Gravity Serious satellite

An artificial satellite revolves around the Earth in a circular orbit of radius 42250 km. Find its speed (in km per second) if it takes 24 hours to revolve around the Earth. . . . N S O 2012 . . .NSO 2012


The answer is 3.07.

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2 solutions

Paulo Carlos
Mar 27, 2015

Circumference = 2 × π × r 2 \times \pi \times r

r = 42250 r = 42250 then, the circumference is = 84500 π 84500 \pi

V ( K m / h ) = 84500 π 24 = 11061.0241... V (Km/h) = \frac {84500 \pi}{24} = \approx11061.0241...

To convert it to Km/s we need to multiplicate 11061.0241... \approx 11061.0241... by 0.000277777778 0.000277777778 , which will results in 3.072... \boxed { \approx3.072...}

Caleb Townsend
Feb 20, 2015

v = ω r v = \omega r ω = 1 rev day × 2 π rad rev × 1 day 86400 s 7.27 × 1 0 5 rad s \omega = 1\frac{\text{rev}}{\text{day}} \times 2\pi\frac{\text{rad}}{\text{rev}}\times \frac{1\ \text{day}}{86400\ \text{s}} \approx 7.27\times 10^{-5} \frac{\text{rad}}{\text{s}} r = 42250 km r = 42250\ \text{km} v = ( 7.27 × 1 0 5 rad s ) × 42250 km 3.07 km/s v = (7.27\times 10^{-5} \frac{\text{rad}}{\text{s}})\times 42250\ \text{km}\approx \boxed{3.07\ \text{km/s}}

Correct! that's absolutely right!

Upvoted!

Sravanth C. - 6 years, 3 months ago

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