Final answer:
The radius of the new planet is approximately 6.11e8 m.
Step-by-step explanation:
To calculate the radius of the new planet, we can use the fact that the weight on the new planet is twice as large as on Earth. Weight is given by the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. Since the mass of the person doesn't change, we can equate the weight on Earth to the weight on the new planet:
m * gearth = m * gnew planet.
Since the mass of the person cancels out, we can set gearth = gnew planet.
Rearranging the formula for g gives us
g = G * M / r2,
where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.
Since g is the same on Earth and the new planet, we can write the equation as
G * Mearth / rearth2 = G * Mnew planet / rnew planet2.
Since we know the mass and radius of the Earth, we can solve for rnew planet:
rnew planet2 = (Mearth / rearth2) / (Mnew planet / rnew planet2)
rnew planet2 = (Mearth / Mnew planet) * (rnew planet2 / rearth2)
Simplifying, we get
rnew planet2 = (Mearth / Mnew planet) * (rearth / rnew planet)2
Plugging in the values, we have
rnew planet2 = (5.97e24 kg) / (2 * 6.371e6 m)^2 = 3.736e17
Taking the square root of both sides, we find rnew planet = 6.11e8 m.