A satellite in a zephyrostationary orbit around the exoplanet Zephyros-7 appears to remain at the same point in the sky when viewed from the planet's equatorial surface.
State one orbital condition required for an orbit around Zephyros-7 to be zephyrostationary.
Calculate the orbital radius of this zephyrostationary satellite.
Mass of Zephyros-7 M=3.2×1024 kg \text{Mass of Zephyros-7 } M = 3.2 \times 10^{24} \text{ kg} Mass of Zephyros-7 M=3.2×1024 kg Rotational period of Zephyros-7 T=5.4×104 s \text{Rotational period of Zephyros-7 } T = 5.4 \times 10^4 \text{ s} Rotational period of Zephyros-7 T=5.4×104 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 centripetal force required for orbit, show that the kinetic energy Ek E_k\,Ek of the satellite is equal to half the magnitude of its gravitational potential energy EpE_pEp, where Ep=−GMmr\displaystyle E_p = -\frac{GMm}{r}Ep=−rGMm.
A small scientific capsule of mass 12.0 kg is launched from rest from the surface of Zephyros-7 into a low circular orbit.
Calculate the minimum total energy that must be supplied to the capsule 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.