QUESTION 12 The mass of the Earth can be determined by which of the following me

Question

QUESTION 12 The mass of the Earth can be determined by which of the following methods? (Mark all that apply.) OA By determining the radial acceleration of the Earth in its orbit around the Sun and knowing the distance from the Earth to the Sun. B By determining the radial acceleration of the Moon in its orbit around the Earth and knowing the distance from the Earth to the Moon. OC.By determining the radial acceleration of a satellite in its orbit around the Earth and knowing the height of the orbit and the radius of the Earth. D By determining the free-fall acceleration of an ideal projectile near the surface of the Earth and knowing the Earth's radius. E. NONE of the other choices

Explanation / Answer

12. the mass of the earth can be determined by the following methods

a. by knoiwing radial acceleration, distanceof earth and sun

ar = v^2/R

v = sqrt(ar*R)

we can find speed of earths orbit around sun using this

but we cant find mass of earth

b. radial acceleration of moon = ar

distance form earth to moon = R

mass of earth = m

Gm/R^2 = ar

hence

m = ar*R^2/G

we can find mass of earth from this

c. just like last case we find mass of earth using this as well

d. byknowing free falla cceleratino near earths surface and knowing the radius is just like case B and can find mass of earth

hence option b, c, d

11. for h = 200 km

R = 6371 km

v^2/(R + h) = GM/(R + h)^2

M = 5.972*10^24 kg

hence

v = sqrt(GM/(R + h))

T = 2*pi(R + h)/sqrt(GM/(R + h)) = 2*pi*(R + h)sqrt((R + h)/GM) = 5302.7878515 s

T = 88.3797975 min = 1.472 hr = 1 hr 28 min22 sec
Hence option D, E, F, I

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