A meteorological monitoring satellite in an astraeastationary orbit around the planet Astraea-Prime appears to remain fixed directly above a station on the planet's equator.
State one dynamic or orbital condition required for an orbit around Astraea-Prime to be astraeastationary.
Calculate the orbital radius of this astraeastationary satellite.
Mass of Astraea-Prime M=4.8×1024 kg \text{Mass of Astraea-Prime } M = 4.8 \times 10^{24} \text{ kg} Mass of Astraea-Prime M=4.8×1024 kg Rotational period of Astraea-Prime T=7.5×104 s \text{Rotational period of Astraea-Prime } T = 7.5 \times 10^4 \text{ s} Rotational period of Astraea-Prime T=7.5×104 s Gravitational constant G=6.67×10−11 m3 kg−1 s−2 \text{Gravitational constant } G = 6.67 \times 10^{-11} \text{ m}^3 \text{ kg}^{-1} \text{ s}^{-2} Gravitational constant G=6.67×10−11 m3 kg−1 s−2A satellite of mass m m\,m is in a circular orbit of radius r r\,r around a planet of mass MMM.
By considering the gravitational force acting as the centripetal force for a circular orbit, show that the kinetic energy Ek E_k\,Ek of the satellite is related to its gravitational potential energy Ep E_p\,Ep by the equation:
Ek=−12Ep E_k = -\frac{1}{2}E_p Ek=−21Epwhere Ep=−GMmr\displaystyle E_p = -\frac{GMm}{r}Ep=−rGMm.
A spectroscopic scanner probe of mass 150 kg is launched from rest from the surface of Astraea-Prime into a low circular orbit.
Calculate the minimum total energy that must be supplied to the probe to place it in this orbit.
31 exam-style questions on OCR A A Level Physics Gravitational fields, covering Point and spherical masses, Newton's law of gravitation, Planetary motion, and Gravitational potential and energy. Each one has a worked solution and a mark scheme showing where the marks go.