Find the approximate gravitational red shift in 500 nm light emitted by a compact star whose mass is that of sun but whose radius is 10 km.

Question

Find the approximate gravitational red shift in 500 nm light emitted by a compact star whose mass is that of sun but whose radius is 10 km.

Answer 1

Z_approx=GM/(c^2 r)

**where G is gravitational constant , M is the mass of the sun and r is the radius

then do the calculations

Answer 2

To find the approximate gravitational redshift in 500 nm light emitted by a compact star, we can use the formula:

Δλ/λ = GM/(rc^2)

Where:
Δλ = change in wavelength
λ = original wavelength
G = gravitational constant (6.67430 × 10^-11 m^3 kg^−1 s^−2)
M = mass of the star (in kg)
r = radius of the star (in meters)
c = speed of light (3.00 × 10^8 m/s)

Let's substitute the values given:

λ = 500 nm = 500 × 10^-9 m
M = mass of the Sun = 1.989 × 10^30 kg
r = 10 km = 10 × 10^3 m

Now we can calculate the gravitational redshift:

Δλ/λ = (6.67430 × 10^-11 m^3 kg^−1 s^−2 × 1.989 × 10^30 kg) / ((10 × 10^3 m) × (3.00 × 10^8 m/s)^2)

Δλ/λ ≈ 442.94 × 10^-11

Therefore, the approximate gravitational redshift in 500 nm light emitted by a compact star with a mass equal to that of the Sun and a radius of 10 km is approximately 442.94 × 10^-11.

Answer 3

To find the gravitational redshift, we need to use the formula:

Δλ/λ = GM/Rc^2

where Δλ is the change in wavelength, λ is the initial wavelength, G is the gravitational constant (6.67430 x 10^-11 m^3 kg^-1 s^-2), M is the mass of the compact star, R is the radius of the star, and c is the speed of light in vacuum (3 x 10^8 m/s).

First, let's convert the given values to appropriate units:

Mass of the Sun (M) = 1.989 x 10^30 kg
Radius of the compact star (R) = 10 km = 10,000 m
Wavelength of light emitted (λ) = 500 nm = 500 x 10^-9 m

Now we can calculate the gravitational redshift using the formula:

Δλ/λ = (GM/Rc^2)

Δλ/λ = (6.67430 x 10^-11 m^3 kg^-1 s^-2 * 1.989 x 10^30 kg) / (10,000 m * (3 x 10^8 m/s)^2)

Simplifying the equation:

Δλ/λ = (1.331 x 10^-20) / (9 x 10^16)

Δλ/λ ≈ 1.5 x 10^-37

Therefore, the approximate gravitational redshift in 500 nm light emitted by a compact star with the mass of the Sun and a radius of 10 km is approximately 1.5 x 10^-37.