Question

5. (Review) SInce the radius of the moon is much smaller than the radius of the earth, why isn't gravity stronger on the moon according to the inverse square law of Newton's law of Universal Gravitation?
6. What is the approximate value of the net centripetal acceleration experienced by a 75.0 kg astronaut located in the ISS, a distance of 254 miles from the earth's surface?

Answer 1

SOLUTION :

5.

Gravity means acceleration due to gravity.

Moon is small so not only radius is small, its mass is also small.  Gravity is directly proportional two mass and inversely proportional to square of the radius.

g moon = G M moon / (R moon)^2 

Now M is directly proportional to R^3 for spherical planets.

So, M moon is proportional too (R moon)^3 

Since, R moon is smaller than earth, its mass will be comparatively lesser than (R moon)^2

Mathematically,

g moon / g earth

= ( G M moon) / ( G M earth)  * (R earth)^2 / (R moon)^2 

=  (R moon)^3 / (R earth)^3 * R earth)^2 / (R moon)^2 

= R moon / R earth 

So, moon, being smaller than earth , yet its gravity is less than earth and directly equal to to the ratio of moon’s radius to earth’s radius.

(ANSWER).

6.

Radius of earth = 6378 km = 6.378*10^6 m 

Mass off the earth = 5.97*10^24 kg 

Height of the astronaut from earth’s surface = 254 miles = 254*1.60934 km

= 408.7622 km = 4.087622*10^5 m 

So distance from earth’s centre, r astronaut :

= 6.378*10^6 + 4.087622*10^5 = 6.7867622*10^6 m

So,

g at the altitude of 254 miles

= G * M / (r astronaut)^2 

= 6.67*10^(-11) * 5.97*10^24 / (6.7867622*10^6)^2

= 8.65 m/s^2 (ANSWER)

Answer 2