In the approximate solar-mass AU-year model, find P for a=4 AU.
Answer and explanation
8 years
P=sqrt(4³)=8 years.
Subjects
Orbital mechanics
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Sample exercises
For μ=100 in compatible units and circular radius 4, find circular speed.
Answer and explanation
5
sqrt(100/4)=5.
What is the semi-major axis a?
- The orbital inclination
- Always the current distance
- Always the nearest distance
- Half the longest diameter of an ellipse
Answer and explanation
Half the longest diameter of an ellipse
The semi-major axis is a geometric orbital parameter.
For μ=18 and radius 4 in compatible units, find escape speed.
Answer and explanation
3
sqrt(2×18/4)=3.
Why can an orbiting astronaut appear weightless?
- The Moon removes all gravity
- Gravity is exactly absent
- Mass becomes zero
- Astronaut and spacecraft are in free fall together
Answer and explanation
Astronaut and spacecraft are in free fall together
Apparent weightlessness is free fall, not generally zero gravitational field.
Why does the simplified P²=a³ relation need units and central mass specified?
Answer and explanation
Its numerical constants incorporate AU, years and a solar-mass approximation. Other units or central masses change the numerical relation.
Credit units and mass dependence.
Study notes
Kepler orbits and gravitational scaling
Keplerian orbits approximate isolated Newtonian two-body motion. Real trajectories can include perturbations, drag or relativistic corrections.
UniversityKepler orbits and gravitational scaling · revision notes
Keplerian orbits approximate isolated Newtonian two-body motion. Real trajectories can include perturbations, drag or relativistic corrections.
UniversityKepler period with a central mass ratio
Use the approximate AU-year-solar-mass two-body model with negligible companion mass.
UniversityKepler period with a central mass ratio · formula reference
Use the approximate AU-year-solar-mass two-body model with negligible companion mass.
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