# Linear Velocity

#### dtippitt

##### New member
Can someone please check my work to this?
The reflecting telescope is deployed in low earth orbit( 600km) with each orbit lasting about 95 min. use the linear velocity formula to solve the problem.

I did 300 * 95 min = 28500. Can someone check my work please? if someone could check it today hat would be great thanks.

#### MarkFL

Staff member
Can someone please check my work to this?
The reflecting telescope is deployed in low earth orbit( 600km) with each orbit lasting about 95 min. use the linear velocity formula to solve the problem.

I did 300 * 95 min = 28500. Can someone check my work please? if someone could check it today hat would be great thanks.
I would use:

$$\displaystyle v=r\omega=\left(r_E+600\right)\frac{2\pi}{95}\,\frac{\text{km}}{\text{min}}$$

where $$r_E$$ is the radius of the Earth in km. Are you given a value for this that you are to use?

#### dtippitt

##### New member
I would use:

$$\displaystyle v=r\omega=\left(r_E+600\right)\frac{2\pi}{95}\,\frac{\text{km}}{\text{min}}$$

where $$r_E$$ is the radius of the Earth in km. Are you given a value for this that you are to use?
the formula they gave me is v=r(radian symbol)/t
I think r stands for radius and t stands for time. I am not sure how to use this formula.

#### MarkFL

Staff member
the formula they gave me is v=r(radian symbol)/t
I think r stands for radius and t stands for time. I am not sure how to use this formula.
Yes, that's the same formula I used. The angular velocity $$\omega$$ is $$2\pi$$ radians (one complete circle) per 95 minutes. The radius of the orbital path is 600 km more than the radius of the Earth.

#### dtippitt

##### New member
Yes, that's the same formula I used. The angular velocity $$\omega$$ is $$2\pi$$ radians (one complete circle) per 95 minutes. The radius of the orbital path is 600 km more than the radius of the Earth.
The only 2 numbers they give are 600km and 95 min.
Here is the problem again.

The reflection telescope is deployed in low earth orbit(600km) with each orbit lasting about 95 minutes. linear velocity is calculated by the formula

#### MarkFL

Staff member
The only 2 numbers they give are 600km and 95 min.
Here is the problem again.

The reflection telescope is deployed in low earth orbit(600km) with each orbit lasting about 95 minutes. linear velocity is calculated by the formula

According to google, the radius of the Earth is about 6,371 km. So, plug that into the formula I posted above...what do you get?

#### dtippitt

##### New member
I think the right answer is 28000 but I don't know how to get that.

#### MarkFL

Staff member
I think the right answer is 28000 but I don't know how to get that.
It appears you are to give the answer in km/hr, in which case you would multiply the result you get from the formula I gave by 60. Your not going to get 28000 km/hr exactly, unless you use a value for the radius of the Earth constructed to give you that value for the linear speed. Using the value I cited, I get about 27663 km/hr.