Please solve with step by step instruction and equations: The existence of the p
ID: 2116375 • Letter: P
Question
Please solve with step by step instruction and equations:The existence of the planet Pluto was proposed based on irregularities in Neptune's orbit. Pluto was subsequently discovered near its predicted position. But it now appears that the discovery was fortuitous, since Pluto is small and the irregularities in Neptune's orbit were not well known. To illustrate that Pluto has a minor effect on the orbit of Neptune compared with other planets: (a) Calculate the acceleration of gravity at Neptune due to Pluto when they are 4.50 x 10^12 m apart, as they are at present. The mass of Pluto is 1.4 x 10^22 kg. (b) Calculate the acceleration of gravity at Neptune due to Uranus, presently about 2.50 x 10^12m apart and compare it with that due to Pluto. The mass of Uranus is 8.62 x 10^25 kg.
Explanation / Answer
(a) Accl due to gravity at Neptune due to Pluto is given by :
gPluto = GMPluto/D2
= (6.67 x 10-11 x 1.4 x 1022)/(4.5 x 1012)2
= 4.6114 x 10-14 m/s2
(b) Accl due to gravity at Neptune due to Uranus is given by :
gUranus = GMUranus/D2
= (6.67 x 10-11 x 8.62 x 1025)/(2.5 x 1012)2
= 9.1579 x 10-10 m/s2
Thus, as clearly seen above, gUranus >> gPluto (around 20000 times)