Question

Supermassive black holes are thought to exist at the center of many galaxies. (a) What is the radius in m of such an object if it has a mass of 1010 Suns? Xm (b) What is this radius in light years?

Answer 1

2.95×10¹³ m

0.00311815 lightyears

Step-by-step explanation:

m = 10¹⁰ times the mass of the sun

mass of the sun = 1.9891 × 10³⁰ kilograms

c = Speed of light = 3×10⁸ m/s

G = Gravitational constant = 6.67408 × 10⁻¹¹ m³/ kgs²

a) Schwarzschild radius

`R_s=(2GM)/(c^2)\\\Rightarrow R_s=(2* 6.67408* 10^(-11)* 10^(10)1.9891* 10^(30))/((3* 10^8)^2)=2.95* 10^(13)\ m`

∴ Radius in meter is 2.95×10¹³ m

b) 1 m = 1.057×10⁻¹⁶ Lightyear

`2.95* 10^(13)\ m=2.95* 10^(13)\ m* 1.057* 10^(-16)=0.00311815\ lightyears`

∴Radius in Lightyear 0.00311815 lightyears