Respuesta :
Answer:
(a). The deflection angle is [tex]2.77\times10^{-9}\ rad[/tex]
(b). The deflection angle is [tex]3.95\times10^{-4}\ rad[/tex]
(c). The deflection angle is [tex]7.41\times10^{-1}\ rad[/tex]
Explanation:
Given that,
Mass of earth [tex]M_{e}=6.0\times10^{24}\ kg[/tex]
Radius of earth [tex]R_{e}=6.4\times10^{6}\ m[/tex]
Mass of white dwarf [tex]M=2.0\times10^{30}\ kg[/tex]
Radius of white dwarf [tex]R=1.5\times10^{7}\ m[/tex]
Mass of Neutron [tex]M=3.0\times10^{30}\ kg[/tex]
Radius of neutron [tex]R=1.2\times10^{4}\ m[/tex]
We need to calculate the deflection angle for earth
Using formula of angle
[tex]\alpha=\dfrac{4G M}{c^2R}[/tex]
Where, R = radius
G = gravitational constant
M = mass
c = speed of light
Put the value into the formula
[tex]\alpha=\dfrac{4\times6.67\times10^{-11}\times6.0\times10^{24}}{(3\times10^{8})^2\times6.4\times10^{6}}[/tex]
[tex]\alpha=2.77\times10^{-9}\ rad[/tex]
The deflection angle is [tex]2.77\times10^{-9}\ rad[/tex]
We need to calculate the deflection angle for white dwarf
Using formula of angle
[tex]\alpha=\dfrac{4G M}{c^2R}[/tex]
Put the value into the formula
[tex]\alpha=\dfrac{4\times6.67\times10^{-11}\times2.0\times10^{30}}{(3\times10^{8})^2\times1.5\times10^{7}}[/tex]
[tex]\alpha=3.95\times10^{-4}\ rad[/tex]
The deflection angle is [tex]3.95\times10^{-4}\ rad[/tex]
We need to calculate the deflection angle for neutron star
Using formula of angle
[tex]\alpha=\dfrac{4G M}{c^2R}[/tex]
Put the value into the formula
[tex]\alpha=\dfrac{4\times6.67\times10^{-11}\times3.0\times10^{30}}{(3\times10^{8})^2\times1.2\times10^{4}}[/tex]
[tex]\alpha=7.41\times10^{-1}\ rad[/tex]
The deflection angle is [tex]7.41\times10^{-1}\ rad[/tex]
Hence, This is the required solution.
