The mass of a certain neutron star is
5 × 10^30kg (2.5 solar masses) and its radius is 2000 m. What is the acceleration of gravity at the
surface of this condensed, burned-out star? The value of the universal gravitational constant is 6.67 × 10^−11N·m2/kg2.
Answer in units of m/s2
g = G M/R^2 is the answer, where
G = 6.67 × 10^−11 N·m^2/kg^2.
R = 2000 m
M = 5 × 10^30 kg
To find the acceleration of gravity at the surface of the neutron star, we can use Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force,
G is the universal gravitational constant (6.67 × 10^-11 N·m^2/kg^2),
m1 and m2 are the masses of the objects (in this case, the neutron star and an object near its surface), and
r is the distance between the centers of the objects.
We can rearrange the equation to solve for the acceleration of gravity (g):
F = m * g
g = G * m1 / r^2
Given:
m1 = 5 × 10^30 kg
G = 6.67 × 10^-11 N·m^2/kg^2
r = 2000 m
Substituting the given values into the equation:
g = (6.67 × 10^-11 N·m^2/kg^2) * (5 × 10^30 kg) / (2000 m)^2
g = (6.67 × 10^-11) * (5 × 10^30) / (2000)^2
Now, let's calculate the value:
g ≈ 8.34 × 10^11 m/s^2
Therefore, the acceleration of gravity at the surface of the neutron star is approximately 8.34 × 10^11 m/s^2.
To find the acceleration of gravity at the surface of the neutron star, we need to use the formula for gravitational acceleration:
a = GM/r^2
Where:
a = acceleration of gravity
G = Universal gravitational constant (6.67 × 10^-11 N·m^2/kg^2)
M = mass of the neutron star
r = radius of the neutron star
Given:
M = 5 × 10^30 kg
r = 2000 m
Substituting these values into the formula, we get:
a = (6.67 × 10^-11 N·m^2/kg^2)(5 × 10^30 kg) / (2000 m)^2
Now, let's solve this equation step by step.
First, let's calculate the numerator:
(6.67 × 10^-11 N·m^2/kg^2)(5 × 10^30 kg) = 3.335 × 10^20 N·m/kg
Next, let's calculate the denominator:
(2000 m)^2 = 4,000,000 m^2 = 4 × 10^6 m^2
Finally, let's divide the numerator by the denominator to obtain the acceleration of gravity:
a = (3.335 × 10^20 N·m/kg) / (4 × 10^6 m^2)
Now, to simplify this expression, we can rearrange the units:
a = (3.335 × 10^20 N·m / 4 × 10^6 m) / kg
Dividing the numerator gives:
a = 8.3375 × 10^13 N/m / kg
Simplifying the units gives:
a = 8.3375 × 10^13 N/kg·m
Finally, we can rewrite this in the desired units:
a = 8.3375 × 10^13 m/s^2
Therefore, the acceleration of gravity at the surface of the neutron star is 8.3375 × 10^13 m/s^2.