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True or False: A Hohmann Transfer is the most efficient transfer between two circular orbits.
True or False: When using a Hohmann transfer to move to a larger circular orbit, the satellite must increase its velocity at the apoapsis of the transfer ellipse to enter the new orbit.
True or False: If performing a pure inclination change (no other orbital elements change), the old and new orbits will not intersect.
Given the mass of the satellite to be 500 kg and the gravitational force exerted on the satellite by the Earth (F=4100 N), what is the specific potential energy of a satellite, U?
F = Gm_{1}m_{2}/r^2
U = - Gm_{1}m_{2}/r
G = 6.674 x 10^{-11} m^{3 }kg^{-1 }s^{-2}
M_{earth} = 5.96×10^{24} kg
m_{1} represents the mass of object 1
m_{2} represents the mass of object 2
r represents the distance separating the objects center
We would like to transfer our satellite from a LEO orbit (r_LEO = r_1 = 7,000 km) to a GEO (r_GEO = r_2 = 42,164 km) orbit using a Hohmann Transfer. What is the total change in velocity required?
Step 1 - Solve for semi-major axis of the Hohmann transfer.
Step 2 - Solve for circular orbit velocities.
Step 3 - Determine the energy of the Hohmann transfer.
Step 4 - Solve for periapsis and apoapsis velocities of the transfer.
Step 5 - Determine the change in velocities for each maneuver. Then find the total change, Δv_{Tot}.
We would like to transfer our satellite from a LEO orbit (r_LEO = r_1 = 7,000 km) to a GEO (r_GEO = r_2 = 42,164 km) orbit with a transfer orbit tangent to the LEO orbit and a v_1 = 2.75 km/s. What is the total Δv required?
Step 1 - Solve for circular orbit velocities.
Step 2 - Determine v_{1} and v_{2} energy of the transfer orbit.
Step 3 - Determine the flight path angle at location of Δv_{2}.
Step 4 - Determine Δv_{2} and Δv_{Tot}.