Answer:
(a)
M = 1.898 x 10^27 kg
(b)
v = 13.74 km/s
(c) E = 0.28 N/kg
Explanation:
Time period, T = 3.55 days = 3.55 x 24 x 3600 second = 306720 s
Radius, r = 6.71 x 10^8 m
G = 6.67 x 10^-11 Nm^2/kg^2
(a) [tex]T=2\pi \sqrt{\frac{r^{3}}{GM}}[/tex]
[tex]M=\frac{4\pi ^{2}r^{3}}{GT^{2}}[/tex]
[tex]M=\frac{4\times3.14^{2}\times 6.71^{3}\times 10^{24}}{6.67\times 10^{-11}\times 306720^{2}}[/tex]
M = 1.898 x 10^27 kg
(b) Let v be the orbital velocity
[tex]v=\frac{2\pi r}{T}[/tex]
[tex]v=\frac{2\times 3.14\times 6.71\times 10^{8}}{306720}[/tex]
v = 13739.5 m/s
v = 13.74 km/s
(b) The gravitational field E is given by
[tex]E = \frac{GM}{r^{2}}[/tex]
[tex]E = \frac{6.67\times10^{-11}\times 1.898\times 10^{27}}{6.71^{2}\times 10^{16}}[/tex]
E = 0.28 N/kg
