Question

A dwarf planet has a mass of 0.0045 times that of the Earth and a diameter on average 0.19 times that of the Earth. What is the escape velocity of the dwarf planet? (Type in the numerical answer and unit, e.g. 10m/s)

Answer 1

The escape velocity of the dwarf planet is 1,721.8 m/s.

The given parameters:

• Mass of the dwarf planet, m = 0.0045 M
• Mass of the Earth = 5.98 x 10²⁴ kg
• Diameter of the planet, d = 0.19 D
• Diameter of the Earth, D = 12,742 km

The mass of the of the dwarf planet is calculated as follows;

$m = 0.0045 \times 5.98 \times 10^{24} \ kg\\\\m = 2.69\times 10^{22} \ kg$

The radius of the dwarf planet is calculated as follows;

$r = \frac{0.19 D}{2} \\\\r = \frac{0.19 \times 12, 742, 000}{2} \\\\r = 1,210,490 \ m$

The escape velocity of the dwarf planet is calculated as follows;

$v _e = \sqrt{\frac{2GM}{r} } \\\\v_e = \sqrt{\frac{2\times 6.67 \times 10^{-11} \times 2.69 \times 10^{22}}{1,210,490}}\\\\v_e = 1,721.8 \ m/s$

Learn more about escape velocity here: brainly.com/question/13726115