A planet has a mass of 6.78 × 102³ kg and a radius of 3.16 × 106 m. (a) What is the acceleration due to gravity on this planet? (b) How much would a 74.2-kg person weigh on this planet?
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
![### Problem Statement
A planet has a mass of \(6.78 \times 10^{23} \, \text{kg}\) and a radius of \(3.16 \times 10^{6} \, \text{m}\).
**(a)** What is the acceleration due to gravity on this planet?
**(b)** How much would a 74.2-kg person weigh on this planet?
### Solution
**(a) Acceleration due to Gravity**
To find the acceleration due to gravity (g) on the surface of the planet, use the formula derived from Newton's law of universal gravitation:
\[ g = \frac{G \cdot M}{R^2} \]
where:
- \( G \) is the universal gravitational constant, \( 6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2 \cdot \text{kg}^{-2} \)
- \( M \) is the mass of the planet, \( 6.78 \times 10^{23} \, \text{kg} \)
- \( R \) is the radius of the planet, \( 3.16 \times 10^{6} \, \text{m} \)
**(b) Weight of a Person**
Weight is the force due to gravity acting on a mass, calculated using:
\[ \text{Weight} = m \cdot g \]
where:
- \( m \) is the mass of the person, which is 74.2 kg in this case
- \( g \) is the acceleration due to gravity on the planet, found in part (a)
By substituting the values obtained from part (a) into this equation, you can determine the weight of a 74.2 kg person on this planet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F445dc1ba-0059-4453-a67d-7747e0259e94%2Ffc992ea8-a1b2-4b3e-b586-1df82eddb622%2Fpvm1snb_processed.png&w=3840&q=75)
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