Question

.what will be the escape speed from earth if the mass of earthis doubled keeping the same size

Answer 1

Answer on Question#37421 – Physics - Mechanics

$V_{1} = 11.2\frac{\mathrm{km}}{\mathrm{s}}$ – escape speed from Earth with mass $M_{\text{Earth}}$ and radius $r$;

$V_{2}$ – escape speed from Earth with mass $2M_{\text{Earth}}$ and radius $r$;

Formula for the escape speed ($G$ – universal gravitational constant):

$$V_{1} = \sqrt{\frac{2GM_{\text{Earth}}}{r}}$$ $$V_{2} = \sqrt{\frac{2G \cdot (2M_{\text{Earth}})}{r}}$$

(2) ÷ (1):

$$\frac{V_{2}}{V_{1}} = \sqrt{\frac{2G \cdot (2M_{\text{Earth}})}{r}} \cdot \sqrt{\frac{r}{2GM_{\text{Earth}}}} = \sqrt{2}$$ $$V_{2} = \sqrt{2}V_{1} = \sqrt{2} \cdot 11.2 \frac{\mathrm{km}}{\mathrm{s}} = 15.8 \frac{\mathrm{km}}{\mathrm{s}}$$

Answer: escape speed from Earth with mass $2M_{\text{Earth}}$ is equal to $15.8\frac{\mathrm{km}}{\mathrm{s}}$.