Activity 3.2.6 Orbital Mechanics Physics
Introduction
Satellites need a tremendous amount of energy to be raised from the Earth’s surface
to the altitude where they can orbit the Earth. Engineers must design systems to
place such satellites in orbit.
In this activity you will calculate the energy required for satellites to orbit Earth.
Equipment
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Engineering notebook
Pencil
Calculator
Notes from Orbital Mechanics Physics presentation
Procedure
Answer the following questions and show all formulas, units, and calculations.
1. A 15,000 kg satellite is orbiting at 800km above the Earth’s surface. How much
potential energy?
U=-(GMm)/R, U=-((6.67*10^11)(5.98*10^24)(15000))/((6.378*10^6)+(8.0*10^5))=-8.33*10^11 J
2. At what distance from the Earth’s surface is a 10,000kg satellite if its potential
energy is equal to -5.58 x 1011J?
D=(-((6.67*10^11)(5.98*10^24)(10000))/(6.378*10^6))-(5.58*10^11)=6.25*10^33 m
3. What is the total energy of a 175,000kg shuttle orbiting the Earth at 600km above
Earth’s surface?
E=((6.67*10^11)(5.98*10^24)(175000))/2((6.378*10^6)+(6.0*10^5))=8.66*10^28 J
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AE Activity 3.2.6 Orbital Mechanics Physics – Page 1
4. A satellite has a total energy of -4.4x1011J. The satellite is orbiting 650km above
Earth’s surface. What is the mass of the satellite?
m=-2R/GM, m=- (2((6.378*10^6)+(6.5*10^5))(-4.4*10^11))/((6.67*10^11)(5.98*10^24))= 15505.6 Kg
5. A research satellite (14000kg) is orbiting planet Julu at an altitude of 400km. The
researchers want their satellite to be at an altitude of 700km to take some
specific pictures. How much energy is needed for this orbit change?
(RJulu=5.4x103km; MJulu=3.74x1021kg)
E_1=-((6.67*10^-11)(3.74*10^21)(1400))/2((5.4*10^3)+(4.0*10^5))= -4.31*10^8
J
E_2=-((6.67*10^-11)( 3.74*10^21)(1400))/2((5.4*10^3)+(7.0*10^5))= -2.47*10^8
J
E=E_2-E_1, E=-2.47*10^8 - -4.31*10^8= 1.83*10^8 J
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AE Activity 3.2.6 Orbital Mechanics Physics – Page 2
Conclusion
1. How will a satellite gain the energy to change its orbit to a higher altitude?
A satellite gains energy from thrusters.
© 2011 Project Lead The Way, Inc.
AE Activity 3.2.6 Orbital Mechanics Physics – Page 3