Question

6.4

Please help me answer & explain all parts! And please make sure handwriting is legible.

4. Every planet (and moon) has its own acceleration due to gravity based on its mass and radius. Use the astronomical data in the back of the book for the following. A. What is the acceleration due to gravity on Venus? B. What is the acceleration due to gravity 'on' Uranus? (This is a gas giant so 'on' is relative.)

Astronomical Data

Answer 1

For a particle of mass m on the surface of a planet of radius R and mass M the weight of the object must be equal to the force between the planet and the object i.e.,

$\dpi{120} mg=G\frac{Mm}{R^2}$

$\dpi{120} or,\ g=\frac{GM}{R^2}$

G is the universal gravitational constant and g is the acceleration due to gravity at that planet.

A) Using the formula above,

Acceleration due to gravity in Venus is

$\dpi{120} g=\frac{6.67\times10^{-11}\times4.88\times10^{24}}{(6.06\times10^6)^2}\ m/s^2$

$\dpi{120} =8.86\ m/s^2$

B) Acceleration due to gravity at Uranus is

$\dpi{120} g=\frac{6.67\times10^{-11}\times8.68\times10^{25}}{(2.33\times10^7)^2}\ m/s^2$

$\dpi{120} =10.66\ m/s^2$