every 24 hours is called a geosynchr

Question

A satellite that goes around the earth once every 24 hours is called a geosynchronous satellite. If a geosynchronous satellite is in an equatorial orbit, its position appears stationary with respect to a ground station, and it is known as a geostationary satellite. Find the radius of the orbit of a geosynchronous satellite that circles the earth. (Note that is measured from the center of the earth, not the surface.) You may use the following constants: The universial gravitional constant G is 6.67*10^-11 N*m^2 /kg^2 The mass of the earth is 5.98*10^24 kg The radius of the earth is 6.38*10^6 m. Give the orbital radius in meters to three significant figures. PLEASE ANSWER THIS QUESTION!

Explanation / Answer

a geosynchronous satellite just means that the centripetal force is the same as the gravitational attraction. in this case, we take: centripetal force = gravitation attraction mrw^2 = GMm/r^2 (w = omega, m = mass of satellite, M = mass of earth, G = gravitational constant, r = radius of orbit))) r^3=GM/w^2 - eqn 1 we now need to work out w (omega). w = 2pi / T (where T is the period of rotation, i.e. length of a day) w = 2pi / (24 x 60 x 60) w = 7.27 x 10^-5 Sub the values into eqn 1 above r^3 = 6.67 x 10^-11 x 5.98 x 10^24 / (7.27 x 10^-5)^2 r^3 = 7.55 x 10^22 r = (7.55 x 10^22)^(1/3) r = 4.23 x 10^7 m = 42259 km from the center of the earth. (the number might vary slightly, due to the degree of accuracy)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.