Question on gravitation(low-altitude satellite)

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A low-altitude satellite near Earth's surface travels at 7.90 km/s, and the discussion revolves around calculating the speed of a similar satellite near the Moon's surface. The relevant equations involve gravitational constants and ratios of mass and radius between Earth and the Moon. An initial calculation yielded a speed of 3.12 km/s, but confusion arose regarding the interpretation of the variables used in the equation. Participants emphasized the need to correctly apply the ratios of mass and radius to derive the satellite's speed. Clarification was sought on the proper use of the gravitational equation to arrive at the correct answer.
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Homework Statement


A low-altitude satellite near the Earth's surface has a speed of 7.90 km s-1. The radius of the Earth is about 4 times that of the moon and the ratio of the average density of the Earth to that of the moon is about 5:4. The speed of a low-altitde satellite near the moon's surface would be

A. 1.77km s-1
B. 2.21km s-1
C. 2.47km s-1
D. 3.57km s-1
E. 4.42km s-1

Homework Equations


v2 = GM/r



The Attempt at a Solution


i got the ans of 3.12km s-1
the ratio of the mass of Earth to moon would be 80:1
n the ratio of radius of Earth to moon is 4:1
so i guess it's 7.92/20 ?

Pls help, i don't know what i did wrong :(
Thz so much
 
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Look at your equation again. What variable does 7.9^2/20 represent?
 
7.9 is the speed of satellite near Earth's surface, and 20 is the ratio of the mass and radius combining, (1/80)*4
 
Not the individual terms, what variable does your answer aka 7.9^2/20 = 3.12 represent? Look carefully; is it the speed of the satellite?
 

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