This question is about a robotic space probe in a circular orbit around Venus.
Define gravitational potential energy of an object at a point in a gravitational field.
The space probe has a mass of 850 kg850\text{ kg}850 kg. The orbital radius of the probe around Venus is 1.5×107 m1.5 \times 10^7\text{ m}1.5×107 m. The orbital period of the probe is 2.02×104 s2.02 \times 10^4\text{ s}2.02×104 s. The mass of Venus is 4.9×1024 kg4.9 \times 10^{24}\text{ kg}4.9×1024 kg. (Take G=6.67×10−11 N m2 kg−2G = 6.67 \times 10^{-11}\text{ N m}^2\text{ kg}^{-2}G=6.67×10−11 N m2 kg−2)
Show that the magnitude of the gravitational potential energy of the probe is about 1.9×1010 J1.9 \times 10^{10}\text{ J}1.9×1010 J.
Show that the kinetic energy of the probe is half the magnitude of its gravitational potential energy.
Calculate the total energy of the probe.
The power source for the scientific equipment on board the probe is a radioisotope thermoelectric generator containing plutonium-238, which initially provides 450 W450\text{ W}450 W of thermal power.
Plutonium-238 decays by α\alphaα-particle emission with a half-life of 88 years88\text{ years}88 years. The kinetic energy of each emitted α\alphaα-particle is 9.0×10−13 J9.0 \times 10^{-13}\text{ J}9.0×10−13 J. (Take 1 year=3.16×107 s1\text{ year} = 3.16 \times 10^7\text{ s}1 year=3.16×107 s)
Calculate the number NNN of plutonium-238 nuclei needed to provide the power of 450 W450\text{ W}450 W initially.
Calculate the power PPP still available from the plutonium-238 source 60 years60\text{ years}60 years later.
