Blog

NASA recently put a really cool rover on Mars — it even took…

NASA recently put a really cool rover on Mars — it even took pictures and audio of what it might be like to live on that planet, someday!   Mars is farther away from the Sun, though. There are all kinds of reasons why that could be good or bad, but one of them is that some of our constants that we have on Earth might be different. The mass of the Sun is 1.98 x 1030 kg, the mass of the Earth is 5.97 x 1024 kg, and the mass of Mars is 6.39 x 1023 kg. The mean distance between the Sun and Earth is 149.6 x 106 km, and the mean distance from the Sun to Mars is 250.3 x 106 km. The radius of Mars is 3400 km and the radius of Earth is 6300 km. The value of Newton’s Gravitational Constant is 6.67 x 10-11 N kg2/m2. Assume uniform circular motion. Answers to the below questions must include a well-labeled free body diagram and supporting work, submitted promptly after electronic submission of the quiz.   a.) What is the average orbital period of the Earth around the Sun? Hint: How far does the Earth move in one revolution around the sun, and with what speed? Remember that the period is the amount of time for the Earth to move back to move from a place in space until it returns back to where it started. . .  b.) What is the average orbital period of Mars around the Sun? c.) If you were to drop an object from a height close to the surface of Mars, what would the acceleration due to gravity be? d.) Let’s say, hypothetically, the rover did a little experiment. It has a spring, with a spring constant of 495 N/m. If you let the spring hang vertically [assume the spring itself is massless] and slowly attached a 5 kg mass to the bottom of it (without letting it bounce back and forth) on Earth, how much longer would it be than its equilibrium length? e.) What if you instead did the same experiment on Mars with the same mass and spring? Would the spring be longer, or shorter, compared to when the mass was attached to it on Earth?