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A satellite in a circular orbit rotates around the Earth every 120 min

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A satellite in a circular orbit rotates around the Earth every 120 min  [#permalink]

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New post 03 Aug 2019, 22:05
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A satellite in a circular orbit rotates around the Earth every 120 minutes. If the Earth’s radius is 4000 miles at sea level, and the satellite’s orbit is 400 miles above sea level, approximately what distance does the satellite travel in 40 minutes?

A. 1400 miles
B. 9210 miles
C. 4400 miles
D. 4120 miles
E. 8000 miles

Source: Test Prep Review

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Re: A satellite in a circular orbit rotates around the Earth every 120 min  [#permalink]

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New post 05 Aug 2019, 09:33
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Top Contributor
SajjadAhmad wrote:
A satellite in a circular orbit rotates around the Earth every 120 minutes. If the Earth’s radius is 4000 miles at sea level, and the satellite’s orbit is 400 miles above sea level, approximately what distance does the satellite travel in 40 minutes?

A. 1400 miles
B. 9210 miles
C. 4400 miles
D. 4120 miles
E. 8000 miles

TPR


This diagram might help
Image

So, the black dot represents the Earth's center.
So, the radius of the satellite's orbit = 4400 miles

circumference of circle = 2πr

So, the circumference of satellite's orbit = 2π(4400) = 8800π

GIVEN: the satellite in a circular orbit rotates around the Earth every 120 minutes.
In other words, the satellite travels 8800π every 120 minutes

So, in 40 minutes, the satellite will travel 1/3 of the 8800π mile orbit (since 40 minutes is 1/3 of 120 minute)

Distance traveled = 8800π/3

PRO TIP: Since π ≈ 3.14, we know that π/3 ≈ 3.14/3 ≈ some number a little bit bigger than 1

So, 8800π/3 = 8800(π/3) = 8800(a number a little bit bigger than 1) = some number a little bit bigger than 8800

Answer: B

Cheers,
Brent
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Re: A satellite in a circular orbit rotates around the Earth every 120 min  [#permalink]

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New post 22 Mar 2020, 23:13
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SajjadAhmad wrote:
A satellite in a circular orbit rotates around the Earth every 120 minutes. If the Earth’s radius is 4000 miles at sea level, and the satellite’s orbit is 400 miles above sea level, approximately what distance does the satellite travel in 40 minutes?

A. 1400 miles
B. 9210 miles
C. 4400 miles
D. 4120 miles
E. 8000 miles

Source: Test Prep Review

Solution:


    • In 120 minutes satellite complete 1 rotation
      o In 1 minutes, satellite will cover \(\frac{1}{120}\) part of one rotation.
      o In 40 minutes, stellite will cover \(\frac{1}{120}*40 = \frac{1}{3}\) part of one revolution
    • Distance between satellite and center of the earth=radius of orbit = 4000 + 400 = 4400 miles
    • Distance travelled in one rotation = circumference of orbit= 2*π*r
    • \(\frac{1}{3}\)rd distance of 1 rotation = \(\frac{1}{3}*2* π*r\) =\(\frac{1}{3}*2*3.14*4400 =\frac{3.14}{3}*8800\) miles (approx.)
    • The final answer is more than 8800, the only answer option more than 8800 is 9210
Hence, the correct answer is Option B.
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Re: A satellite in a circular orbit rotates around the Earth every 120 min  [#permalink]

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New post 23 Mar 2020, 00:00
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SajjadAhmad wrote:
A satellite in a circular orbit rotates around the Earth every 120 minutes. If the Earth’s radius is 4000 miles at sea level, and the satellite’s orbit is 400 miles above sea level, approximately what distance does the satellite travel in 40 minutes?

A. 1400 miles
B. 9210 miles
C. 4400 miles
D. 4120 miles
E. 8000 miles

Source: Test Prep Review


The radius of the satellite from the centre of the Earth is 4000 + 400 = 4400 miles

Circumference (distance covered by the satellite) = \(2*\pi*4400\)

In 1/3rd of the time, it will cover =\( 2*\pi*4400 / 3 = 9210\) miles
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Re: A satellite in a circular orbit rotates around the Earth every 120 min   [#permalink] 23 Mar 2020, 00:00

A satellite in a circular orbit rotates around the Earth every 120 min

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