Final answer:
The weight of the stone on the heavenly body is approximately 9.49 N.
Step-by-step explanation:
To find the weight of the stone on the heavenly body, we can use the formula for calculating the weight of an object:
Weight = mass x gravitational acceleration
On Earth, the stone weighs 100 N. Let's assume the mass of the stone is m kg. Therefore, the weight of the stone on Earth is given by:
100 N = m kg x 9.8 m/s2
Solving for m, we find m = 10.2 kg.
Since the heavenly body has a mass equal to half of the Earth's mass, the mass of the heavenly body is 5.97 x 1024 kg / 2 = 2.99 x 1024 kg.
The radius of the heavenly body is half of Earth's radius, which is 6.38 x 106 m / 2 = 3.19 x 106 m.
Now, we can find the weight of the stone on the heavenly body using the same formula:
Weight = mass x gravitational acceleration
Weight = 10.2 kg x gheavenly body
To find gheavenly body, we can use Newton's law of universal gravitation:
F = G x (m1 x m2) / r2
Solving for gheavenly body, we get:
gheavenly body = G x mheavenly body / rheavenly body2
Substituting the values, we have:
gheavenly body = (6.67 x 10-11 N m2/kg2) x (2.99 x 1024 kg) / (3.19 x 106 m)2
Calculating gheavenly body, we find it to be approximately 0.931 m/s2.
Finally, we can find the weight of the stone on the heavenly body:
Weight = 10.2 kg x 0.931 m/s2 = 9.49 N
Therefore, the weight of the stone on the heavenly body is approximately 9.49 N.