A spherical exoplanet has radius 4.0×106m and surface gravitational field strength 15.0N kg−1. A small satellite is placed in a circular orbit at radius 8.0×106m from the planet centre. Determine (a) the planet mass and (b) the satellite orbital period.
From the surface field,
g=R2GM⇒M=GgR2.M=6.67×10−11(15.0)(4.0×106)2=3.60×1024kg.
For the orbit,
T=2πGMr3=2π(6.67×10−11)(3.60×1024)(8.0×106)3=9.18×103s.
This is 9.18×103/3600=2.55h.
Rearranges surface-field equation.
[1 mark]
Calculates planet mass.
[2 marks]
Uses orbital-period relationship.
[1 mark]
Calculates orbital period.
[1 mark]
Converts or interprets period appropriately.
[1 mark]
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.