Newton's Law of Gravity Video Lessons

Concept

# Problem: In recent years, astronomers have found planets orbiting nearby stars that are quite different from planets in our solar system. Kepler-12b, has a diameter that is 1.7 times that of Jupiter (RJupiter = 6.99 × 107 m), but a mass that is only 0.43 that of Jupiter (MJupiter = 1.90 × 1027 kg ).What is the value of g on this large, but low-density, world?

###### FREE Expert Solution

From Newton's second law:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}}$

Gravitational force is:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{G}\mathbf{M}\mathbf{m}}{{\mathbf{R}}^{\mathbf{2}}}}$

Equating:

$\begin{array}{rcl}\frac{\mathbf{G}\overline{)\mathbf{m}}\mathbf{M}}{{\mathbf{R}}^{\mathbf{2}}}& \mathbf{=}& \overline{)\mathbf{m}}\mathbf{g}\\ \mathbf{g}& \mathbf{=}& \frac{\mathbf{G}\mathbf{M}}{{\mathbf{R}}^{\mathbf{2}}}\end{array}$

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###### Problem Details

In recent years, astronomers have found planets orbiting nearby stars that are quite different from planets in our solar system. Kepler-12b, has a diameter that is 1.7 times that of Jupiter (RJupiter = 6.99 × 107 m), but a mass that is only 0.43 that of Jupiter (MJupiter = 1.90 × 1027 kg ).

What is the value of g on this large, but low-density, world?