4. The gravitational force of attraction between two masses is 25N. Determine the size of the force if: M₁ is tripled the distance between the masses is 1/3 M2 is doubled, the distance is doubled b C

1. predict what would happen to the force between the spacecraft and the Mystery Planet when the distance between them doubles. 2.predict the new distance between the spacecraft and the Mystery Planet when they experience a nine-fold increase in the force between them.

F= Gm,m₂ 2 r Two masses, m₁ and m2 are separated by a distance, r. The force of attraction between the two masses is F. A) If m₁ increases by 9, how does F change? B) If r is halved (1/2), how would F change? C) If r is not changed but both masses increase by a factor 7, how would F change? D) If all variables (r. m₁ and m₂) increase by 4, how would F change?

59. Gravitational Time Dilation on Earti. For a relatively weak gravitational field, such as that of a ptanet or an ordinary star, the following formula tells us the iractional amount of gravitational time dilation at a distanes r from the center of an object of mass Mobject- GMobject (G = 6.67 × 10-ll m³/(kg × s²); c = 3 × 10° m/s.] example, while 1 hour passes in deep space far from the object, the amount of time that passes at a distance r is 1 hour multiplied by the factor above. (This formula does not apply to strong gravitational fields, like those near black holes.) Calculate the amount of time that passes on Earth's surface while 1 hour passes in deep space. 60/Gravitational Time Dilation on the Sun. Use the formula given in Problem 59 to calculate the percentage by which time runs slower on the surface of the Sun than in deep space. Based on your answer, approximately how much of a gravitational redshift should you expect for a spectral line with a rest wavelength of 121.6 nm?…