A geostationary satellite is positioned 35,800 km above Earth’s surface. It takes 24 hours to complete one orbit. The radius of Earth is about 6400 km.
a) What distance does the satellite travel in 1 h? 3 h? 2.5 h? 25 h?
b) After how many hours has the satellite traveled 200,00 km?

Question

A geostationary satellite is positioned 35,800 km above Earth’s surface. It takes 24 hours to complete one orbit. The radius of Earth is about 6400 km.
a) What distance does the satellite travel in 1 h? 3 h? 2.5 h? 25 h?
b) After how many hours has the satellite traveled 200,00 km?

jack1 · Answer

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anonymous · Answer

That is literally the only part I know how to figure out. :P

anonymous · Answer

Would I just find the circumference of the orbit and then divide into chunks based on the time intervals??

jack1 · Answer

perfect, that solution sounds really good

jack1 · Answer

compare answers here?

anonymous · Answer

Circumference = approx. 265,016

so, 1 hr = 11,042.34 km?
3 hr = 33,127?
2.5 hr = 27,605.84?
25 hr = 276,058.34?

I think this is correct, but how would I calcualate how long it took to travel 200,000 km?

anonymous · Answer

*calculate

anonymous · Answer

wait... I would just divide the circumference by 200,000 to find that... huh?

jack1 · Answer

yep, what percentage of the circumference is 200000?

anonymous · Answer

75%

so, 18 hrs?

jack1 · Answer

so flip ur idea and reverse it
divide (200000/ circumference) *100 = % of circumference

jack1 · Answer

yep perfect dude

anonymous · Answer

well, like 18.1 because the percent is not perfect. :P

jack1 · Answer

I got:
circumference = 265150 km
so
it travels 265150km every 24 hours
therefore 11048 km per hour
so 3 hours = 3*11048 = 33134 km
2.5 hrs = 27619.8 km
25 hrs = 276198

and 75.43 % so 18 hrs and 6 minutes

jack1 · Answer

but i recon they'll let the rounding slide in this case, sig figs an all that

anonymous · Answer

Sweet, I feel a little less stupid. Thanks for working with me on this! :)

jack1 · Answer

always welcome dude

anonymous · Answer

Also, do you know how to use cosine functions and such? If you have a minute, I am going to post another problem. I really don't understand them. Could you help me?

jack1 · Answer

dude, im sorry, is 3am here and i'm beat, so i'm gonna bail on you, sorry again, need zzzz's tho
hit up @ganeshie8 , he's my goto mathlete

anonymous · Answer

haha, okay. Well thank you anyways! Have a good night!! :)

ganeshie8 · Answer

sorry WTFork im going out for a while... cya

anonymous · Answer

No worries! Thanks anyways! :)