Question

Two satellites are in circular orbits around a planet that has radius 9.00x10^6 m. One satellite has mass 53.0 kg , orbital radius 8.20×10^7 m, and orbital speed 4800 m/s. The second satellite has mass 54.0 kg and orbital radius 7.00×10^7 m.

A) What is the orbital speed of this second satellite?
v=?

Answer 1

The orbital speed of this second satellite is 5195.16 m/s.

Step-by-step explanation:

Given that,

Orbital radius of first satellite
`r_(1)= 8.20*10^(7)`

Orbital radius of second satellite
`r_(2)=7.00*10^(7)\ m`

Mass of first satellite
`m_(1)=53.0\ kg`

Mass of second satellite
`m_(2)=54.0\ kg`

Orbital speed of first satellite = 4800 m/s

We need to calculate the orbital speed of this second satellite

Using formula of orbital speed

`v=\sqrt{(GM)/(r)}`

From this relation,

`v_(1)\propto(1)/(√(r))`

Now,
`(v_(1))/(v_(2))=\sqrt{(r_(2))/(r_(1))}`

`v_(2)=v_(1)*\sqrt{(r_(1))/(r_(2))}`

Put the value into the formula

`v_(2)=4800*\sqrt{( 8.20*10^(7))/(7.00*10^(7))}`

`v_(2)=5195.16\ m/s`

Hence, The orbital speed of this second satellite is 5195.16 m/s.