Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

If the Earth\'s mass were double what it actually is, in what ways would the Moo

ID: 2033789 • Letter: I

Question

If the Earth's mass were double what it actually is, in what ways would the Moon's orbit be different?

Check all that apply.

The product rv2 would have to increase by 2?. The Moon's speed in orbit would have to double (other parameters remained constant). The product rv would have to increase by 2?. The radius of the Moon's orbit would have to increase by 2? (other parameters remained constant). The Moon's speed in orbit would have to decrease by 2? (other parameters remained constant). The product rv2 would have to double. The product rv would have to double. The product rv would have to remain constant. The radius of the Moon's orbit would have to double (other parameters remained constant). The radius of the Moon's orbit would have to decrease by 2? (other parameters remained constant). The Moon's speed in orbit would have to increase by 2? (other parameters remained constant). The product rv2 would have to remain constant. The orbit would remain unchanged.

Explanation / Answer

the orbit would have to be faster or farther away. If the mass was doubled, the gravitational force would also double if the distance remained the same. So it has to be farther away to keep it's orbit. To remain in orbit, the moon has to be moving in the x direction at the same speed that the gravity is pulling down on it in the y direction. So Either increase the speed to match the gravitational force, or push the moon away to decrease gravity and set it equal to it's x-speed that way. Of course you can have a little bit of both mixed in there

Gravity acts in this case as a centripetal acceleration, being the net force on the Moon (well, ignoring lots of little forces, which we can safely do for the moment). So, if you double the centripetal force, you need to either go faster (higher v) or get closer (lower r) to satisfy things. If you want to keep the same period (same omega), then you need to go farther out, doubling v and r so that v-squared over r is also double.

Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
Chat Now And Get Quote