Understanding Orbits: Sun-Earth System and Spacecraft

1. Understanding Orbits Assessment Questions 11-10-25 Morehead State University Morehead, KY Prof. Bob Twiggs RJTwiggs@gmail.com

2. Understanding Orbits Sun – Earth System Earth’s rotation axis Equator Eclipse Sun’s rays Spacecraft orbit plane Orbiting Spacecraft Why are the suns rays assumed parallel when reaching the earth? Sun is far away and large that the rays can be assumed parallel. SSE-120

3. Understanding Orbits Earth System Orbit plane Orbit inclination q Ascending node crossing the equator r Earth radius h Orbit altitude How much is the earth tilted on it’s axis? 23.5 degrees SSE-120

4. Understanding Orbits Earth System Orbit plane Orbit inclination q Ascending node crossing the equator r Earth radius h Orbit altitude Does the earth have the axis tilted all year long? Yes SSE-120

5. Understanding Orbits Earth System Orbit plane Orbit inclination q Ascending node crossing the equator r Earth radius h Orbit altitude What is the nadir point of a spacecraft? The point directly below the SC toward the center of gravity. SSE-120

6. Understanding Orbits Earth System Orbit plane Orbit inclination q Ascending node crossing the equator r Earth radius h Orbit altitude How is the inclination of a LEO spacecraft orbit defined? Angle between equator and orbit plane for an ascending node. SSE-120

7. Understanding Orbits Earth System Orbit plane Orbit inclination q Ascending node crossing the equator r Earth radius h Orbit altitude Why is inclination defined only for an ascending node (nadir point crossing the equator? Need to have a unique reference. Ascending node make it unique. SSE-120

8. Understanding Orbits Earth System Orbit plane Orbit inclination q Ascending node crossing the equator r Earth radius h Orbit altitude What is the approx. inclination of the orbit shown? 30 degrees SSE-120

9. Understanding Orbits Earth System Orbit plane Orbit inclination q Ascending node crossing the equator r Earth radius h Orbit altitude If a spacecraft could change directions of flight by 180 degrees, how would that change the inclination? Inclination would now be 180 degrees minus original inclination = 150 degrees. SSE-120

10. Understanding Orbits Earth System Orbit plane Orbit inclination q Ascending node crossing the equator r Earth radius h Orbit altitude Will the inclination change with increase in altitude? No nonono. SSE-120

11. Understanding Orbits Earth System Orbit plane Orbit inclination q Ascending node crossing the equator r Earth radius h Orbit altitude Will the inclination change if the orbit were elliptical? No SSE-120

12. Understanding Orbits Earth’s rotation around the sun Equinox Winter Summer Equinox If there are no perturbations to the orbit, can you draw a terminator orbit for each season? Super bunch!!!!!!!!!!!!!!!!!!!!!!!!!!!!! SSE-120

13. Understanding Orbits Earth’s rotation around the sun Equinox Winter Summer Equinox Does the eclipse of the earth change with seasons? Changes directions, but not shape or size. SSE-120

14. Understanding Orbits All orbits go thru the center of the earth Why must all earth orbits rotate around the earth’s center of gravity? Forces of gravity make it that way. That is just the way it is. Nature is in control. SSE-120

15. Understanding Orbits Earth’s rotation around the sun Equinox Winter Summer Equinox Does the terminator or noon-midnight orbit differ for each season? Both change if no perturbations. SSE-120

16. Understanding Orbits Noon – Midnight Orbit Spacecraft enters eclipse Spacecraft Leaves eclipse Will the eclipse time of the spacecraft change with an increase in altitude? Why? Because the time in eclipse is almost constant, but orbit time will increases. SSE-120

17. Understanding Orbits Noon – Midnight Orbit What would be the percentage of eclipse time if a spacecraft could orbit at zero altitude? Half the period or 50%. SSE-120

18. Understanding Orbits Calculating eclipse time for a noon-midnight orbit r h r + h q f f Solution q Q = cos-1 [r/(r+h)] f = 90 - Q Eclipse time = [(2* f)/360] * orbit time What is the eclipse time for an altitude of 750 km for the noon-midnight orbit? Make a Excel (spread sheet) chart for eclipse time from 300 km to 800 km by steps of 50 km. SSE-120

20. Understanding Orbits Calculating eclipse time for a noon-midnight orbit r h r + h q f f Solution q Q = cos-1 [r/(r+h)] f = 180 - Q Eclipse time = [(2* f)/360] * orbit time What would be the maximum eclipse time for a 750 km altitude orbit if the inclination was 90 degrees? Do you need more information? Need orbit orientation toward sun --- noon-midnight, terminator, or in between? SSE-120

21. Understanding Orbits T Changing orbit inclination. Change of eclipse time. A B N-M C How does the eclipse vary with inclination? From a terminator orbit, decrease in inclination will increase eclipse time after entering the eclipse. SSE-120

22. Understanding Orbits Earth’s rotation around the sun for a GEO stationary spacecraft. Equinox Winter Summer Equinox Does an eclipse occur with a GEO stationary spacecraft? Yes, during equinoxes. SSE-120

23. Understanding Orbits Earth’s rotation around the sun for a GEO stationary spacecraft. Equinox Winter Summer Equinox How often during the year will there be an eclipse of a GEO stationary spacecraft? Twice – each equinox. SSE-120

24. Understanding Orbits GEO stationary spacecraft. Start here Thursday for Menifee Equinox What is the max eclipse time? How would you calculate the maximum time of the GEO eclipse? Same way as for the LEO spacecraft. Only altitude of GEO is larger. SSE-120

25. Understanding Orbits GEO stationary spacecraft. Equinox Before Equinox After Equinox http://www.satellite-calculations.com/Satellite/satellite_suneclipse_info.htm How long would be the period that the GEO would continue to have some eclipse twice a year? Find when time between entrance to eclipse to exit from eclipse. (days) SSE-120

26. Understanding Orbits Done SSE-120