Re:An analysis of the Lego City deep space rocket
by wh313 on Sunday May 10, 2020 @02:23AM
(#23130688)
It'll actually still be 1/30th of the Earth, since from Newton's law of universal gravitation:
F = G * (m_1 * m_2) / r^2
m_2 * a = G * (m_1 * m_2) / r^2
a = G * m_1 / r^2
If we make m_1 1/30th of its original size and to the same to r:
a = G * (m_1 / 30^3) / (r / 30)^2
a = G * (m_1) / r / 30
As escape velocity v_e is where GPE + KE = 0:
v_e = sqrt(2 * g * r) from the surface of the planet
If g is now 1/30th of it's original amount as shown above, the escape velocity would be sqrt(30) = 5.477 times less, or about 2042 m/s. So yup, they would make it if it's at 1/30th the size of the Earth, with thrust to spare for air resistance.
F = G * (m_1 * m_2) / r^2
m_2 * a = G * (m_1 * m_2) / r^2
a = G * m_1 / r^2
If we make m_1 1/30th of its original size and to the same to r:
a = G * (m_1 / 30^3) / (r / 30)^2
a = G * (m_1) / r / 30
As escape velocity v_e is where GPE + KE = 0:
v_e = sqrt(2 * g * r) from the surface of the planet
If g is now 1/30th of it's original amount as shown above, the escape velocity would be sqrt(30) = 5.477 times less, or about 2042 m/s. So yup, they would make it if it's at 1/30th the size of the Earth, with thrust to spare for air resistance.