Calculating Gravitational Field Constants for Mars, Jupiter, and Mercury

Click For Summary
SUMMARY

This discussion focuses on calculating the gravitational field constants for Mars, Jupiter, and Mercury using Newton's Second Law of Motion and Newton's Universal Law of Gravitation. The correct gravitational field constants are 3.61 m/s² for Mars, 24.6 m/s² for Jupiter, and 3.31 m/s² for Mercury. The confusion arose from the incorrect application of the gravitational force equation, F = Gm1m2/r², without properly eliminating one of the masses. The key takeaway is to substitute F = mg into the gravitational equation to isolate the gravitational field constant.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Familiarity with Newton's Universal Law of Gravitation
  • Basic knowledge of gravitational field strength calculations
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the derivation of gravitational field strength from Newton's laws
  • Learn how to apply dimensional analysis in gravitational calculations
  • Explore the differences in gravitational constants across celestial bodies
  • Investigate the implications of gravitational field strength on planetary motion
USEFUL FOR

Students learning physics, educators teaching gravitational concepts, and anyone interested in planetary science and gravitational calculations.

Dyna
Messages
9
Reaction score
0
1. Calculate the gravitational field constants for the following:
Mars (r=3.43 x 10^6m , m= 6.37 x 10^23 kg)
Jupiter (r= 7.18 x 10^7 , m = 1.90 x 10^27kg)
Mercury (r=2.57 x 10^6m , m= 3.28 x 10^23 kg)

2. F = mg
Fg = Gm1m2
r^2

3. So i tried subbing these given masses into the second equation but it does not give me the correct answer.
Am i not using the correct equation?
I only just learned this in school on Friday and it was quite confusing as to what i should be using to find my answers.
The answer key says:
Mars: 3.61 m/s^2
jupiter: 24.6m/s^2
mercury: 3.31m/s^2
 
Physics news on Phys.org
Use Newton's Second Law of Motion in conjunction with Newton's Universal Law of Gravitation.
 
In other words, since you're only given one mass (the planet's mass, call it m2), you've got to get rid of the second mass m1. You have the right equation to do this, F=mg. If you sub that into the left side, one of your m's will drop out, and you're left with g on the left side, and the correct answer on the right :)
 

Similar threads

  • · Replies 23 ·
Replies
23
Views
5K
  • · Replies 6 ·
Replies
6
Views
16K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
2
Views
2K
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
15
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K