Physics

A satellite of mass 220 kg is launched from a site on Earth's equator into an orbit at 200 km above the surface of Earth.
(a) Assuming a circular orbit, what is the orbital period of this satellite?
5310 s

(b) What is the satellite's speed in its orbit?
7790m/s

(c) What is the minimum energy necessary to place the satellite in orbit, assuming no air friction?

I was able to get a and b, but i don't know about c.

Thanks

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3. 👁 183
1. You have to lift the body to orbit and then speed it up to orbit speed.
m v^2/r = G m M/r^2 in orbit
so (1/2)m v^2 = G m M/(2r) = Ke in or!@#\$%^&ange in Potential energy to lift it to orbit
= G m M/(r-Rearth)

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posted by Damon
2. how do i get small r?

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posted by Ana
3. is it R_e + height?

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posted by Ana
4. Yes, earth radius + height

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posted by Damon
5. (6.67E-11*220*5.98E24)/(6.38E6+2.0E5)-(6.38E6)=
1.33295653E10J

Is this right? I want to make sure if this is right before I insert into the site.

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posted by Ana
6. both terms should be positive

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posted by Damon
7. What do you mean?

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posted by Ana
8. (6.67E-11*220*5.98E24)/[2(6.38E6+2.0E5)]
note 2 in denominator
+ (6.67E-11*220*5.98E24) / 2^10^5

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posted by Damon
9. 8.78*10^16 [ 1/1.32E7 + 1/2E5 ]

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posted by Damon
10. so is it 6770873457?

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posted by Ana
11. Change in Potential energy to lift it to orbit
= G m M [1/Rearth - 1/r ]

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posted by Damon
12. 8.78*10^16 [ 1/1.32E7 + 1/6.38E6 - 1/6.58E6 ]

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posted by Damon
13. this is my last try....is it 6904053501?

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posted by Ana
14. 7.07*10^9 Joules

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posted by Damon
15. We are close to each other. My arithmetic is failing, after bedtime.

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posted by Damon
16. Your professor must like arithmetic !

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posted by Damon
17. Yes, we are. Some of the problems are very difficult but thank you so much for your help. I really appreciate.

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posted by Ana

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