Let us assume the satellites move in a circular orbit around the Earth, whose ra
ID: 1691173 • Letter: L
Question
Let us assume the satellites move in a circular orbit around the Earth, whose radius is RE=6378 km. To stay in orbit the centripetal force must balance the gravitational force, i.e.,mv2/R = GmEm/R2
where v is the tangential velocity, m is the satellite mass, G is the gravitational constant (G=6.673x10-11 Nm-2 kg-2), mE is the mass of Earth, and R is the orbit radius.
a) If the period of the orbit is defined as express the period in terms of R, G, and mE.
b) A geostationary satellite moves in a counterclockwise sense at exactly the same speed as the Earth at a chosen altitude above the equator. Find the altitude of the satellite.
(Hint: Angular velocity of Earth is 7.29221x10-5 s-1 and angular velocity of the satellite is given by )
Let us assume the satellites move in a circular orbit around the Earth, whose radius is RE=6378 km. To stay in orbit the centripetal force must balance the gravitational force, i.e.,
mv2/R = GmEm/R2
where v is the tangential velocity, m is the satellite mass, G is the gravitational constant (G=6.673x10-11 Nm-2 kg-2), mE is the mass of Earth, and R is the orbit radius.
a) If the period of the orbit is defined as express the period in terms of R, G, and mE.
b) A geostationary satellite moves in a counterclockwise sense at exactly the same speed as the Earth at a chosen altitude above the equator. Find the altitude of the satellite.
(Hint: Angular velocity of Earth is 7.29221x10-5 s-1 and angular velocity of the satellite is given by )
Explanation / Answer
(a) mv^2 / R = Gmm_E /R^2 v^2 = Gm_E / R velocity = sqrt(Gm_E / R) time period T = 2*pi*R / v = 2*pi*R /sqrt(Gm_E / R) Here R is radius of the earth m_E mass of the earth ------------------------------ (b) g = Gm_E / R^2 here R = R_E + h h is height from the surface of the earth R_E + h = sqrt (Gm_E /g ) alltitude h = sqrt (Gm_E /g ) - R_ERelated Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.