Question

The planet Neptune was initially discovered by looking at irregularities in the orbit of Uranus. In the late 19th century, the existence of the dwarf planet Pluto was proposed in the same manner, and Pluto was eventually discovered in 1930 near its predicted position. However, we now know that Pluto is extremely small, and could not have been the cause of the measured irregularities. In this problem we will calculate the acceleration due to the gravitational force on Neptune from Pluto and Uranus. (Note that we also now have better measurements of Uranus's orbit, which shows there are no other large bodies in the solar system acting on it). No Attempt No Attempt 33%
Part (a) Calculate the magnitude of the gravitational field of Pluto at the location of Neptune, in meters per square second, when they are 4.45×1012 m apart, as they are at present. The mass of Pluto is 1.40×1022 kg. No Attempt No Attempt 33%

Part (b) Calculate the magnitude of the gravitational field of Uranus at the location of Neptune, in meters per square second, when they are 2.32×1012 m apart, as they are at present. The mass of Uranus 8.62×1025 kg. show answer No Attempt 33%

Part (c) Calculate the ratio of the gravitational field of Uranus to the gravitational field of Pluto, at the location of Neptune. gNU/gNP =

Answer 1

Answer:

a) gNP = 4.71 x 10^-14 m/s²

b) gNU = 1.06 x 10^-9 m/s²

c) gNU/gNP = 22505.3

Explanation:

The formula for calculating the gravitational field at a planet is given by Newton's Gravitational law. Since the force exerted by 1st planet on 2nd will be equal to weight of the second planet

F = W = mg = GMm/R^2

g = GM/R^2

where,

m = mass of other planet

g = gravitational field at the surface of planet

G = Universal Gravitational Constant = 6.67 x 10^-11 N.m²/kg²

M = Mass of the planet

R = Distance between planets

a)

gNP = (6.67 x 10^-11 N.m²/kg²)(1.4 x 10^22 kg)/(4.45 x 10^12 m )²

gNP = 4.71 x 10^-14 m/s²

b)

gNU = (6.67 x 10^-11 N.m²/kg²)(8.62 x 10^25 kg)/(2.32 x 10^12 m )²

gNU = 1.06 x 10^-9 m/s²

c)

gNU/gNP = (1.06 x 10^-9 m/s²)/(4.71 x 10^-14 m/s²)

gNU/gNP = 22505.3