Question

Compute g at a distance of 7.3 x 108 m from the center of a spherical object whose mass is 3.0 x 1027 kg.

Answer 1

Approximately
`0.38\; {\rm m\cdot s^(-2)}`, assuming that the density of the sphere is uniform.

Step-by-step explanation:

Under the assumptions, the gravitational field strength
`g` outside the sphere can be calculated as if the sphere is a point mass at its center:

`\begin{aligned}g &= (G\, M)/(r^(2))\end{aligned}`, where:

• 
  `G \approx 6.67 * 10^(-11)\; {\rm m^(3)\, kg^(-1)\, s^(-2)}` is the gravitational constant,
• 
  `M = 3.0 * 10^(27)\; {\rm kg}` is the total mass of the sphere, and
• 
  `r = 7.3* 10^(8)\; {\rm m}` is the distance from the center of the sphere.

Substitute in these values and evaluate to find the value of
`g`:

`\begin{aligned}g &= (G\, M)/(r^(2)) \\ &\approx \frac{(6.67* 10^(-11)\; {\rm m^(3)\, kg^(-1)\, s^(-2)})\, (3.0 * 10^(27)\; {\rm kg})}{(7.3 * 10^(8)\; {\rm m})^(2)} \\ &= ((6.67 * 10^(-11))\, (3.0 * 10^(27)))/((7.3 * 10^(8))^(2))\; {\rm m\cdot s^(-2)} \\ &\approx 0.38\; {\rm m\cdot s^(-2)}\end{aligned}`.