physics - Universal Gravitation?

👨🏻‍🏫 學術台物理學

Ric2008

2010-05-20 7:11 am

On a planet X, the acceleration of gravity on the planet's surface g = 9.8 m/s^2 --- the same as on Earth. 1.00 x 10^3 km above the planet surface, the acceleration of gravity is 5.00% less. Gravitational constant G = 6.67 x 10^-11 Nm^2/kg^2

1.)Find the radius of the planet.

2.)Find the mass of the planet

更新1:

To oldprof: But shouldn't it be: 9.31/9.8 = (r+h)^2/r^2 = 0.95 according to your ratio comparison? because 9.31 is the acceleration for r+h

回答 (1)

oldprof

2010-05-20 7:39 am

✔ 最佳答案

Take the ratio g'/g = (r^2/R^2) = .95, where g = 9.8 m/sec^2 at the surface radius r and R = r + h, which h = 1E3 km above the surface. Then r^2 = .95(r^2 + 2rh + h^2) = .95r^2 + 1.9 rh + .95 h^2 and .05 r^2 - 1.9*1E3 r - .95*1E6 = 0

1) Then r = 3.8494e+4 km by solving the quadratic for the radius

2) Let g = GM/r^2 = 9.8 m/sec^2; so that M = gr^2/G = 9.8*(3.85E4)^2/6.67E-11 = 2.18E20 kg is the mass.

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