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Houston, we have a problem


You are members of the crew of Earth’s first community development ship. On your way to the planet Proxima Centauri B your ship was damaged. You are not going to be able to land your ship on the planet as anticipated. You will have to take precautions when constructing your lander to arrive safely on the surface. Before you begin construction on your lander you will need to determine the gravitational acceleration between your ship and the planet.


Data:


Your spacecraft is equipped with advanced sensing equipment and you have measured the following information based on your current situation.


You are currently in a stable orbit 9 000 000 m from the center of planet Proxima Centauri B.

According to the calculations done by NASA, Planet Proxima Centauri B has a mass of approximately 6x10^24 kg.

Based on fuel consumption and expected material aboard the ship, your colony ship lander has a mass of approximately 1.1x105 kg.


1. Using Newton's Law of Universal Gravitation, determine what the force of gravity on your ship at that orbit be using the early measurements. Please show all work.


2.Using Newton’s second law determine the acceleration of your lander due to gravity. Please show your work.


3.Upon arrival, you measure the actual force of gravity to be 6x105 N,which is different from your calculated value in question 1. Identify a specific possible causes that would account for the difference in expected vs. actual values, and why they would affect the calculation.

Sagot :

1. The force of gravity on the ship at that orbit be using the early measurements be 5.435 × 10^5 N..

2.  The acceleration of your lander due to gravity be 4.94 m/s^2..

What is force?

The definition of force in physics is: The push or pull on a massed object changes its velocity.

An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.

Given that:

Planet Proxima Centauri B has a mass of approximately 6x10^24 kg.

colony ship lander has a mass of approximately 1.1x10^5 kg.

stable orbit  radius of 9000000 m from the center of planet Proxima Centauri B.

1. Using Newton's Law of Universal Gravitation,  the force of gravity on the ship at that orbit be using the early measurements = GMm/r²

= (6.67 × 10⁻¹¹)×(6x10^24)(1.1x10^5)/(9000000)² N

= 5.435 × 10^5 N.

2.  the acceleration of your lander due to gravity: a = F/m

=  5.435 × 10^5 N/ 1.1x10^5 kg.

= 4.94 m/s^2.

3.The possible causes that would account for the difference in expected vs. actual values are:

  • mass distribution of the planet may not be uniform. So, the center of mass of the planet does not locate at the geometrical center.
  • Path of orbiting does not circular, it may be elliptical.

Learn more about force here:

https://brainly.com/question/13191643

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