Question

What planet has a similar size as Earth?

Answer 1

Hint: Size of the planet at ground level can basically be understood on the basis of the mass and the density. Density also at ground levels is a consequence of the gravitational pull. So two planets will have a similar size only if their mass is approximately the same.
Formula used:
$g=\dfrac{GM}{{{r}^{2}}}$

Complete step-by-step solution:
Let us say a planet has a mass ‘M’ and the radius of the planet is ‘r’ and the gravitational constant is ‘G’. Then the gravitational pull or the acceleration of the body near the surface of the planet is given by,
$g=\dfrac{GM}{{{r}^{2}}}$
Hence the central force on any planet will be proportional to that of ‘g’. The gravity also affects the size of the planet and vice versa. Hence we can say that if for two planets ‘g’ is similar then the dimensions of any two will also be the same .Venus has the similar surface acceleration as well as the mass as that of the Earth. It implies that the radius will also be similar for both these planets. Therefore we can conclude that Venus has a similar size as that of the Earth.

Note: It is to be noted that Venus and Earth will not have the exact values for mass, average density and so on. But more precisely they have similar or close values of the factors affecting the acceleration of their respective surfaces. Although Venus is similar in terms of the size, Mars is more similar to the Earth in other ways. Mars as well as the Earth have the axis of rotation tilted the same way as well as the duration of the day.