Chapter 8, problem 64 of Essentials of University Physics Vol.1,Richard Wolfson.
For a circular orbit around a massive gravitating body, the speeddepends on the radius according to Equation 8.3; for ellipticalorbits, the speed varies according to the equation Vsquared=2GM{(1/r)-(1/2a)}, where r is the distance from the massivebody and a is the semi major axis of the ellipse(i.e., half the sumof the closest and farthest distances). A satellite can betransferred from one circular orbit (at radius r1) to a higherorbit (at r2) by boosting the circular speed v1 at r1 to theappropriate speed for an elliptical orbit at r2 to the circularspeed v2. This is called a Hohmann transfer.
a) How much energy is required for the first boost in such atransfer to take a 250 kg satellite from a circular orbit at a 400km altitude to the altitude of a geosynchronous orbit?
b) How much energy is required for the second boost?
c) Check that the sum of your answers to parts (a) and (b) equalsthe difference in the total energies in the two circularorbits.
Chapter 8, problem 64 of Essentials of University Physics Vol.1,Richard Wolfson.
For a circular orbit around a massive gravitating body, the speeddepends on the radius according to Equation 8.3; for ellipticalorbits, the speed varies according to the equation Vsquared=2GM{(1/r)-(1/2a)}, where r is the distance from the massivebody and a is the semi major axis of the ellipse(i.e., half the sumof the closest and farthest distances). A satellite can betransferred from one circular orbit (at radius r1) to a higherorbit (at r2) by boosting the circular speed v1 at r1 to theappropriate speed for an elliptical orbit at r2 to the circularspeed v2. This is called a Hohmann transfer.
a) How much energy is required for the first boost in such atransfer to take a 250 kg satellite from a circular orbit at a 400km altitude to the altitude of a geosynchronous orbit?
b) How much energy is required for the second boost?
c) Check that the sum of your answers to parts (a) and (b) equalsthe difference in the total energies in the two circularorbits.
