In Larry Niven’s science fiction novel
Ringworld, a ring of material of radius
1.54 × 1011 m rotates about a star with a ro-
tational speed of 1.38 × 106 m/s. The inhab-
itants of this ring world experience a normal
contact force ~n. Acting alone, this normal
force would produce an inward acceleration of
9.28 m/s2. Additionally, the star at the cen-
ter of the ring exerts a gravitational force on
the ring and its inhabitants.
The difference between the total acceleration
and the acceleration provided by the normal
force is due to the gravitational attraction of
the central star.
Find the approximate mass of the star.
**** u guys
To find the approximate mass of the star in Larry Niven's science fiction novel Ringworld, we can use the concept of gravitational force and Newton's second law of motion.
First, let's consider the gravitational force between the star and the ring world. According to Newton's law of universal gravitation, the gravitational force between two objects is given by:
F = G * (m1 * m2) / r^2,
where F is the gravitational force, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2), m1 and m2 are the masses of the objects, and r is the distance between their centers.
In this case, the gravitational force exerted by the star on the ring world is responsible for the difference between the total acceleration and the acceleration provided by the normal force.
The total acceleration experienced by the inhabitants of the ring world, when the gravitational force is taken into account, can be given as:
a_total = a_normal + a_gravity,
where a_total is the total acceleration, a_normal is the acceleration provided by the normal force, and a_gravity is the acceleration due to the gravitational force.
Given that the inward acceleration produced by the normal force alone is 9.28 m/s^2, we can write:
a_total = 9.28 m/s^2.
Now, let's find the value of a_gravity. The gravitational force exerted by the star on the ring world can be equated to the mass of the ring world (which we'll assume to be negligible compared to the star's mass) multiplied by the acceleration due to gravity:
F_gravity = m_ring * a_gravity.
Substituting the equation for gravitational force, we can write:
G * (m_star * m_ring) / r^2 = m_ring * a_gravity.
Simplifying, we get:
a_gravity = G * m_star / r^2.
Now, let's substitute the given values:
a_gravity = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * m_star / (1.54 × 10^11 m)^2.
Finally, we can solve for the mass of the star, m_star:
m_star = (a_total - a_normal) * (1.54 × 10^11 m)^2 / (6.67430 × 10^-11 m^3 kg^-1 s^-2).
Calculating this expression should give you the approximate mass of the star in Larry Niven's Ringworld.