Centripetal acceleration of the satellite?

[magnolia1]

Homework Statement

An Earth satellite moves in a circular orbit 790 km above the Earth's surface. The period of the motion is 100.5 min.
(a) What is the speed of the satellite?
(b) What is the magnitude of the centripetal acceleration of the satellite?

Homework Equations

a= v² / r

T = (2 Pi r)/ V

The Attempt at a Solution

Converting km to m: 790km*(10³m / 1km) = 7.90*10⁵m
Converting min to seconds: 100.5min*(60seconds/1min) = 6.03*10³seconds

Now that I have the conversions, I will solve for the unknown variables in the above formulas:
I think the radius is 7.90*10⁵m and period is 6.03*10³seconds

(a) Speed of satellite:
v=(2 pi (7.90*10⁵m)) / (6.03*10³s)
v=8.27*10²m/s

Correct answer: 7460 m/s

because the speed is incorrect, the error follows through to part (b) when substituting in speed.
How is it that it's so far off?
Thanks :)

 

[ehild]

r should be the radius of the orbit, centred at the centre of Earth. The height of the satellite above the surface of Earth is 790 km, how far is it from the centre of Earth?

ehild

 

[magnolia1]

I had to look it up, but 6371 km is from the surface of Earth to its centre. So I will try now with the new radius of (6371km+790km) * (10^3m/1km) = 7.16*10^6metres.
ANS: 7460.63 = 7461m/s

Thanks for your help!

 

[ehild]

I had to look it up, but 6371 km is from the surface of Earth to its centre. So I will try now with the new radius of (6371km+790km) * (10^3m/1km) = 7.16*10^6metres.
ANS: 7460.63 = 7461m/s

Thanks for your help!

You are welcome.

ehild

 

[Nickie]

As a scientist, it is important to carefully check and review your calculations to ensure accuracy. In this case, the error may be due to rounding off numbers too early in the calculation or using the incorrect values for the radius and period.

Let's review the equations used:

a = v^2 / r

T = (2πr) / v

In the first equation, the radius (r) should be the distance from the center of the Earth to the satellite's orbit, which is the sum of the Earth's radius (6.37*10^6 m) and the satellite's altitude (790 km or 7.90*10^5 m). So the radius (r) should be 7.97*10^6 m.

In the second equation, the period (T) should be in seconds. So the period (T) should be 100.5 min * (60 seconds / 1 min) = 6030 seconds.

Now let's plug in the correct values:

(a) Speed of satellite:
v = (2π * 7.97*10^6 m) / (6030 s)
v = 8.29*10^3 m/s

(b) Magnitude of centripetal acceleration:
a = (8.29*10^3 m/s)^2 / (7.97*10^6 m)
a = 8.59*10^-2 m/s^2

Therefore, the correct answers are:

(a) Speed of satellite: 8290 m/s
(b) Magnitude of centripetal acceleration: 0.0859 m/s^2

It is important to double check your calculations and use accurate values for the variables in your equations to ensure the correct answer. Additionally, using scientific notation can help avoid errors and provide more accurate results.