Q163 · Practice questionComplex familiar4 marks
QUESTION 163 (4 marks)
A planet orbits a star on an ellipse. Its closest and farthest centre-to-centre distances are and . Points P and A indicate these positions.
a)[2 marks]
State where the star lies and explain why the planet travels faster near P than near A.
b)[2 marks]
Calculate the ratio of gravitational force magnitudes .
WORKED SOLUTION
4 marksPractice marking scheme
ANSWER
(a) The star lies at one focus. Equal areas in equal times require faster motion near P. (b) .
Worked solution
(a) Kepler's first law places the star at a focus, not at the centre of the ellipse. The radius line sweeps equal areas in equal times; at a smaller distance from the star, a greater angular sweep and faster tangential motion are required.
(b) Using , .
Equivalent physically justified methods and consistent equivalent units accepted.
Displayed decimals are model answers; accept appropriate significant figures and consistent rounding from stated constants.
Part a: Place the star at one focus.
Part a: Link the speed difference to equal swept areas in equal times.
Part b: Use inverse-square scaling with the correct ratio.
Part b: Calculate the force ratio.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
View the QCAA syllabusHow many marks did you earn?
Compare your working with the guide above.