Question

Can someone help me calculate the speed of this please? Thank you very much!

Answer 1

`1021.05color(white)(i) ms^-1`

Explanation:

Orbital speed `= sqrt(gR)`

Here,

• `g_"at moon's distance"=(6.7*10^-11*5.97219 * 10^24)/( 3.85 × 10^8)^2`
  `=0.00270795635color(white)(i)ms^-2`

• Orbital radius of Moon `= 385,000 color(white)(i)km = 3.85 × 10^8 m`

`therefore`Orbital speed `= sqrt(0.00270795635color(white)(i)ms^-2 xx 3.85 xx 10^8 m)`

`~~ 1021.05color(white)(i) ms^-1`

Answer 2

`1023.22 "m"/"s"`

Explanation:

`"Speed"=color(red)"Distance"/color(blue)"Time"`

Here,

• `"Distance of Moon from Earth (avg.)"=384,400" km"`
  `=384,400xx1000" m"`
• `"Distance travelled by Moon"="Circumference"`
  `=2pir=color(red)(2xxpixx384,400xx1000 " m"`
• `"Time taken to complete one orbit"=27.32" days"`
  `color(blue)(=27.32xx24xx60xx60" s"`

`=color(red)(2xxpixx384,400xx1000 " m")/color(blue)(27.32xx24xx60xx60 " s")`

`=color(red)(2415256432.1" m")/color(blue)(2360448" s")`

`=1023.22 "m"/"s"`