Final answer:
Pluto's gravitational influence on Neptune is negligible. Using Newton's law of universal gravitation to calculate the acceleration due to gravity at Neptune due to Pluto results in an acceleration of approximately 4.58 × 10^-22 m/s^2, demonstrating Pluto's minor effect.
Step-by-step explanation:
The influence of Pluto on Neptune's orbit was initially thought to be significant due to suspected irregularities in Neptune's trajectory. However, further analysis showed that Pluto's mass and size were not sufficient to cause such perturbations. When measuring gravitational effects, the formula to use is Newton's law of universal gravitation, which can be written as F = G(m1*m2)/r^2, where F is the gravitational force, G is the gravitational constant (6.674 × 10-11 N·m2/kg2), m1 and m2 are the masses of the two bodies, and r is the distance between their centers. To calculate the acceleration due to gravity (g) that Pluto exerts on Neptune, we simplify this to g = G*m/r^2 (as acceleration due to gravity is force per unit mass). Using the given values:
- Mass of Pluto (m): 1.4 × 1022 kg
- Distance between Pluto and Neptune (r): 4.50 × 1012 m
The acceleration due to gravity at Neptune due to Pluto can be calculated as:
g = (6.674 × 10-11 N·m2/kg2 × 1.4 × 1022 kg) / (4.50 × 1012 m)2g ≈ 4.58 × 10-22 m/s2
This illustrates that Pluto's gravitational influence on Neptune is extremely minor compared to that of other celestial bodies like Uranus, which is the closest major planet to Neptune. Therefore, the discovery of Pluto based on these orbital irregularities was indeed fortuitous and suggests that Pluto's gravitational pull is too weak to have been the cause of the observed anomalies in Neptune's orbit.