To calculate the radius of another planet from which the man could escape by jumping, we need to equate the gravitational potential energy on the surface of the planet (where he jumps) to the kinetic energy he gains while jumping.

The gravitational potential energy is given by the formula:
PE = mgh

Where:
m = mass of the man
g = acceleration due to gravity on the surface of the planet
h = height the man jumps

The kinetic energy gained while jumping is given by the formula:
KE = (1/2)mv^2

Where:
m = mass of the man
v = velocity gained while jumping

Since the man jumps vertically, the initial velocity is zero, and the final velocity is given by:
v = √(2gh)

Now, let's equate the gravitational potential energy to the kinetic energy:

mgh = (1/2)mv^2

Canceling out the mass (m) from both sides, we get:

gh = (1/2)v^2

Now, let's substitute the expression for v:

gh = (1/2)(√(2gh))^2
gh = (1/2)(2gh)

Simplifying further:

gh = gh

This equation tells us that the height (h) to which the man can jump is the same on both planets, as it only depends on the acceleration due to gravity (g) and the height (h) itself.

So, we can write:

1.5m(9.81m/s^2) = h(√(GMe/Re^2))
1.5(9.81) = h(√(GM/Re^2))

Where:
G = gravitational constant
Me = mass of the Earth
Re = radius of the Earth

Now, let's rearrange the equation to solve for Re:

Re^2 = GM/(1.5(9.81))^2

Since the density is the same, we can write:

Me/Re^3 = M/Re^3

Where:
M = mass of the other planet

Thus:

Re^3 = Me/M * R^3

Re = (Me/M)^(1/3) * R

Now, let's substitute the known values:

Re = (5.972 × 10^24 kg / M)^(1/3) * 6.41 × 10^6 m

To escape the gravitational field by jumping, the man would need to jump to a height greater than the radius of the planet. Therefore, we can equate Re to h:

h = (5.972 × 10^24 kg / M)^(1/3) * 6.41 × 10^6 m

Given that h = 1.5 m, we can solve for M:

1.5 = (5.972 × 10^24 kg / M)^(1/3) * 6.41 × 10^6

Cubing both sides:

1.5^3 = (5.972 × 10^24 kg / M) * (6.41 × 10^6)^3

Simplifying:

3.375 = (5.972 × 10^24 kg / M) * (2.607281 × 10^19 kg)

Now, let's solve for M:

M = (5