Question

1) Find the mass of a blackhole with a radius equal to the distance between the earth and the sun

2) find the value of gravity 600 km above the earths surface also find the value of gravity at 36000km abover the earths surface. b) find the obrital speed (m/s) and periods in hours for spacecraft at each location at the orbital locations

Answer 1

1)

use,

schwarzschild radius,

r=2M*G/C^2

1.49*10^11-2*M*6.67*10^-11/(3*10^8)^2

====> mass, M=1.0052*10^18 kg

mass of the blackhole,M=1.0052*10^18 kg

2)

b)

use,

at h=600km =6*10^5 m

g'=G*M/(R+h)^2

=6.67*10^-11*5.97*10^24/(6.4*10^6+6*10^5)^2

=8.13 m/sec^2

and

at h=36000km = 3.6*10^7 m

g'=G*M/(R+h)^2

=6.67*10^-11*5.97*10^24/(6.4*10^6+3.6*10^7)^2

=0.221 m/sec^2

c)

orbital speed, Vo=sqrt(g'*(R+h))

at h=6*10^5 m

Vo=sqrt(8.13*((6.4*10^6+6*10^5))

vo=7.543*10^3 m/sec

and

at h=3.6*10^7 m

orbital speed, Vo=sqrt(g'*(R+h))

Vo=sqrt(8.13*((6.4*10^6+3.6*10^7))

vo=1.86*10^4 m/sec

d)

to find the period,

T=2pi*(R+h)/vo

==>

at h=6*10^5m

T=2pi*(6.4*10^6+6*10^5)/(7.543*10^3)

T=5.83*10^3 sec

T=97.18 min

and

at h=3.6*10^7m

T=2pi*(6.4*10^6+3.6*10^7)/(1.86*10^4)

T=1.43*10^4 sec

T=238.72 min