Untitled Lesson

GRAVITATIONAL FIELD

¢During the 19th century, the notion of the “field” entered physics (via Michael Faraday).

¢Objects with mass create an invisible disturbance in the space around them that is felt by other massive objects - this is a gravitational field.

¢So, since the Sun is very massive, it creates an intense gravitational field around it, and the Earth responds to the field. No more “action at a distance.”

¢Near the surface of the Earth, g = F/m = 9.8 N/kg = 9.8 m/s2.

¢In general, g = GM/r2, where M is the mass of the object creating the field, r is the distance from the object’s center, and G = 6.67 x10-11 Nm2/kg2.
g = GM/r²,
M=Gg/r^2​

The mass of the Earth is 6.0x10²⁴ kg and its radius is 6378 km.  What is the gravitational field strength at Earth’s surface?
g = GM/r²
ng = GM/r²

ng = (6.67x10-11 Nm2/kg2)(6.0x1024 kg) / (6.378x106 m)2

ng = 9.8 m/s2

ng = (6.67x10-11 Nm2/kg2)(6.0x1024 kg) / (6.378x106 m)2

nA planet has a radius of 3500 km and a surface gravity of 3.8 m/s².  What is the mass of the planet?
M=Gg/r^2​

= (6.67x10-11 Nm²/kg²) (3.8 m/s²) / (3.5x10⁶ m)2

nM = 6.9x10²³ kg

Multiple Choice

Compute g for the surface of the moon. Its radius is 1.7 x10⁶ m and its mass is 7.4 x 10²² kg.  

• 2.5m/s²

• 8.2m/s²

• 3.7m/s²

• 1.7m/s²

Multiple Choice

Compute g at a distance of 4.5 x 10⁷m from the center of a spherical object whose mass is 3.0 x 10²³

• 8.21 x 10²⁵ m/s²

• 5.75 x 10¹⁵ m/s²

• 9.88 x 10^-3 m/s²

• 3.41 x 10^-23 m/s²

Multiple Choice

Compute g for the surface of the sun.  Its radius is 7.0 x10⁸ m and its mass is 2.0 x 10³⁰ kg.  

 

• 2 x 10²

• 2.72 x 10²

• 3 x 10³

• 4.75 x 10³

Multiple Choice

4.       Compute g for the surface of Mars.  Its radius is 3.4 x10⁶ m and its mass is 6.4 x 10²³ kg.

 

• 4.5 m/s²

• 8.9m/s²

• 3.7m/s²

• 1.5m/s²

Multiple Choice

A planet has a surface gravity of 3.7m/s² and radius of 5m. What is the mass of this planet?

• 4.78 x 10^-10 kg

• 6.12 x 10²² kg

• 9.87 x 10^-12 kg

• 5.18 x 10⁶ kg

Multiple Choice

Suppose there is a planet with a radius of 6.5 x 10⁶m and a surface gravity of 8.2 m/s². What is the mass of this planet?

 

• 1.29 x 10^-23 kg

• 6.75 x 10²⁹ kg

• 4.41 x 10^-27 kg

• 5.38 x 10¹² kg

Multiple Choice

A planet has a surface gravity of 4.5m/s² and radius of 5789cm. What is the mass of this planet?

• 9.85 x 10^-24 kg

• 5.42 x 10¹⁴ kg

• 3.81x 10^-14 kg

• 8.96 x 10^-14 kg