Question

the magnitude of the force the sun exerts on uranus is 1.41 x 10^21 n even though it is much further away than neptune. explain how it is possible for the sun to exert a greater force on uranus than neptune exerts on uranus.
a mass of the sun (msun): 1.989×1030 kg mass of uranus (muranus): 8.681×1025 kg distance (rsun-uranus): 2.872×1012 m for the sun and earth mass of earth (mearth): 5.972×1024 kg distance (rsun-earth): 1.496×1011 m
b sun to uranus approx 1.013×10^20
c the sun is much more massive than neptune. the gravitational constant g = 6.674 × 10^-11 n·m²/kg² the formula for calculating the gravitational force between two masses is: f = g·m₁·m₂/r² ; where f = force of gravity the magnitude of the force the sun exerts on uranus is 1.41 x 10^21
d the sun exerts a greater force on uranus than neptune does because the sun is significantly more massive than neptune, meaning its gravitational pull is much stronger, even though it is further away; this is due to the relationship between gravitational force and mass in the universal gravitation equation, where the force is directly proportional to the product of the masses involved and inversely proportional to the square of the distance between them
e earth and sun

Explanation:

The gravitational force \(F = G\frac{m_1m_2}{r^2}\) (where \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between them) shows that force depends on both mass and distance. The Sun has a much larger mass (\(m_{Sun}=1.989\times 10^{30}\ kg\)) compared to Neptune (\(m_{Neptune}\approx 1.024\times 10^{26}\ kg\)). Although the Sun is farther from Uranus than Neptune is, the large mass of the Sun makes the product \(m_{Sun}m_{Uranus}\) large enough so that \(F_{Sun - Uranus}\) is greater than \(F_{Neptune - Uranus}\) when considering the \(r^2\) (distance - squared) factor in the universal gravitation formula.

Answer:

D. The Sun exerts a greater force on Uranus than Neptune does because the Sun is significantly more massive than Neptune, meaning its gravitational pull is much stronger, even though it is further away; this is due to the relationship between gravitational force and mass in the universal gravitation equation, where the force is directly proportional to the product of the masses involved and inversely proportional to the square of the distance between them.