1. To find the force of gravity (Fgrav) between the earth and a football player with a mass of 100 kg, we can use the formula:
Fgrav = G * (m1 * m2) / d^2
where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 is the mass of the earth (5.97 x 10^24 kg), m2 is the mass of the football player (100 kg), and d is the distance between their centers of mass.
Since the football player is standing on the surface of the earth, we can assume that the distance between their centers of mass is equal to the radius of the earth (6.37 x 10^6 m).
Plugging in the values, we get:
Fgrav = (6.67 x 10^-11 Nm^2/kg^2) * (5.97 x 10^24 kg) * (100 kg) / (6.37 x 10^6 m)^2
Fgrav = 981 N
Therefore, the force of gravity between the earth and the 100 kg football player is approximately 980 N (rounded to the nearest whole number).
2. To find the radius of the moon when an astronaut with a mass of 70 kg is experiencing a gravitational force of 117 N while standing on the surface of the moon, we can use the same formula as above:
Fgrav = G * (m1 * m2) / d^2
where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 is the mass of the moon (7.35 x 10^22 kg), m2 is the mass of the astronaut (70 kg), and d is the distance between their centers of mass, which is equal to the radius of the moon (r).
Plugging in the values, we get:
117 N = (6.67 x 10^-11 Nm^2/kg^2) * (7.35 x 10^22 kg) * (70 kg) / r^2
Solving for r, we get:
r = 1.74 x 10^6 m
Therefore, the radius of the moon when an astronaut with a mass of 70 kg is experiencing a gravitational force of 117 N while standing on the surface of the moon is approximately 1.74 x 10^6 m.
3. To determine the mass of Jupiter if a gravitational force on a scientist whose weight is 686 N on earth is Fgrav = 1823 N, we can use the same formula as above:
Fgrav = G * (m1 * m2) / d^2
where G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 is the mass of Jupiter, m2 is the mass of the scientist (weight on earth divided by gravitational acceleration on earth, which is 9.81 m/s^2), and d is the distance between their centers of mass, which is the radius of Jupiter (r).
Plugging in the values, we get:
1823 N = (6.67 x 10^-11 Nm^2/kg^2) * (m1) * (686 N / 9.81 m/s^2) / (r^2)
Solving for m1, we get:
m1 = 1.90 x 10^27 kg
Therefore, the mass of Jupiter is approximately 1.90 x 10^27 kg.