<h2>
Answer:</h2>
(a) 1500N
(b) 150kg, 150kg
<h2>
Explanation:</h2>
Consider the following equation from Newton's law of gravitational force between two bodies A and B;
= m x g
<em>Where;</em>
= gravitational force between A and B on a space (e.g moon or earth)
m = mass of A or B
g = acceleration due to gravity on the given space. (e.g moon or earth)
<em>Also;</em>
The acceleration due to gravity (
) on the earth is 6 times the acceleration due to gravity (
) on the moon. i.e
= 6 x 
=>
=
/ 6
<em>Assume in this case and;</em>
Let body A be the suited astronaut
Let body B be the moon or the earth
<em>This implies that;</em>
= m x
------------------(ii)
<em>Where;</em>
= gravitational force between suited astronaut and Earth on Earth = Weight of the suited astronaut on Earth.
m = mass of suited astronaut
= acceleration due to gravity on the Earth (e.g moon or earth)
<em>And;</em>
= m x
------------------(iii)
<em>Where;</em>
= gravitational force between suited astronaut and the moon = Weight of the suited astronaut on the moon
m = mass of suited astronaut
g = acceleration due to gravity on the moon.
From equations (ii) and (iii)
[Remember that
= 6 x
], substitute this into equation (ii) as follows;
= m x 6 x
[re-arranging]
= 6 x m x
[Put
for m x
]
= 6 x
------------------(iv)
(a) To get the weight of the suited astronaut on Earth, we use equation (iv) as follows;
= 6 x
------------------------(v)
Where;
= the weight of the suited astronaut on the moon = 250N
Substitute this into equation (v)
= 6 x 250
= 1500N
Therefore, the weight of the suited astronaut on the Earth is 1500N
(b)
(i) to get the mass on the moon, use equation (iii) as follows;
= m x 
Where;
= 250N and
=
/ 6 [
= g = 10m/s²]
= 10 / 6
= 1.6666667m/s²
<em>Substitute these values into the equation above;</em>
250 = m x 1.6666667
Solve for m;
m = 
m = 150kg
(ii) to get the mass on the Earth, use equation (ii) as follows;
= m x 
Where;
= 1500N and
= g = 10m/s²
<em>Substitute these values into the equation above;</em>
1500 = m x 10
Solve for m;
m = 
m = 150kg
Therefore the masses of the suited astronaut on Moon and on Earth are the same and equal to 150kg