What is the magnitude of the free-fall acceleration at a point that is a distanc

Question

What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth, where K is the radius of the Earth? Three 5.0-kg masses are located at points in the xy plane as shown in the figure. Use this exhibit to answer the following question(s). What is the magnitude of the resultant force (caused by the other two masses) on the mass at the origin? A satellite circles planet Roton every 2.8 h in an orbit having a radius of 1.2 Times 10^7m If the radius of Roton is 5.0 Times 10^6 m. what is the magnitude of the free-fall acceleration on the surface of Roton? The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 Times 10^6 m. What is the mass of planet Nutron?

Explanation / Answer

1) b) 1.1 m/s^2

g = G*M/(R + 2*R)^2

= (1/9)*g*M/R^2

= g/9

= 9.8/9

= 1.1 m/s^2

2) b)2.12*10^-8 N

Fx = G*m^2/x^2 = 6.67*10^-11*5^2/0.4^2 = 1.042*10^-8 N

Fy = G*m^2/y^2 = 6.67*10^-11*5^2/0.3^2 = 1.853*10^-8 N

Fnet = sqrt(Fx^2 + Fy^2) = 2.12*10^08 N

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