An astronaut on the moon . Measure the acceleration due to gravity and finds it to be 1.67m/sec . He knows that the earth is about 80 times . More massive then the moon . What is his estimate of the radius of earth to that of moon ?
Answers
Explanation:
search-icon-image
Class 11
>>Physics
>>Gravitation
>>Variation in Value of Acceleration due to Gravity
>>An astronaut on the moon measures the ac
Question
Bookmark
An astronaut on the moon measures the acceleration due to gravity as 1.67m/s
2
. He knows that the Earth is 80 times more massive than the moon. What is the estimate of ratio of the radius of the Earth to that of the moon?
Medium
Solution
verified
Verified by Toppr
Acceleration due to gravity =
r
2
GM
where M is the mass of the celestial body on which acceleration due
to gravity is to be measured .
Acceleration due to gravity on the Earth = 10 ms
−2
Acceleration due to gravity on the Moon = 1.67 ms
−2
Therefore ,
r
moon
2
GM
moon
= 1.67 ms
−2
...(i)
r
earth
2
GM
earth
= 10 ms
−2
...(ii)
Dividing equation (i) by (ii) :
M
earth
r
moon
2
M
moon
r
earth
2
=
6
1
r
moon
2
r
earth
2
=
6
80
Hence ,
r
moon
r
earth
= 3.65