Answer:
The orbital speed of this second satellite is 5195.16 m/s.
Explanation:
Given that,
Orbital radius of first satellite [tex]r_{1}= 8.20\times10^{7} [/tex]
Orbital radius of second satellite [tex]r_{2}=7.00\times10^{7}\ m[/tex]
Mass of first satellite [tex]m_{1}=53.0\ kg[/tex]
Mass of second satellite [tex]m_{2}=54.0\ kg[/tex]
Orbital speed of first satellite = 4800 m/s
We need to calculate the orbital speed of this second satellite
Using formula of orbital speed
[tex]v=\sqrt{\dfrac{GM}{r}}[/tex]
From this relation,
[tex]v_{1}\propto\dfrac{1}{\sqrt{r}}[/tex]
Now, [tex]\dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{r_{2}}{r_{1}}}[/tex]
[tex]v_{2}=v_{1}\times\sqrt{\dfrac{r_{1}}{r_{2}}}[/tex]
Put the value into the formula
[tex]v_{2}=4800\times\sqrt{\dfrac{ 8.20\times10^{7}}{7.00\times10^{7}}}[/tex]
[tex]v_{2}=5195.16\ m/s[/tex]
Hence, The orbital speed of this second satellite is 5195.16 m/s.
